Project 5: Cost of Capital, Risk/Return, and Capital Budgeting

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Project 5 Report

Instructions

Answer the five questions below. They focus entirely on the financing, risk/return, Cost of Capital and Budget Forecasting of Largo Global Inc. (LGI) based on the investing activities that took place in project 4. Base your analysis on the data provided and calculated in the Excel workbook. Provide support for your reasoning from the readings in Project 5, Step 1, and the discussion in Project 5, Step 3. Be sure to cite your sources.

Provide a detailed response below each question. Use 12-point font and double spacing. Maintain the existing margins in this document. Your final Word document, including the questions, should not exceed 5 pages. Include a title page in addition to the five pages. Any tables and graphs you choose to include are also excluded from the five-page limit. Name your document as follows: P5_Final_lastname_Report_date.

You must address all five questions and make full use of the information on all tabs of project 5 as well as data in other Excel workbooks (e.g. from project 1: ratio, common-size, and cash flow analysis).

You are strongly encouraged to exceed the requirements by refining your analysis. Consider other tools and techniques that were discussed in the required and recommended reading for Project 5. This means adding an in-depth explanation of what happened in that year for which data was provided to make precise recommendations to LGI.

Title Page

Name

Course and section number

Faculty name

Submission date

Questions

1. How would you assess the evolution of the
capital structure of LGI? Reflecting on your work in Project 1, would you consider the risk exposure under control? If not, what are your recommendations?

[insert your answer here]

2. What kind of information do you find valuable in
CAPM to guide you in assessing the risk of LGI compared to other firms and the market in general?


[insert your answer here]

3. Identify and differentiate the stakeholders of LGI and explain how each one should perceive and weigh the
risk and/or
return of the firm.

[insert your answer here]

4. Would you consider the investment made in Project 4 optimally financed considering the proportion of debt that is bearable by LGI? How did the current
WACC in Project 5 depart from the state of the firm in Project 1?

[insert your answer here]

5. If you had to advise a potential investor interested in having a minority stake in LGI, what kind of information would you provide to help the investor make a decision? Would you be bullish or have reservations? Support your answer with facts and data from all MBA 620 projects as well as your
budget projections.

[insert your answer here]

Step 3: Participate in the Required Project 5 Discussion

You have finished reviewing the material and performing the exercises, but you have some questions. Participate in the Project 5 class discussion. Respond to the two questions below by posting in the discussion; then, respond to two of your classmates’ discussion posts by the end of the week.

Discussion

Answer the following questions:

1. Discuss the concepts that were most challenging for you in the readings and review material. How did the practice exercises help clarify these?

2. What did you learn that will help you determine the most appropriate way to finance the investments you previously recommended for LGI?

Step 2: Review and Practice

Using the 
Project 5 Review and Practice Guide, review the options for financing investments available to LGI. Then, apply what you have learned by completing the exercises and problems referenced in the 
Project 5 Review and Practice Guide

You must review the guide and do the practice exercises and problems so that you

· are prepared to have informed discussions with your team about capital structure and appropriate leverage,

· understand risk and return,

· can make recommendations for financing LGI’s investments, and

· can complete your mission, turning around LGI.

Step 4: Complete the Analysis Calculation for Project 5

Your team has provided you with an Excel workbook containing LGI’s financials. You will use the 
Project 5 Excel workbook to perform advanced capital budgeting techniques to assess the viability of the investment you made in the previous project. 

Complete the analysis calculation for the project:

· Download the 
Project 5 Excel Workbook, click the Instructions tab, and read the instructions.

· Calculate cost of debt and equity as well as weighted average cost of capital (WACC).

· Apply the capital asset pricing model (CAPM).

· Develop a capital budget.

If you would like instructor feedback on this step, submit your Excel file to the Assignments folder as a milestone by the end of Week 9. This is optional. If you choose to submit the milestone, you will receive instructor feedback you may use to make corrections before submitting your final Project 5. To distinguish the milestone submission from the file you will submit in Step 5, label your file as follows: P5_milestone_lastname_Calculation_date

Step 5: Prepare the Analysis Report for Project 5

You have developed an in-depth understanding of LGI’s operating efficiency related to costing and how that impacts the bottom line. You feel confident that your investment choices will positively boost LGI’s productivity and improve the company’s operations. Thanks to your efforts, the company will have a plan for financing its investments appropriately. LGI will finally be on a path of a sustainable future. Answer the questions in the 

Project 5 Questions – Report Template
 document. Prepare your analysis report including recommendations for how the company can improve its financial situation.

Complete the analysis report:

· Download the 

Project 5 Questions – Report Template

· Read the instructions.

· Answer all the questions.

· Include your recommendations.

· Submit the analysis report (Word document) and analysis calculation (Excel file) to the dropbox as your final deliverable at the end of Week 10. Label your files as follows:

· P5_Final_lastname_Report_date.docx

· P5_Final_lastname_Calculation_date.xlsx

Scenario

Your team’s work with Largo Global Inc. (LGI) is nearly complete. In your consulting role, you have recommended steps for improving the company’s financial health. You have offered advice on a revenue target, recommended steps for optimizing operations, and suggested investments that will improve LGI’s competitive position. In your final project, you will continue working on capital budgeting with a focus on the best way for LGI to finance the investments you recommend.

Your Project 5 business report will focus on ensuring LGI’s capital structure is sound and that the company is on a financially sustainable path. You will recommend a plan for financing investments that does not expose LGI to unnecessary risk. By the end of this project, the company’s financial statements should demonstrate that it has returned to a competitive position. 

Step 1: Prepare for the Project

For the next two weeks, you will focus on the concepts of risk and return, the cost of capital, and capital budgeting. You will ensure that the financing plan you recommend supports LGI’s long-term financial position. 
Log into O’Reilly by following these instructions and complete the required reading.

Instructions

INSTRUCTIONS
Complete the Cost of Capital tab
o   Find the cost of Equity using the Capital Asset Pricing Model (CAPM)
o   Find the Weighted Average Cost of Capital (WACC)
Complete the Payback tab
o   Complete the After-tax Cash Flow re-evaluation table
o   Complete the DCF Payback timeline
o   Complete the questions on the tab
Complete the Budget Projections tab
o   Revenue increases 4% annually
o   Expense increases 2¾% annually

Cost of Capital

Instructions:
1 Find the cost of Equity using the Capital Asset Pricing Model (CAPM)
2 Find the Weighted Average Cost of Equity (WACC)
1
RF RM = CAPM
————————————–
2
E
D
Total Capital (V) $ – 0
Last Fiscal Year End Interest Expense
Tax Rate (TC)
1. Find the weight of equity = E / (E + D).
2. Find the weight of debt = D / (E + D).
Re 3. Find the cost of equity using CAPM.
Rd 4. Find the cost of debt.
WACC 5. Find the weighted average cost of capital.

WACC Information from Largo Global
a. As of today, Largo Global market capitalization (E) is $6,373,341,000.1
b. Largo Global’s Market value of debt is $761,000,000.
c. Cost of Equity = CAPM from question 1
d. Cost of Debt = Last Fiscal Year End Interest Expense2 / Market Value of Debt (D).
e. Use the tax rates given in Project 4 Tab 3.

_________
1 Market value of equity (E), also known as market cap, is calculated using the following equation:
Market Cap = Share Price x Shares Outstanding from Project 1
2 From Project 1. Note that the Cost of Debt formula expressed at here is different from the cost of debt formula introduced in most textbooks. Most textbooks only consider the long-term debt (i.e., bond) as the debt and use the bond valuation formula when calculating the cost of debt and WACC.

Payback

Payback Table View
Table 1 – Data
Cost of new equipment (at year 0) 191.10 million
Corporate income tax rate – Federal 26.0%
Corporate income tax rate – State of Maryland 8.0%
Discount rate for the project using WACC
Loan Amount million
Loan Interest rate (Prime + 2) 5.25%
Table 2 – After-tax Cash Flow Table
(all figures in $ millions)
Year Projected Cash Inflows from Operations Projected Cash Outflows from Operations Depreciation Expense Interest Expense Projected Taxable Income Projected Federal Income Taxes Projected State Income Taxes Projected After-tax Cash Flows PV NPV1 IRR NPV2
Excel function to use : SLN IPMT PV NPV IRR NPV
0
1 $850.0 $840.0 $23.89 $0.00 ($13.89) ($3.61) ($1.11) $14.72
2 $900.0 $810.0
3 $990.0 $870.0
4 $1,005.0 $900.0
5 $1,200.0 $1,100.0
6 $1,300.0 $1,150.0
7 $1,350.0 $1,300.0
8 $1,320.0 $1,300.0
PV
NPV1 – calculated NPV including interest expense NPV
NPV2 – calculated NPV at the lower discount rate of 5.02% IRR
Payback Timeline View Example of Actual Cash Flows
0 1 2 3 4 5 6 7 8
| | | | | | | | |
Cash Flow ($191.10) $8.76 $62.18 $82.63 $73.42 $70.84 $104.60 $39.40 $20.44 $271.17
Cummulative Cash Flow
($191.10) ($182.34) ($120.16) ($37.53) $35.89 $106.73 $211.33 $250.73 $271.17
Payback Period 3 years 6 months
0 1 2 3 4 5 6 7 8 PV
| | | | | | | | | $0.00
Discounted Cash Flow (DCF) $0.00
$0.00
Cummulative DCF
Payback Period years months
ANSWER THESE QUESTIONS:
1. What is the total depreciation for tax purposes?
2. What is the total PV of the Cash Flows using the WACC rate?
3. What is the NPV using the WACC rate?
4. What is the NPV using the alternative rate?
5. What is the IRR?
6. What is the payback period using the DCF?
7. Should the project be accepted? Why?

After-Tax Cash Flow Re-evlauation and Payback Timelines Instructions
Technologically advanced distribution equipment proposal re-evaluation
 The CFO has asked you to re-evaluate the cash flow projections associated with the equipment purchase proposal due to the proposed loan agreement, and recommend whether the purchase should go forward. Table 1 shows the data and Table 2 shows projections of the cash inflows and outflows that would occur during the first eight years using the new equipment.
 
Keep the following in mind: Row 34 has a suggested Excel function to use. Complete all the blank cells within the tables.
 
I. In the Data Table:
A. Use the WACC calulated on the Cost of Capital tab
B. Calulate the loan amount with a 10% down payment
II. In the After-tax Cash Flow:
C. Complete the Depreciation Expense from Project 4 (straight line, $0 Salvage)
D. Complete the interest expense using the loan interest rate.
E. Complete the After-tax Cash Flow Table including the interest expense
F. Compute the PV, NPV1, IRR, and adjusted NPV2
III. In the Payback Timeline View:
G. Complete the discounted cash flow Payback Timeline View of Discounted Cash Flows
i) complete the timeline amounts based on the DCF (DCF is the same as PV)
ii) complete the timeline amountss for the Cummulative DCF
iii) calulate the payback period in years and months
IV. Answer the following questions:

1. What is the total depreciation for tax purposes?
2. What is the total PV of the Cash Flows using the WACC rate?
3. What is the NPV using the WACC rate?
4. What is the NPV using the alternative rate?
5. What is the IRR?
6. What is the payback period using the DCF?
7. Should the project be accepted? Why?

Budget Projections

INSTRUCTIONS:
1). Complete the budget projections for years 2021-2024 using the following information
Revenue increases 4% annually
Expense increases 2¾% annually
For Depreciation and Interest expenses assume the Acutal 2020 figure as the base for the budget and and forecast then add the amount calculated in the Payback tab for both budget and forecast.
2). Answer the question below the forecast.
1). Largo Global Income Statement of December 31, 2020 (millions)
ACTUAL BUDGET FORECAST
2020 2021 2022 2023 2024
Sales (net sales) $2,013
Cost of goods sold 1400
Gross profit 613 0 0 0 0
Selling, general, and administrative expenses 125
Earnings before Interest, taxes, depreciation, and amortization (EBITDA) 488 0 0 0 0
Depreciation and amortization 174
Earning before interest and taxes (EBIT) Operating income (loss) 314 0 0 0 0
Interest expense 141
Earnings before taxes (EBT) 173 0 0 0 0
Taxes (34%) 59
Net earnings (loss)/Net Income $ 114 0 0 0 0
2). Based on the changes suggested throughout the 5 projects, is Largo Global in a better financial position?

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UMGC
MBA 620: Financial

Decision Making

Project 5: Review and

Practice Guide

Project 5: Review and

Practice Guide

Cost of Capital, Risk/Return & Capital Budgeting

Contents

Topic 1: Capital Budgeting ……………………………………………………………………………………………………………. 3

The Finance Balance Sheet ……………………………………………………………………………………………………….. 3

Introduction to Capital Budgeting ……………………………………………………………………………………………… 3

What is CAPEX? ……………………………………………………………………………………………………………………….. 3

Key Reasons for Making Capital Expenditures ……………………………………………………………………………… 3

Methods to Inform Capital Expenditure Decisions ……………………………………………………………………….. 3

Net Present Value Method: Calculating the NPV of a Project ………………………………………………………… 4

Net Present Value (NPV): Calculation Example ……………………………………………………………………………. 4

NPV: The Best Capital-Budgeting Technique ……………………………………………………………………………….. 5

NPV: The Five-step Approach ……………………………………………………………………………………………………. 5

Summary of NPV Method …………………………………………………………………………………………………………. 5

Key Advantages ……………………………………………………………………………………………………………………. 5

Key Disadvantage …………………………………………………………………………………………………………………. 5

Internal Rate of Return (IRR) Method …………………………………………………………………………………………. 6

Excel Function: IRR …………………………………………………………………………………………………………………… 6

IRR Example ……………………………………………………………………………………………………………………………. 6

NPV or IRR? …………………………………………………………………………………………………………………………….. 7

Unconventional Cash Flows ………………………………………………………………………………………………………. 7

Payback Period Method ……………………………………………………………………………………………………………. 7

Computing Payback Period ……………………………………………………………………………………………………….. 7

Payback Period Calculation: Example and Formula ………………………………………………………………………. 8

Discounted Payback Period……………………………………………………………………………………………………….. 8

Discounted Payback Period Cash Flows and Calculations ……………………………………………………………… 8

Evaluating the Payback Rule ……………………………………………………………………………………………………… 8

Topic 2: Cost of Capital and Financing Decisions ……………………………………………………………………………… 9

What is Capital? ………………………………………………………………………………………………………………………. 9

Sources of Capital for a Start-up ………………………………………………………………………………………………… 9

Estimating the Cost of Capital ……………………………………………………………………………………………………. 9

Cost of Capital and Risks …………………………………………………………………………………………………………. 10

Risk Is Uncertainty………………………………………………………………………………………………………………….. 10

Risk and Return Trade-off ……………………………………………………………………………………………………….. 10

How to Measure Return …………………………………………………………………………………………………………. 10

Example: Holding Period Return ………………………………………………………………………………………………. 11

Example: Expected Return ………………………………………………………………………………………………………. 11

Four Measures of Risk …………………………………………………………………………………………………………….. 11

Measuring Risk: Calculate Variance ………………………………………………………………………………………….. 11

Risk and Diversification …………………………………………………………………………………………………………… 12

Diversification: Individuals vs Companies ………………………………………………………………………………….. 12

Equity Securities …………………………………………………………………………………………………………………….. 12

Estimating the Cost of Equity …………………………………………………………………………………………………… 13

Method 1: Capital Asset Price Model (CAPM) ……………………………………………………………………………. 13

Estimating Beta ……………………………………………………………………………………………………………………… 13

Market-Risk Premium (Rm − Rf) ………………………………………………………………………………………………… 13

Assumptions of CAPM …………………………………………………………………………………………………………….. 14

Method 2: Constant-Growth Dividend Model ……………………………………………………………………………. 14

Bank Loans and Corporate Bonds …………………………………………………………………………………………….. 14

Yield to Maturity (YTM) …………………………………………………………………………………………………………… 15

Taxes and the Cost-of-Debt Equation ……………………………………………………………………………………….. 15

Weighted Average Cost of Capital (WACC) ………………………………………………………………………………… 15

Limitations of WACC ………………………………………………………………………………………………………………. 15

Alternatives to WACC ……………………………………………………………………………………………………………… 15

Problems/Exercises ……………………………………………………………………………………………………………………. 16

What to Do ……………………………………………………………………………………………………………………………. 16

Self Study Problems ……………………………………………………………………………………………………………….. 16

Advanced Problems and Questions 10.36 …………………………………………………………………………………. 16

Solution to Problem 10.36 ………………………………………………………………………………………………………. 16

Advanced Problems and Questions 10.38 …………………………………………………………………………………. 18

Solution to Problem 10.38 ………………………………………………………………………………………………………. 19

Advanced Problems and Questions 10.39 …………………………………………………………………………………. 20

Solution to Problem 10.39 ………………………………………………………………………………………………………. 21

References ……………………………………………………………………………………………………………………………. 23

Project 5 Review and Practice Guide

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Topic 1: Capital Budgeting

The Finance Balance Sheet

Introduction to Capital Budgeting
• Capital Budgeting determines the long-term productive assets that will create wealth.

• Capital investments are large cash outlays and long-term commitments not easily reversed that

affect performance in the long run.

• Capital-budgeting techniques help management systematically analyze potential opportunities

to decide which are worth undertaking (Parrino et al., 2012).

What is CAPEX?
CAPEX—capital expenditures, or a company’s key long-term expenses

Key Reasons for Making Capital Expenditures
• Renewal—equipment repair, overhaul, rebuilding, or retrofitting. Usually does not require an

elaborate analysis and are made on a routine basis.

• Replacement—to address equipment malfunction or obsolescence. Typically involves decisions at

the plant level.

• Expansion—involves strategic decisions requiring complex, detailed analysis.

• Regulatory

• Other

Methods to Inform Capital Expenditure Decisions

• Net present value (NPV)—Use the cost of capital to discount the cash flow of a project. Choose

the project with positive net present value.

• Internal Rate of Return (IRR)—Calculate the rate of return of a project. Choose the highest one

or the one that has a higher rate of return than the cost of capital.

• Payback Period—Calculate how long does it take for a project to pay back itself. Choose the one

with shorted payback period.

Based on Parrino et al. (2012)

(2012(2012)

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Net Present Value Method: Calculating the NPV of a Project

Net Present Value (NPV): Calculation Example
You can use the cash flow timeline below and Excel to calculate NPV for this project in which the cost of

capital is 15%:


= +

=

+
++

+
+

+
+=

n

0t
t

t

n

n

2

21
0

k)(1

NCF

(10.1)
k)(1

NCF

k)(1

NCF

k1

NCF
NCFNPV

91.16$

69.5474.45$60.52$49.60$57.69$300$

)15.1(

30$80$

)15.1(

80$

)15.1(

80$

)15.1(

80$

)15.1(

80$
300$

54321

−=

+++++−=

+
+++++−=

B
P

Based on Parrino et al. (2012)

Source: Parrino et al. (2012)

Project 5 Review and Practice Guide

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NPV: The Best Capital-Budgeting Technique
• Net Present Value (NPV) represents the current value of the project after accounting for

expected cash flow and the cost of capital.

• The NPV of a project is the difference between the present values of its expected cash inflows

and expected cash outflows.

• NPV is the best capital-budgeting technique because it is consistent with goal of maximizing

shareholder wealth.

• Positive NPV projects increase shareholder wealth and negative NPV projects decrease

shareholder wealth. (Parrino et al., 2012)

NPV: The Five-step Approach
1. Estimate project cost

o Identify and add the present value of expenses related to the project.

o There are projects whose entire cost occurs at the start of the project, but many

projects have costs occurring beyond the first year.

o The cash flow in year 0 (NCF0) on the timeline is negative, indicating an outflow

2. Estimate project net cash flows

o Both cash inflows (CIF) and cash outflows (COF) are likely in each year. Estimate the net

cash flow (NCFn) = CIFn − COFn for each year.

o Include salvage value of the project in its terminal year.

3. Determine project risk and estimate cost of capital

o The cost of capital is the discount rate (k) used to determine the present value of

expected net cash flows.

o The riskier a project, the higher its cost of capital (Parrino et al., 2012)

4. Compute the project’s NPV

o Determine the difference between the present values of the expected net cash flows

from the project and the expected cost of the project.

5. Make a decision

o Accept a project if it has a positive NPV, reject it if the NPV is negative.

Summary of NPV Method
• Decision rule

o NPV > 0 Accept the project

o NPV < 0 Reject the project

Key Advantages
o Uses the discounted cash flow valuation technique to adjust for the time value of money

o Provides a direct (dollar) measure of how much a capital project will increase the value

of a company

o Is Consistent with the goal of maximizing stockholder value

Key Disadvantage
o Can be difficult to understand without an accounting and finance background (Parrino

et al., 2012).

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Internal Rate of Return (IRR) Method
• IRR is the discount rate at which a project has an NPV equal to zero.

• A project is acceptable if its IRR is greater than the firm’s cost of capital.

• The IRR is an important and legitimate alternative to the NPV method (Parrino et al., 2012).

Excel Function: IRR
IRR(values, [guess])

The IRR function syntax has the following arguments:

Values Required. An array or a reference to cells that contain numbers for which you want to calculate

the internal rate of return.

• Values must contain at least one positive value and one negative value to calculate the internal

rate of return.

• IRR uses the order of values to interpret the order of cash flows. Be sure to enter your payment

and income values in the sequence you want.

• If an array or reference argument contains text, logical values, or empty cells, those values are

ignored.

Guess Optional. A number that you guess is close to the result of IRR. (Microsoft, n.d.)

IRR Example
Expected Cash Flow from a CAPEX


= +

=

+
++

+
+

+
+=

n

0t
t

t

n

n

2

21
0

k)(1

NCF

(10.1)
k)(1

NCF

k)(1

NCF

k1

NCF
NCFNPV

Based on Parrino et al. (2012)

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NPV or IRR?
Is NPV or IRR a better measure for capital budgeting? Consider these points:

• IRR is the discount rate when NPV is zero, when the project is breakeven, so many times the two

methods yield consistent results.

• IRR’s biggest strength is also its limitation: A single discount rate does not consider the change in

interest rate level.

• IRR is ineffective when the projects have strings of positive and negative cash flows.

• IRR has the advantage of summarizing the rate of return of the project in one number, so it is a

popular method.

Unconventional Cash Flows
The IRR technique may provide more than one rate of return, making the calculation unreliable.

Therefore, it should not be used to determine whether to accept or reject a project.

Following are examples of unconventional cash flows:

• Positive cash flow followed by negative net cash flows.

• Simultaneous positive and negative net cash flows.

• Conventional followed by a negative net cash flow at the end of a project’s life.

Payback Period Method
Payback period—the time it takes for the sum of the net cash flows from a project to equal the project’s

initial investment

o One of the most popular tools for evaluating capital projects

o Can serve as a risk indicator—the quicker a project’s cost recovery, the less risky the

project

o Decision criteria: payback period shorter than a specific amount of time (Parrino et al.,

2012)

Computing Payback Period
The following timeline shows the net and cumulative net cash flow (NCF) for a proposed capital project

with an initial cost of $80,000. This data is used to compute the payback period, 2.5 years.

4 3 2 1 0
Year

NCF -$80,000 $35,000 $35,000 $20,000 $25,000

Cumulative NCF -$80,000 -$45,000 -$10,000 $10,000 $35,000

Based on Parrino et al. (2012)

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Payback Period Calculation: Example and Formula
= 2 years + $10,000

$20,000

= 2 years + 0.5

= 2.5 years

To compute the payback period, estimate a project’s cost and its future net cash flows:

Discounted Payback Period
• Future cash flows are discounted by the firm’s cost of capital.

• The major advantage of the discounted payback is that it tells management how long it takes a

project to reach a positive NPV (Parrino et al., 2012).

Discounted Payback Period Cash Flows and Calculations

Net cash flow (NCF) -$80,000 $40,000 $40,000 $40,000

Cumulative NCF -$80,000 -$40,000 $0,0000 $40,000

Discounted NCF (at 10%) -$80,000 $36,364 $33,058 $30,053

Cumulative discount NCF -$80,000 -$43,636 -$10,578 $19,478

Payback Period =2 years + $0/$40,000 = 2 years

Discounted payback period = 2 years + $10,578/$30,053 = 2.35 years

NPV = $99,475 – $80,000 = $19,475

Cost of capital = 10%

Evaluating the Payback Rule
The ordinary payback period is easy to calculate and provides a simple measure of an investment’s

liquidity risk. However, it

• ignores the time value of money,

• has no economic rationale that makes the payback method consistent with shareholder wealth

maximization, and

• is biased against long-term projects, such as R&D or new product development.

Its biggest weakness is the failure to consider cash flows after the payback period (Parrino et al., 2012).

PB = Years before cost recovery +
Remaining cost to recover

Cash flow during the year

0 1 2 3
Year

Based on Parrino et al. (2012)

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Topic 2: Cost of Capital and Financing Decisions

What is Capital?
Capital—money available to pay for day-to-day operations and future growth funding

Sources of Capital for a Start-up
• Self, friends, family

• Loans or lines of credit: small and short-term loans

• Small business grants from foundations and government

• Incubators that provide resources in exchange for equity

• Angel investors (typically 25k to 250k)

• Venture capital, typically above 1 million (investors exert control of the start-up)

• Crowdfunding through an online platform that enables small contributions from many investors

(Clendenen, 2020)

• Commitment by a major customer for which the customer receives priority to buy the product

of their investment before other customers (Zwilling, 2010)

Estimating the Cost of Capital
The cost of capital can be estimated using the weighted average cost of each security issued by the

company. For a project, the cost of capital includes the following (Parrino et al., 2012):

• Discount rate used to calculate NPV (see the table on the following page)

• Required rate of return

• The opportunity cost to the holders of a company’s securities

To determine the weighted average cost of capital (WACC), divide the costs of capital into debt and

equity and use the following equations:

• = +

where is the percentage of debt and

is the percentage of equity

Kdebt is the cost of debt

Kequity is the cost of equity

• WACC after tax is

o , −

= + , − (1 – tax rate)

o = + + (1 − )

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Cost of Capital and Risks
When the Cost of Capital is used as discount rate to evaluate a new project (CAPEX), the risk of a project

should be considered (Brealy & Myers, 2003).

Category Discount Rate

Speculative ventures 30%

New Products 20%

Expansion of existing business 15% (company cost of capital)

Cost improvement, known
technology

10%

Risk Is Uncertainty
• Of future cash inflows due to

o Market risk—market conditions that affect revenue

o Credit risk—customer’s availability to pay

o Operational risk—production unpredictability

o Interest rate risk—changes in interest rate level

• Of future cash outflows due to

o Liquidity risk—the company’s ability to pay

o Interest rate risk—changes in interest rate level

Risk and Return Trade-off
People do not want to lose money! Therefore, a higher-risk investment must offer a potential return

high enough to make it as attractive as the lower-risk alternative. At the same time, an investor must

accept a higher level of risk to achieve higher gains (Chen, 2020).

• The potential return required depends on the amount of risk—the probability of being

dissatisfied with an outcome.

• The higher the risk, the higher the required rate-of-return (Parrino et al., 2012)

How to Measure Return
• Expected vs realized return

o Expected return

▪ estimated or predicted before the outcome is known

▪ Expected Return (ER) = (Probability 1 * Return 1) + (Probability 2 * Return 2) + …

o Realized return

▪ calculated after the outcome is known

▪ Realized Return = (Selling price − Purchase price) / Purchase Price

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Example: Holding Period Return
Ella buys a stock for $26.00. After one year, the stock price is $29.00 and she receives a dividend of

$0.80. What is her return for the period?

Example: Expected Return
o There is 30% chance the total return on Dell stock will be -3.45%, a 30% chance it will be

+5.17% , a 30% chance it will be +12.07% and a 10% chance that it will be +24.14%.

Calculate the expected return.

Four Measures of Risk
• Four most commonly used terms in measuring risks

o Volatility

o Variance

o Standard Deviation

o Beta

Measuring Risk: Calculate Variance
1. Square the difference between each possible outcome and the mean

2. Multiply each squared difference by its probability of occurring

3. Add

o If all possible outcomes are equally likely, the formula becomes

o Standard deviation is the square root of the variance

= + =
+ 1

0

=
($29.00 − $26.00) + $0.80

$26.00

=
$3.80

$26.00
= 0.14615   14.62%

( ) =
2 = ∑{ × [ − ( )]2}

=1

2 =

∑ [ − ( )]2
=1


2 =

( ) = [. 30 × (−0.0345)] + (. 30 × 0.0517) + (. 30 × 0.1207) + (. 10 × 0.2414)

= −0.010305 + 0.01551 + 0.03621 + 0.02414

= 0.0655 6.55%

Source: Parrino et al. (2012)

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Risk and Diversification
Diversification eliminates unique risk but not market risk.

• Investing in two or more assets with returns that do not always move in the same direction at

the same time can reduce the risk in an investment portfolio.

• Diversification can nearly eliminate unique risk to individual assets, but the risk common to all

assets in the market remains.

• Risk that cannot be diversified away is non-diversifiable, or systematic risk. This is the risk

inherent in the market or economy (Brealey & Myers, 2003).

Diversification: Individuals vs Companies
• Individual investors can diversify easily and cheaply but it is much more expensive for a

company to diversify product lines.

• Individual investors do not pay extra to companies that are diversified or less to companies that

are not diversified.

• A company’s value neither increases nor decreases based on its degree of diversification. The

value of a company is the sum of its parts, no more no less (Brealey & Myers, 2003).

Equity Securities
Common stock and preferred stock—two types of ownership interest in a corporation; the most

prevalent types of equity securities

o Dividend payments do not affect a company’s taxes

o Have limited liability for stockholders; claims made against the corporation cannot

include a stockholder’s personal assets

o Generally viewed as perpetuities; do not have maturity dates

o Dividends are promised rather than guaranteed to preferred stockholders (Parrino et al.,

2012)

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Estimating the Cost of Equity
Market information is used to estimate the cost of equity. There are two other methods for estimating

the cost of common stock:

o Method 1: Capital Asset Pricing Model (CAPM)

o Method 2: Constant-Growth Dividend Model

The most appropriate method depends on the availability and reliability of information (Parrino et al.,

2012)

Method 1: Capital Asset Price Model (CAPM)
Expected Return of an asset can be broken down into risk- free rate and compensation to investors for

taking more risk:

( ) = + [ ( ) − ]

• Expected Return = Risk Free Rate + Beta × Market Risk

• Beta measures the risks of a stock relative to its market

o Beta > 1: The stock is more volatile than the market

o Beta < 1: The stock is less volatile than the market

• Betas by sector and the companies included in each industry are available online (Damodaran,

2021)

Estimating Beta
To estimate beta for a non-publicly traded firm

o Identify a “comparable” company with publicly traded stock that is in the same business

and that has a similar amount of debt

o use an average of the betas for the public firms in the same industry

Levered vs unlevered beta

o Levered beta is the market beta, considering the capital structure of the firm as is.

o Unlevered beta removes the influence of debt, enabling comparison between

companies.

Market-Risk Premium (Rm − Rf)
• Market-risk premium cannot be observed: the rate of return investors expect is unknown

• Market-risk premium usually estimates the average risk premium investors have earned in the

past as an indication of the risk premium they might require today

o From 1926 through 2015, the US stock market exceeded actual returns on long-term US

government bonds by an average of 5.92% per year

o If a financial analyst believes that the market-risk premium in the past is a reasonable

estimate of the risk premium today, then he or she might use a similar percentage as

the market risk premium for the future (Parrino et al., 2012)

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Assumptions of CAPM
The following assumptions underlie the capital asset pricing model (CAPM):

• Many investors who are all price takers, i.e., financial markets, are competitive.
• All investors plan to invest over the same time horizon.
• There are no distortionary taxes or transaction costs.
• All investors can borrow and lend at same risk-free rate.
• Investors care only about their expected return (like) and variance (dislike).
• All investors have same information and beliefs about the distribution of returns.
• The market portfolio that determines beta consists of all publicly traded assets (Parrino et al.,

2012).

Method 2: Constant-Growth Dividend Model
The constant-growth dividend model is useful for a company that pays dividends that will grow at a
constant rate—such as an electric utility—rather than a fast-growing high-tech firm.

• Present Value of Perpetuity: 0 =

• Value of stocks with fixed dividend level: 0 =

• Value of stocks with dividend growing at the rate of g: 0 =
1

• The equation above can be rearranged to solve for the required rate of return (R), which is also
the cost of common stock (KCS)

=
1

0
+

In practice, most people use the CAPM to estimate the cost of equity if the result is going to be used in
the discount rate for evaluating a project (Parrino et al., 2012).

Bank Loans and Corporate Bonds
• Investors’ required rate of return is often not directly observable.

• The market value (price) of securities is often used to estimate the required rate of return.

• To estimate the cost of debt, long-term debt (i.e., maturity longer than one year) is of particular

interest; long-term debt can be considered permanent, since companies often issue new debt to

pay off the old (Parrino et al., 2012).

• The interest rate (or historical interest rate determined when the debt was issued) the firm is

paying on its outstanding debt does not necessarily reflect its current cost of debt.

• The current cost of long-term debt is the appropriate cost of debt for weighted average cost of

capital (WACC) calculations; WACC is the opportunity cost of capital for the firm’s investors as of

today.

• Use yield to maturity (YTM) to determine the cost of debt and adjust for the tax deductibility of

interest on debt (Parrino et al., 2012).

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Yield to Maturity (YTM)
Yield to maturity is the internal rate of return (IRR) of a bond investment if the investor holds the bond

to maturity and all payments are made as scheduled.

• YTM accounts for the time value of money (TVM) and the bond purchase price.

• The current YTM of a bond reflects the required rate of return for the bondholder.

• YTM is used to estimate the cost of debt to a company (Parrino et al., 2012).

Taxes and the Cost-of-Debt Equation
The after-tax cost of interest payments equals the pre-tax cost times 1, minus the tax rate (Parrino

et al., 2012):

− = − × (1 − )

Weighted Average Cost of Capital (WACC)
• After-tax weighted-average cost of capital equation:

= (1 − ) + +

• Use market values, not book values, to calculate WACC.

• A list of estimated WACC per industry in the US is at

https://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/wacc.htm

Limitations of WACC
WACC can be used as a discount rate for evaluating projects under the following conditions (Parrino et

al., 2012):

1. The level of systematic risk for the project is the same as that of the portfolio of projects

that currently comprise the firm.

2. The project uses the same financing mix—proportions of debt, preferred shares, and

common shares—as the firm as a whole.

Alternatives to WACC
• Using a public company in a similar, or pure-play comparable business (often difficult to find)

• Classifying projects into categories based on their systematic risks and specifying a discount rate

for each

Category Discount Rate

Speculative ventures 30%

New products 20%

Expansion of existing business 15%

Cost Improvement, known technology 10%

Source: Parrino et al. (2012)

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Problems/Exercises

What to Do
Complete all the practice exercises from the book and the custom exercise that follows to gain the

knowledge and skills to complete the final Project 5 deliverable. The answers are provided, so you

can check your work.

Self Study Problems
• Chapter 7 Self Study problems (all)

• Chapter 10 Self Study problems (all)

• Chapter 13 Self Study problems (all)

Advanced Problems and Questions 10.36
10.36 Quasar Tech Co. is investing $6 million in new machinery to produce next-generation routers.

Sales will amount to $1.75 million for the next three years and increase to $2.4 million for the three

years after that. The project is expected to last six years. Operating costs, excluding depreciation, will be

$898,620 annually. The machinery will be depreciated to a salvage value of $0 over 6 years using the

straight-line method. The company’s tax rate is 30 percent, and the cost of capital is 16 percent.

A. What is the payback period?

B. What is the average accounting return (ARR)?

C. Calculate the project NPV.

D. What is the IRR for the project?

Solution to Problem 10.36
A.

Year

Net Income

Depreciation

Project 1 Cash

Flows
Cumulative CF

0 $(6,000,000) $(6,000,000)

1 $(104,034) $1,000,000 895,966 (5,104,034)

2 $(104,034) $1,000,000 895,966 (4,208,068)

3 $(104,034) $1,000,000 895,966 (3,312,102)

4 350,966 $1,000,000 1,350,966 (1,961,136)

5 350,966 $1,000,000 1,350,966 (610,170)

6 350,966 $1,000,000 1,350,966 740,796
PB = Years before cost recovery + (Remaining cost to recover/ Cash flow during the year) = 5 +

($610,170 / $1,350,966) = 5.45 years

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B.

Year 1 Year 2 Year 3 Year 4 Year 5 Year 6

Sales $ 1,750,000 $ 1,750,000 $ 1,750,000 $ 2,400,000 $ 2,400,000 $ 2,400,000

Expenses 898,620 898,620 898,620 898,620 898,620 898,620

Depreciation 1,000,000 1,000,000 1,000,000 1,000,000 1,000,000 1,000,000

EBIT $(1,48,620) $(1,48,620) $(1,48,620) $ 501,380 $ 501,380 $ 501,380

Taxes (30%) 44,586 44,586 44,586 (150,414) (150,414) (150,414)

Net income $ (104,034) $ (104,034) $ (104,034) $ 350,966 $ 350,966 $ 350,966

Beginning BV 6,000,000 5,000,000 4,000,000 3,000,000 2,000,000 1,000,000

Less: Depreciation 1,000,000 1,000,000 1,000,000 1,000,000 1,000,000 1,000,000

Ending BV $ 5,000,000 $ 4,000,000 $ 3,000,000 $ 2,000,000 $ 1,000,000 $ 0

Average after-tax income = $123,466

Average book value of equipment = $3,000,000
Accounting rate of return = Average after-tax income = $123,466 = 4.1%
Average book value $3,000,000

C.

Cost of this project = $6,000,000

Required rate of return = k =16%

Length of project = n = 6 years

= ∑

(1 + )

=0

= −$6,000,000 + $895,966 × [
1 −

1
(1.16)3

0.16
] + $1,350,966 × [

1 −
1

(1.16)3

0.16
] ×

1

(1.16)3

= −$6,000,000 + $2,012,241 + $1,943,833 = −$2,043,927

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D.

To compute the IRR, try rates lower than 16 percent. Try IRR = 3%.

Try IRR = 3.1%.

The IRR of the project is approximately 3.1%.

Advanced Problems and Questions 10.38
10.38 Trident Corp. is evaluating two independent projects. The following table lists the costs and

expected cash flows. The cost of capital is 10 percent.

Year A B

0 -$312,500 -$395,000

1 121,450 153,552

2 121,450 158,711

3 121,450 166,220

4 121,450 132,000

5 121,450 122,00

A. Calculate the projects’ NPV.

B. Calculate the projects’ IRR.

C. Which project should be chosen based on NPV? Based on IRR? Is there a conflict?

D. If you are the decision maker for the firm, which project or projects will be accepted? Explain

your reasoning.

= 0 = ∑

(1 + )

=0

0

= −$6,000,000 + $895,966 × [

1 −
1

(1.03)3

0.03
] + $1,350,966 × [

1 −
1

(1.03)3

0.03
] ×

1

(1.03)3

= −$6,000,000 + $2,534,340 + $3,497,084 = $31,424

= 0 − ∑

(1 + )

=0

0

= −$6,000,000 + $895,966 × [

1 −
1

(1.031)3

0.031
] + $1,350,966 × [

1 −
1

(1.031)3

0.031
] ×

1

(1.031)3

= −$6,000,000 + $2,529,475 + $3,480,225 = $9,700

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Solution to Problem 10.38

A.

Project A:

Cost of this project = $312,500

Annual cash flows = $121,450

Required rate of return = k = 10%

Length of project = n = 5 years

Project B:

Cost of this project = $395,000

Required rate of return = k = 10%

Length of project = n = 5 years

B.

Project A:

Since NPV > 0, to compute the IRR, try rates higher than 10%.

Try IRR = 27%.

Try IRR = 27.2%

The IRR of Project A is approximately 27.2 percent. Using a financial calculator, we find that the IRR is

27.187 percent.

= ∑

(1 + )

=0

= −312,500 + $121,450 × [
1 −

1
(1.10)5

0.10
]

= −$312,500 + 460,391

= $147,891

= ∑

(1 + )

=0

= −$395,000 +
$153,552

(1.10)1
+

$158,711

(1.10)2
+

$166,220

(1.10)3
+

$132,000

(1.10)4
+

$122,000

(1.10)5

= −395,000 + $139,593 + $131,166 + $124,884 + 90,158 + 75,752 = $166,553

= 0 = ∑

(1 + )

=0

0 = −312,500 + $121,450 × [
1 −

1
(1.27)5

0.27
]

= −$312,500 + 313,666 ≠ $1,166

= 0 = ∑

(1 + )

=0

0 = −312,500 + $121,450 × [
1 −

1
(1.272)5

0.272
]

= −$312,500 + 312,418 = −$82 ≅ 0

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Project B:

Since NPV > 0, to compute the IRR, try rates higher than 10 percent. Try IRR = 26%

The IRR of Project A is approximately 27.2 percent. Using a financial calculator, the solution reached is

27.187 percent.

Try IRR = 26.1%

The IRR of Project B is approximately 26.1 percent.

C.

There is no conflict between the NPV and IRR decisions. Using NPV decision criteria, both projects have

positive NPVs; they are independent projects; both should be accepted. Using IRR decision criteria, both

projects have IRRs greater than the cost of capital; both will be accepted.

D.

Based on NPV, both projects will be accepted.

Advanced Problems and Questions 10.39
10.39 Tyler, Inc., is considering switching to a new production technology. The cost of the required

equipment will be $4 million. The discount rate is 12%. The cash flows the firm expects the new

technology to generate are as follows.

Years CF

1-2 0

3-5 $ 845,000

6-9 $ 1,845,000

A. Compute the payback and discounted payback periods for the project.

B. What is the NPV for the project? Should the firm proceed with the project?

C. What is the IRR? Based on IRR, what would the decision be?

= 0 = ∑

(1 + )

=0

0 = −$395,000 +
$153,552

(1.261)1
+

$158,711

(1.261)2
+

$166,220

(1.261)3
+

$132,000

(1.261)4
+

$122,000

(1.261)5

= −$395,000 + $121,770 + $99,811 + $82,897 + $52,205 + $38,263 = −$54 ≅ 0

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Solution to Problem 10.39
A.

Year

Cash Flows

PVCF

Cumulative CF Cumulative PVCF

0 $(4,000,000) $(4,000,000) $(4,000,000) $(4,000,000)

1 — — (4,000,000) (4,000,000)

2 — — (4,000,000) (4,000,000)

3 845,000 601,454 (3,155,000) (3,398,546)

4 845,000 537,013 (2,310,000) (2,861,533)

5 845,000 479,476 (1,465,000) (2,382,057)

6 1,450,000 734,615 (15,000) (1,647,442)

7 1,450,000 655,906 1,435,000 (991,536)

8 1,450,000 585,631 2,885,000 (405,905)

9 1,450,000 522,885 4,335,000 116,979

= +

ℎ ℎ

= 6 +
$15,000

$1,450,000
= 6.01

= +

ℎ ℎ

= 8 +
$405,905

$522,885
= 8.8

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B.

Cost of this project = $4,000,000

Required rate of return = k = 12%

Length of project = n = 9 years

Since NPV > 0, the project should be accepted.

C.

Given a positive NPV, to compute the IRR, one should try rates higher than 12%.

Try IRR = 12.5%.

Using a financial calculator and 12.5% returns an IRR of 12.539%. The IRR exceeds the cost of capital

(12%); the project should be accepted.

= ∑

(1 + )

=0

= −$4,000,000 + 0 + 0 + $845,000 × [
1 −

1
(1.12)3

0.12
] ×

1

(1.12)2

+ $1,450,000 × [
1 −

1
(1.12)4

0.12
] ×

1

(1.12)5
= −$4,000,000 + 0 + 0 + $1,617,943 + $2,499,037

= $116,980

= ∑

(1 + )

=0

= −$4,000,000 + 0 + 0 + $845,000 × [
1 −

1
(1.125)3

0.125
] ×

1

(1.125)2

+ $1,450,000 × [
1 −

1
(1.125)4

0.125
] ×

1

(1.125)5

= −$4,000,000 + 0 + 0 + $1,589,915 + $2,418,479 = $8,394

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References
Brealey, R. A. & Myers, S. C. (2003). Principles of Corporate Finance 7th ed. McGraw-Hill.

Chen, J. (2020, February 3). Risk-return tradeoff. Investopedia. Retrieved August 9, 2021, from
https://www.investopedia.com/terms/r/riskreturntradeoff.asp

Clendenen, D. (2020, March 19). 23 of the best fundraising websites for small business. LendGenius.
https://www.lendgenius.com/blog/fundraising-websites/

Damodaran, A. (2021, January). Total betas by sector (for computing private company cost of equity)—
US. Damodaran Online. Retrieved August 9, 2021, from
https://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/totalbeta.html

Microsoft. (n.d.). Excel functions (by category). Retrieved July 22, 2021, from
https://support.microsoft.com/en-us/office/excel-functions-by-category-5f91f4e9- 7b42-
46d2-9bd1-63f26a86c0eb

Parrino, R., Kidwell, D. S., & Bates, T. W. (2012). Fundamentals of corporate finance. Wiley.

Zwilling, M. (2010, February 12). Top 10 sources of funding for start-ups. Forbes. Retrieved August 9,
2021, from https://www.forbes.com/2010/02/12/funding-for-startups-entrepreneurs-finance-
zwilling.html?sh=46bb828b160f

Now that you have read this Review and Practice Guide and completed the exercises, you are
ready to participate in the assignment in Step 3.

  • Structure Bookmarks
      • Textbox
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        • Project 5: Review and Practice Guide
      • Textbox
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        • Cost of Capital, Risk/Return & Capital Budgeting
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        • Project 5: Review and Practice Guide
      • Contents
        • Topic 1: Capital Budgeting
          • Topic 1: Capital Budgeting
            • Topic 1: Capital Budgeting
          • ……………………………………………………………………………………
          • ………………………. 3
        • The Finance Balance Sheet
          • The Finance Balance Sheet
            • The Finance Balance Sheet
          • ……………………………………………………………………………………
          • ………………….. 3
        • Introduction to Capital Budgeting
          • Introduction to Capital Budgeting
            • Introduction to Capital Budgeting
          • ……………………………………………………………………………………
          • ………… 3
        • What is CAPEX?
          • What is CAPEX?
            • What is CAPEX?
          • ………………………………………………………………………………………………………………..
          • ……… 3
        • Key Reasons for Making Capital Expenditures
          • Key Reasons for Making Capital Expenditures
            • Key Reasons for Making Capital Expenditures
          • ……………………………………………………….
          • …………………….. 3
        • Methods to Inform Capital Expenditure Decisions
          • Methods to Inform Capital Expenditure Decisions
            • Methods to Inform Capital Expenditure Decisions
          • ……………………………………………………….
          • ………………. 3
        • Net Present Value Method: Calculating the NPV of a Project
          • Net Present Value Method: Calculating the NPV of a Project
            • Net Present Value Method: Calculating the NPV of a Project
          • ……………………………………………………….
          • .. 4
        • Net Present Value (NPV): Calculation Example
          • Net Present Value (NPV): Calculation Example
            • Net Present Value (NPV): Calculation Example
          • ……………………………………………………….
          • …………………… 4
        • NPV: The Best Capital-Budgeting Technique
          • NPV: The Best Capital-Budgeting Technique
            • NPV: The Best Capital-Budgeting Technique
          • ……………………………………………………….
          • ………………………. 5
        • NPV: The Five-step Approach
          • NPV: The Five-step Approach
            • NPV: The Five-step Approach
          • ……………………………………………………………………………………
          • ………………. 5
        • Summary of NPV Method
          • Summary of NPV Method
            • Summary of NPV Method
          • ……………………………………………………………………………………
          • ……………………. 5
        • Key Advantages
          • Key Advantages
            • Key Advantages
          • ………………………………………………………………………………………………………………..
          • ….. 5
        • Key Disadvantage
          • Key Disadvantage
            • Key Disadvantage
          • ………………………………………………………………………………………………………………..
          • .. 5
        • Internal Rate of Return (IRR) Method
          • Internal Rate of Return (IRR) Method
            • Internal Rate of Return (IRR) Method
          • ……………………………………………………………………………………
          • ……. 6
        • Excel Function: IRR
          • Excel Function: IRR
            • Excel Function: IRR
          • ………………………………………………………………………………………………………………..
          • …. 6
        • IRR Example
          • IRR Example
            • IRR Example
          • ………………………………………………………………………………………………………………..
          • ………….. 6
        • NPV or IRR?
          • NPV or IRR?
            • NPV or IRR?
          • ………………………………………………………………………………………………………………..
          • …………… 7
        • Unconventional Cash Flows
          • Unconventional Cash Flows
            • Unconventional Cash Flows
          • ……………………………………………………………………………………
          • …………………. 7
        • Payback Period Method
          • Payback Period Method
            • Payback Period Method
          • ……………………………………………………………………………………
          • ………………………. 7
        • Computing Payback Period
          • Computing Payback Period
            • Computing Payback Period
          • ……………………………………………………………………………………
          • ………………….. 7
        • Payback Period Calculation: Example and Formula
          • Payback Period Calculation: Example and Formula
            • Payback Period Calculation: Example and Formula
          • ……………………………………………………….
          • ……………… 8
        • Discounted Payback Period
          • Discounted Payback Period
            • Discounted Payback Period
          • ……………………………………………………………………………………
          • ………………….. 8
        • Discounted Payback Period Cash Flows and Calculations
          • Discounted Payback Period Cash Flows and Calculations
            • Discounted Payback Period Cash Flows and Calculations
          • ……………………………………………………….
          • …….. 8
        • Evaluating the Payback Rule
          • Evaluating the Payback Rule
            • Evaluating the Payback Rule
          • ……………………………………………………………………………………
          • ………………… 8
        • Topic 2: Cost of Capital and Financing Decisions
          • Topic 2: Cost of Capital and Financing Decisions
            • Topic 2: Cost of Capital and Financing Decisions
          • ……………………………………………………….
          • …………………….. 9
        • What is Capital?
          • What is Capital?
            • What is Capital?
          • ………………………………………………………………………………………………………………..
          • …….. 9
        • Sources of Capital for a Start-up
          • Sources of Capital for a Start-up
            • Sources of Capital for a Start-up
          • ……………………………………………………………………………………
          • …………… 9
        • Estimating the Cost of Capital
          • Estimating the Cost of Capital
            • Estimating the Cost of Capital
          • ……………………………………………………………………………………
          • ………………. 9
        • Cost of Capital and Risks …………………………………………………………………………………………………………. 10
          • Cost of Capital and Risks …………………………………………………………………………………………………………. 10
            • Cost of Capital and Risks …………………………………………………………………………………………………………. 10
        • Risk Is Uncertainty………………………………………………………………………………………………………………….. 10
          • Risk Is Uncertainty………………………………………………………………………………………………………………….. 10
            • Risk Is Uncertainty………………………………………………………………………………………………………………….. 10
        • Risk and Return Trade-off ……………………………………………………………………………………………………….. 10
          • Risk and Return Trade-off ……………………………………………………………………………………………………….. 10
            • Risk and Return Trade-off ……………………………………………………………………………………………………….. 10
        • How to Measure Return …………………………………………………………………………………………………………. 10
          • How to Measure Return …………………………………………………………………………………………………………. 10
            • How to Measure Return …………………………………………………………………………………………………………. 10
        • Example: Holding Period Return ………………………………………………………………………………………………. 11
          • Example: Holding Period Return ………………………………………………………………………………………………. 11
            • Example: Holding Period Return ………………………………………………………………………………………………. 11
        • Example: Expected Return ………………………………………………………………………………………………………. 11
          • Example: Expected Return ………………………………………………………………………………………………………. 11
            • Example: Expected Return ………………………………………………………………………………………………………. 11
        • Four Measures of Risk …………………………………………………………………………………………………………….. 11
          • Four Measures of Risk …………………………………………………………………………………………………………….. 11
            • Four Measures of Risk …………………………………………………………………………………………………………….. 11
        • Measuring Risk: Calculate Variance ………………………………………………………………………………………….. 11
          • Measuring Risk: Calculate Variance ………………………………………………………………………………………….. 11
            • Measuring Risk: Calculate Variance ………………………………………………………………………………………….. 11
        • Risk and Diversification …………………………………………………………………………………………………………… 12
          • Risk and Diversification …………………………………………………………………………………………………………… 12
            • Risk and Diversification …………………………………………………………………………………………………………… 12
        • Diversification: Individuals vs Companies ………………………………………………………………………………….. 12
          • Diversification: Individuals vs Companies ………………………………………………………………………………….. 12
            • Diversification: Individuals vs Companies ………………………………………………………………………………….. 12
        • Equity Securities …………………………………………………………………………………………………………………….. 12
          • Equity Securities …………………………………………………………………………………………………………………….. 12
            • Equity Securities …………………………………………………………………………………………………………………….. 12
        • Estimating the Cost of Equity …………………………………………………………………………………………………… 13
          • Estimating the Cost of Equity …………………………………………………………………………………………………… 13
            • Estimating the Cost of Equity …………………………………………………………………………………………………… 13
        • Method 1: Capital Asset Price Model (CAPM) ……………………………………………………………………………. 13
          • Method 1: Capital Asset Price Model (CAPM) ……………………………………………………………………………. 13
            • Method 1: Capital Asset Price Model (CAPM) ……………………………………………………………………………. 13
        • Estimating Beta ……………………………………………………………………………………………………………………… 13
          • Estimating Beta ……………………………………………………………………………………………………………………… 13
            • Estimating Beta ……………………………………………………………………………………………………………………… 13
        • Market-Risk Premium (Rm − Rf) ………………………………………………………………………………………………… 13
          • Market-Risk Premium (Rm − Rf) ………………………………………………………………………………………………… 13
            • Market-Risk Premium (Rm − Rf) ………………………………………………………………………………………………… 13
        • Assumptions of CAPM …………………………………………………………………………………………………………….. 14
          • Assumptions of CAPM …………………………………………………………………………………………………………….. 14
            • Assumptions of CAPM …………………………………………………………………………………………………………….. 14
        • Method 2: Constant-Growth Dividend Model ……………………………………………………………………………. 14
          • Method 2: Constant-Growth Dividend Model ……………………………………………………………………………. 14
            • Method 2: Constant-Growth Dividend Model ……………………………………………………………………………. 14
        • Bank Loans and Corporate Bonds …………………………………………………………………………………………….. 14
          • Bank Loans and Corporate Bonds …………………………………………………………………………………………….. 14
            • Bank Loans and Corporate Bonds …………………………………………………………………………………………….. 14
        • Yield to Maturity (YTM)
          • Yield to Maturity (YTM)
            • Yield to Maturity (YTM)
            • …………………………………………………………………………………………………………… 15
        • Taxes and the Cost-of-Debt Equation ……………………………………………………………………………………….. 15
          • Taxes and the Cost-of-Debt Equation ……………………………………………………………………………………….. 15
            • Taxes and the Cost-of-Debt Equation ……………………………………………………………………………………….. 15
        • Weighted Average Cost of Capital (WACC) ………………………………………………………………………………… 15
          • Weighted Average Cost of Capital (WACC) ………………………………………………………………………………… 15
            • Weighted Average Cost of Capital (WACC) ………………………………………………………………………………… 15
        • Limitations of WACC ………………………………………………………………………………………………………………. 15
          • Limitations of WACC ………………………………………………………………………………………………………………. 15
            • Limitations of WACC ………………………………………………………………………………………………………………. 15
        • Alternatives to WACC ……………………………………………………………………………………………………………… 15
          • Alternatives to WACC ……………………………………………………………………………………………………………… 15
            • Alternatives to WACC ……………………………………………………………………………………………………………… 15
        • Problems/Exercises
          • Problems/Exercises
            • Problems/Exercises
            • ……………………………………………………………………………………………………………………. 16
        • What to Do ……………………………………………………………………………………………………………………………. 16
          • What to Do ……………………………………………………………………………………………………………………………. 16
            • What to Do ……………………………………………………………………………………………………………………………. 16
        • Self Study Problems ……………………………………………………………………………………………………………….. 16
          • Self Study Problems ……………………………………………………………………………………………………………….. 16
            • Self Study Problems ……………………………………………………………………………………………………………….. 16
        • Advanced Problems and Questions 10.36 …………………………………………………………………………………. 16
          • Advanced Problems and Questions 10.36 …………………………………………………………………………………. 16
            • Advanced Problems and Questions 10.36 …………………………………………………………………………………. 16
        • Solution to Problem 10.36 ………………………………………………………………………………………………………. 16
          • Solution to Problem 10.36 ………………………………………………………………………………………………………. 16
            • Solution to Problem 10.36 ………………………………………………………………………………………………………. 16
        • Advanced Problems and Questions 10.38 …………………………………………………………………………………. 18
          • Advanced Problems and Questions 10.38 …………………………………………………………………………………. 18
            • Advanced Problems and Questions 10.38 …………………………………………………………………………………. 18
        • Solution to Problem 10.38 ………………………………………………………………………………………………………. 19
          • Solution to Problem 10.38 ………………………………………………………………………………………………………. 19
            • Solution to Problem 10.38 ………………………………………………………………………………………………………. 19
        • Advanced Problems and Questions 10.39 …………………………………………………………………………………. 20
          • Advanced Problems and Questions 10.39 …………………………………………………………………………………. 20
            • Advanced Problems and Questions 10.39 …………………………………………………………………………………. 20
        • Solution to Problem 10.39 ………………………………………………………………………………………………………. 21
          • Solution to Problem 10.39 ………………………………………………………………………………………………………. 21
            • Solution to Problem 10.39 ………………………………………………………………………………………………………. 21
        • References ……………………………………………………………………………………………………………………………. 23
          • References ……………………………………………………………………………………………………………………………. 23
            • References ……………………………………………………………………………………………………………………………. 23
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      • Topic 1: Capital Budgeting
      • The Finance Balance Sheet
      • Figure
      • Based on Parrino et al. (2012) (2012(2012)
        • Based on Parrino et al. (2012) (2012(2012)
        • • Capital Budgeting determines the long-term productive assets that will create wealth.
          • • Capital Budgeting determines the long-term productive assets that will create wealth.
            • • Capital Budgeting determines the long-term productive assets that will create wealth.
          • • Capital investments are large cash outlays and long-term commitments not easily reversed that affect performance in the long run.
            • • Capital investments are large cash outlays and long-term commitments not easily reversed that affect performance in the long run.
      • Artifact
      • Introduction to Capital Budgeting
      • • Capital-budgeting techniques help management systematically analyze potential opportunities to decide which are worth undertaking (Parrino et al., 2012).
        • • Capital-budgeting techniques help management systematically analyze potential opportunities to decide which are worth undertaking (Parrino et al., 2012).
          • • Capital-budgeting techniques help management systematically analyze potential opportunities to decide which are worth undertaking (Parrino et al., 2012).
      • What is CAPEX?
      • CAPEX—capital expenditures, or a company’s key long-term expenses
      • Key Reasons for Making Capital Expenditures
      • • Renewal—equipment repair, overhaul, rebuilding, or retrofitting. Usually does not require an elaborate analysis and are made on a routine basis.
        • • Renewal—equipment repair, overhaul, rebuilding, or retrofitting. Usually does not require an elaborate analysis and are made on a routine basis.
          • • Renewal—equipment repair, overhaul, rebuilding, or retrofitting. Usually does not require an elaborate analysis and are made on a routine basis.
        • • Replacement—to address equipment malfunction or obsolescence. Typically involves decisions at the plant level.
          • • Replacement—to address equipment malfunction or obsolescence. Typically involves decisions at the plant level.
        • • Expansion—involves strategic decisions requiring complex, detailed analysis.
          • • Expansion—involves strategic decisions requiring complex, detailed analysis.
        • • Regulatory
          • • Regulatory
        • • Other
          • • Other
            • • Other
            • • Net present value (NPV)—Use the cost of capital to discount the cash flow of a project. Choose the project with positive net present value.
              • • Net present value (NPV)—Use the cost of capital to discount the cash flow of a project. Choose the project with positive net present value.
                • • Net present value (NPV)—Use the cost of capital to discount the cash flow of a project. Choose the project with positive net present value.
              • • Internal Rate of Return (IRR)—Calculate the rate of return of a project. Choose the highest one or the one that has a higher rate of return than the cost of capital.
                • • Internal Rate of Return (IRR)—Calculate the rate of return of a project. Choose the highest one or the one that has a higher rate of return than the cost of capital.
              • • Payback Period—Calculate how long does it take for a project to pay back itself. Choose the one with shorted payback period.
                • • Payback Period—Calculate how long does it take for a project to pay back itself. Choose the one with shorted payback period.
      • Methods to Inform Capital Expenditure Decisions
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      • Net Present Value Method: Calculating the NPV of a Project
      • Figure
      • Source: Parrino et al. (2012)
        • Source: Parrino et al. (2012)
      • Artifact
      • Net Present Value (NPV): Calculation Example
      • You can use the cash flow timeline below and Excel to calculate NPV for this project in which the cost of capital is 15%:
      • Figure
      • Artifact
      • Artifact
      • Based on Parrino et al. (2012)
        • Based on Parrino et al. (2012)
        • • Net Present Value (NPV) represents the current value of the project after accounting for expected cash flow and the cost of capital.
          • • Net Present Value (NPV) represents the current value of the project after accounting for expected cash flow and the cost of capital.
            • • Net Present Value (NPV) represents the current value of the project after accounting for expected cash flow and the cost of capital.
              • • Net Present Value (NPV) represents the current value of the project after accounting for expected cash flow and the cost of capital.
              • 1. Estimate project cost
                • 1. Estimate project cost
                  • 1. Estimate project cost
                • o Identify and add the present value of expenses related to the project.
                  • o Identify and add the present value of expenses related to the project.
                • o There are projects whose entire cost occurs at the start of the project, but many projects have costs occurring beyond the first year.
                  • o There are projects whose entire cost occurs at the start of the project, but many projects have costs occurring beyond the first year.
                • o The cash flow in year 0 (NCF0) on the timeline is negative, indicating an outflow
                  • o The cash flow in year 0 (NCF0) on the timeline is negative, indicating an outflow
                • o Both cash inflows (CIF) and cash outflows (COF) are likely in each year. Estimate the net cash flow (NCFn) = CIFn − COFn for each year.
                  • o Both cash inflows (CIF) and cash outflows (COF) are likely in each year. Estimate the net cash flow (NCFn) = CIFn − COFn for each year.
                • o Include salvage value of the project in its terminal year.
                  • o Include salvage value of the project in its terminal year.
                • o The cost of capital is the discount rate (k) used to determine the present value of expected net cash flows.
                  • o The cost of capital is the discount rate (k) used to determine the present value of expected net cash flows.
                • o The riskier a project, the higher its cost of capital (Parrino et al., 2012)
                  • o The riskier a project, the higher its cost of capital (Parrino et al., 2012)
                • o Determine the difference between the present values of the expected net cash flows from the project and the expected cost of the project.
                  • o Determine the difference between the present values of the expected net cash flows from the project and the expected cost of the project.
                • o Accept a project if it has a positive NPV, reject it if the NPV is negative.
                  • o Accept a project if it has a positive NPV, reject it if the NPV is negative.
                • • Decision rule
                  • • Decision rule
                • o NPV > 0 Accept the project
                  • o NPV > 0 Accept the project
                • o NPV < 0 Reject the project
                  • o NPV < 0 Reject the project
                • o Uses the discounted cash flow valuation technique to adjust for the time value of money
                  • o Uses the discounted cash flow valuation technique to adjust for the time value of money
                • o Provides a direct (dollar) measure of how much a capital project will increase the value of a company
                  • o Provides a direct (dollar) measure of how much a capital project will increase the value of a company
                • o Is Consistent with the goal of maximizing stockholder value
                  • o Is Consistent with the goal of maximizing stockholder value
                • o Can be difficult to understand without an accounting and finance background (Parrino et al., 2012).
                  • o Can be difficult to understand without an accounting and finance background (Parrino et al., 2012).
                • • IRR is the discount rate at which a project has an NPV equal to zero.
                  • • IRR is the discount rate at which a project has an NPV equal to zero.
                • • A project is acceptable if its IRR is greater than the firm’s cost of capital.
                  • • A project is acceptable if its IRR is greater than the firm’s cost of capital.
                • • The IRR is an important and legitimate alternative to the NPV method (Parrino et al., 2012).
                  • • The IRR is an important and legitimate alternative to the NPV method (Parrino et al., 2012).
          • • The NPV of a project is the difference between the present values of its expected cash inflows and expected cash outflows.
            • • The NPV of a project is the difference between the present values of its expected cash inflows and expected cash outflows.
          • • NPV is the best capital-budgeting technique because it is consistent with goal of maximizing shareholder wealth.
            • • NPV is the best capital-budgeting technique because it is consistent with goal of maximizing shareholder wealth.
          • • Positive NPV projects increase shareholder wealth and negative NPV projects decrease shareholder wealth. (Parrino et al., 2012)
            • • Positive NPV projects increase shareholder wealth and negative NPV projects decrease shareholder wealth. (Parrino et al., 2012)
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      • NPV: The Best Capital-Budgeting Technique
      • NPV: The Five-step Approach
      • 2. Estimate project net cash flows
        • 2. Estimate project net cash flows
          • 2. Estimate project net cash flows
        • 3. Determine project risk and estimate cost of capital
          • 3. Determine project risk and estimate cost of capital
        • 4. Compute the project’s NPV
          • 4. Compute the project’s NPV
        • 5. Make a decision
          • 5. Make a decision
      • Summary of NPV Method
      • Key Advantages
      • Key Disadvantage
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      • Internal Rate of Return (IRR) Method
      • Figure
      • Excel Function: IRR
      • IRR(values, [guess])
      • The IRR function syntax has the following arguments:
      • Values Required. An array or a reference to cells that contain numbers for which you want to calculate the internal rate of return.
      • • Values must contain at least one positive value and one negative value to calculate the internal rate of return.
        • • Values must contain at least one positive value and one negative value to calculate the internal rate of return.
          • • Values must contain at least one positive value and one negative value to calculate the internal rate of return.
        • • IRR uses the order of values to interpret the order of cash flows. Be sure to enter your payment and income values in the sequence you want.
          • • IRR uses the order of values to interpret the order of cash flows. Be sure to enter your payment and income values in the sequence you want.
        • • If an array or reference argument contains text, logical values, or empty cells, those values are ignored.
          • • If an array or reference argument contains text, logical values, or empty cells, those values are ignored.
      • Guess Optional. A number that you guess is close to the result of IRR. (Microsoft, n.d.)
      • IRR Example
      • Expected Cash Flow from a CAPEX
      • Based on Parrino et al. (2012)
        • Based on Parrino et al. (2012)
        • • IRR is the discount rate when NPV is zero, when the project is breakeven, so many times the two methods yield consistent results.
          • • IRR is the discount rate when NPV is zero, when the project is breakeven, so many times the two methods yield consistent results.
            • • IRR is the discount rate when NPV is zero, when the project is breakeven, so many times the two methods yield consistent results.
              • • IRR is the discount rate when NPV is zero, when the project is breakeven, so many times the two methods yield consistent results.
              • • Positive cash flow followed by negative net cash flows.
                • • Positive cash flow followed by negative net cash flows.
                  • • Positive cash flow followed by negative net cash flows.
                • • Simultaneous positive and negative net cash flows.
                  • • Simultaneous positive and negative net cash flows.
                • • Conventional followed by a negative net cash flow at the end of a project’s life.
                  • • Conventional followed by a negative net cash flow at the end of a project’s life.
                • o One of the most popular tools for evaluating capital projects
                  • o One of the most popular tools for evaluating capital projects
                • o Can serve as a risk indicator—the quicker a project’s cost recovery, the less risky the project
                  • o Can serve as a risk indicator—the quicker a project’s cost recovery, the less risky the project
                • o Decision criteria: payback period shorter than a specific amount of time (Parrino et al., 2012)
                  • o Decision criteria: payback period shorter than a specific amount of time (Parrino et al., 2012)
          • • IRR’s biggest strength is also its limitation: A single discount rate does not consider the change in interest rate level.
            • • IRR’s biggest strength is also its limitation: A single discount rate does not consider the change in interest rate level.
          • • IRR is ineffective when the projects have strings of positive and negative cash flows.
            • • IRR is ineffective when the projects have strings of positive and negative cash flows.
          • • IRR has the advantage of summarizing the rate of return of the project in one number, so it is a popular method.
            • • IRR has the advantage of summarizing the rate of return of the project in one number, so it is a popular method.
      • Figure
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      • NPV or IRR?
      • Is NPV or IRR a better measure for capital budgeting? Consider these points:
      • Unconventional Cash Flows
      • The IRR technique may provide more than one rate of return, making the calculation unreliable. Therefore, it should not be used to determine whether to accept or reject a project.
      • Following are examples of unconventional cash flows:
      • Payback Period Method
      • Payback period—the time it takes for the sum of the net cash flows from a project to equal the project’s initial investment
      • Computing Payback Period
      • The following timeline shows the net and cumulative net cash flow (NCF) for a proposed capital project with an initial cost of $80,000. This data is used to compute the payback period, 2.5 years.
      • Figure
      • Year
        • Year
      • NCF -$80,000 $35,000 $35,000 $20,000 $25,000
        • NCF -$80,000 $35,000 $35,000 $20,000 $25,000
        • Cumulative NCF -$80,000 -$45,000 -$10,000 $10,000 $35,000
      • Based on Parrino et al. (2012)
        • Based on Parrino et al. (2012)
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      • Payback Period Calculation: Example and Formula
      • = 2 years + $10,000
      • Figure
      • $20,000
      • = 2 years + 0.5
      • = 2.5 years
      • To compute the payback period, estimate a project’s cost and its future net cash flows:
      • PB=Years
        • PB=Years
          • PB=Years
          • before
          • cost
          • recovery+Remaining
          • cost
          • to
          • recoverCash
          • flow
          • during
          • the
          • year
        • • Future cash flows are discounted by the firm’s cost of capital.
          • • Future cash flows are discounted by the firm’s cost of capital.
            • • Future cash flows are discounted by the firm’s cost of capital.
          • • The major advantage of the discounted payback is that it tells management how long it takes a project to reach a positive NPV (Parrino et al., 2012).
            • • The major advantage of the discounted payback is that it tells management how long it takes a project to reach a positive NPV (Parrino et al., 2012).
      • Discounted Payback Period
      • Discounted Payback Period Cash Flows and Calculations
      • Figure
      • Net cash flow (NCF) -$80,000 $40,000 $40,000 $40,000
      • Cumulative NCF -$80,000 -$40,000 $0,0000 $40,000
      • Discounted NCF (at 10%) -$80,000 $36,364 $33,058 $30,053
      • Cumulative discount NCF -$80,000 -$43,636 -$10,578 $19,478
      • Artifact
      • Payback Period =2 years + $0/$40,000 = 2 years
      • Discounted payback period = 2 years + $10,578/$30,053 = 2.35 years
      • NPV = $99,475 – $80,000 = $19,475
      • Cost of capital = 10%
      • Based on Parrino et al. (2012)
        • Based on Parrino et al. (2012)
        • • ignores the time value of money,
          • • ignores the time value of money,
            • • ignores the time value of money,
          • • has no economic rationale that makes the payback method consistent with shareholder wealth maximization, and
            • • has no economic rationale that makes the payback method consistent with shareholder wealth maximization, and
          • • is biased against long-term projects, such as R&D or new product development.
            • • is biased against long-term projects, such as R&D or new product development.
      • Evaluating the Payback Rule
      • The ordinary payback period is easy to calculate and provides a simple measure of an investment’s liquidity risk. However, it
      • Its biggest weakness is the failure to consider cash flows after the payback period (Parrino et al., 2012).
        • • Self, friends, family
          • • Self, friends, family
            • • Self, friends, family
          • • Loans or lines of credit: small and short-term loans
            • • Loans or lines of credit: small and short-term loans
          • • Small business grants from foundations and government
            • • Small business grants from foundations and government
          • • Incubators that provide resources in exchange for equity
            • • Incubators that provide resources in exchange for equity
          • • Angel investors (typically 25k to 250k)
            • • Angel investors (typically 25k to 250k)
          • • Venture capital, typically above 1 million (investors exert control of the start-up)
            • • Venture capital, typically above 1 million (investors exert control of the start-up)
          • • Crowdfunding through an online platform that enables small contributions from many investors (Clendenen, 2020)
            • • Crowdfunding through an online platform that enables small contributions from many investors (Clendenen, 2020)
          • • Commitment by a major customer for which the customer receives priority to buy the product of their investment before other customers (Zwilling, 2010)
            • • Commitment by a major customer for which the customer receives priority to buy the product of their investment before other customers (Zwilling, 2010)
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      • Topic 2: Cost of Capital and Financing Decisions
      • What is Capital?
      • Capital—money available to pay for day-to-day operations and future growth funding
      • Sources of Capital for a Start-up
      • Estimating the Cost of Capital
      • The cost of capital can be estimated using the weighted average cost of each security issued by the company. For a project, the cost of capital includes the following (Parrino et al., 2012):
      • • Discount rate used to calculate NPV (see the table on the following page)
      • • Required rate of return
      • • The opportunity cost to the holders of a company’s securities
      • To determine the weighted average cost of capital (WACC), divide the costs of capital into debt and equity and use the following equations:
      • • = +
        • • = +
          • • = +
      • where is the percentage of debt and is the percentage of equity Kdebt is the cost of debt Kequity is the cost of equity
      • • WACC after tax is
        • • WACC after tax is
          • • WACC after tax is
            • • WACC after tax is
            • o , − = + , − (1 – tax rate)
              • o , − = + , − (1 – tax rate)
                • o , − = + , − (1 – tax rate)
              • o = + + (1− )
                • o = + + (1− )
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      • Cost of Capital and Risks
      • When the Cost of Capital is used as discount rate to evaluate a new project (CAPEX), the risk of a project should be considered (Brealy & Myers, 2003).
      • Category
        • Category
          • Category
            • Category
              • Category
            • Discount Rate
              • Discount Rate
        • Speculative ventures
          • Speculative ventures
            • Speculative ventures
              • Speculative ventures
            • 30%
              • 30%
          • New Products
            • New Products
              • New Products
            • 20%
              • 20%
          • Expansion of existing business
            • Expansion of existing business
              • Expansion of existing business
            • 15% (company cost of capital)
              • 15% (company cost of capital)
          • Cost improvement, known technology
            • Cost improvement, known technology
              • Cost improvement, known technology
            • 10%
              • 10%
      • Risk Is Uncertainty
      • • Of future cash inflows due to
        • • Of future cash inflows due to
          • • Of future cash inflows due to
            • • Of future cash inflows due to
            • o Market risk—market conditions that affect revenue
              • o Market risk—market conditions that affect revenue
                • o Market risk—market conditions that affect revenue
              • o Credit risk—customer’s availability to pay
                • o Credit risk—customer’s availability to pay
              • o Operational risk—production unpredictability
                • o Operational risk—production unpredictability
              • o Interest rate risk—changes in interest rate level
                • o Interest rate risk—changes in interest rate level
        • • Of future cash outflows due to
          • • Of future cash outflows due to
            • • Of future cash outflows due to
            • o Liquidity risk—the company’s ability to pay
              • o Liquidity risk—the company’s ability to pay
                • o Liquidity risk—the company’s ability to pay
              • o Interest rate risk—changes in interest rate level
                • o Interest rate risk—changes in interest rate level
      • Risk and Return Trade-off
      • People do not want to lose money! Therefore, a higher-risk investment must offer a potential return high enough to make it as attractive as the lower-risk alternative. At the same time, an investor must accept a higher level of risk to achieve higher gains (Chen, 2020).
      • • The potential return required depends on the amount of risk—the probability of being dissatisfied with an outcome.
        • • The potential return required depends on the amount of risk—the probability of being dissatisfied with an outcome.
          • • The potential return required depends on the amount of risk—the probability of being dissatisfied with an outcome.
            • • The potential return required depends on the amount of risk—the probability of being dissatisfied with an outcome.
            • • The higher the risk, the higher the required rate-of-return (Parrino et al., 2012)
              • • The higher the risk, the higher the required rate-of-return (Parrino et al., 2012)
                • • The higher the risk, the higher the required rate-of-return (Parrino et al., 2012)
              • • Expected vs realized return
                • • Expected vs realized return
              • o Expected return
                • o Expected return
                  • o Expected return
                  • ▪ estimated or predicted before the outcome is known
                    • ▪ estimated or predicted before the outcome is known
                      • ▪ estimated or predicted before the outcome is known
                    • ▪ Expected Return (ER) = (Probability 1 * Return 1) + (Probability 2 * Return 2) + …
                      • ▪ Expected Return (ER) = (Probability 1 * Return 1) + (Probability 2 * Return 2) + …
              • o Realized return
                • o Realized return
                  • o Realized return
                  • ▪ calculated after the outcome is known
                    • ▪ calculated after the outcome is known
                      • ▪ calculated after the outcome is known
                    • ▪ Realized Return = (Selling price − Purchase price) / Purchase Price
                      • ▪ Realized Return = (Selling price − Purchase price) / Purchase Price
      • How to Measure Return
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      • Example: Holding Period Return
      • Ella buys a stock for $26.00. After one year, the stock price is $29.00 and she receives a dividend of $0.80. What is her return for the period?
      • = + = + 1 0
        • = + = + 1 0
          • = + = + 1 0
          • =($29.00−$26.00)+$0.80$26.00
          • =$3.80$26.00=0.14615   14.62%
        • o There is 30% chance the total return on Dell stock will be -3.45%, a 30% chance it will be +5.17% , a 30% chance it will be +12.07% and a 10% chance that it will be +24.14%. Calculate the expected return.
          • o There is 30% chance the total return on Dell stock will be -3.45%, a 30% chance it will be +5.17% , a 30% chance it will be +12.07% and a 10% chance that it will be +24.14%. Calculate the expected return.
            • o There is 30% chance the total return on Dell stock will be -3.45%, a 30% chance it will be +5.17% , a 30% chance it will be +12.07% and a 10% chance that it will be +24.14%. Calculate the expected return.
      • Example: Expected Return
      • ( )=[.30×(−0.0345)]+(.30×0.0517)+(.30×0.1207)+(.10×0.2414)=−0.010305+0.01551+0.03621+0.02414
        • ( )=[.30×(−0.0345)]+(.30×0.0517)+(.30×0.1207)+(.10×0.2414)=−0.010305+0.01551+0.03621+0.02414
          • ( )=[.30×(−0.0345)]+(.30×0.0517)+(.30×0.1207)+(.10×0.2414)=−0.010305+0.01551+0.03621+0.02414
          • =0.0655 6.55%
        • • Four most commonly used terms in measuring risks
          • • Four most commonly used terms in measuring risks
            • • Four most commonly used terms in measuring risks
          • o Volatility
            • o Volatility
          • o Variance
            • o Variance
          • o Standard Deviation
            • o Standard Deviation
          • o Beta
            • o Beta
      • Four Measures of Risk
      • Measuring Risk: Calculate Variance
      • 1. Square the difference between each possible outcome and the mean
        • 1. Square the difference between each possible outcome and the mean
          • 1. Square the difference between each possible outcome and the mean
        • 2. Multiply each squared difference by its probability of occurring
          • 2. Multiply each squared difference by its probability of occurring
        • 3. Add
          • 3. Add
            • 3. Add
            • ( )= 2=∑{ ×[ − ( )]2} =1
              • ( )= 2=∑{ ×[ − ( )]2} =1
                • ( )= 2=∑{ ×[ − ( )]2} =1
              • o If all possible outcomes are equally likely, the formula becomes
                • o If all possible outcomes are equally likely, the formula becomes
                  • o If all possible outcomes are equally likely, the formula becomes
      • 2=∑[ − ( )]2 =1
        • 2=∑[ − ( )]2 =1
        • o Standard deviation is the square root of the variance
          • o Standard deviation is the square root of the variance
            • o Standard deviation is the square root of the variance
      • √ 2=
        • √ 2=
      • Source: Parrino et al. (2012)
        • Source: Parrino et al. (2012)
        • • Investing in two or more assets with returns that do not always move in the same direction at the same time can reduce the risk in an investment portfolio.
          • • Investing in two or more assets with returns that do not always move in the same direction at the same time can reduce the risk in an investment portfolio.
            • • Investing in two or more assets with returns that do not always move in the same direction at the same time can reduce the risk in an investment portfolio.
              • • Investing in two or more assets with returns that do not always move in the same direction at the same time can reduce the risk in an investment portfolio.
              • • Individual investors can diversify easily and cheaply but it is much more expensive for a company to diversify product lines.
                • • Individual investors can diversify easily and cheaply but it is much more expensive for a company to diversify product lines.
                  • • Individual investors can diversify easily and cheaply but it is much more expensive for a company to diversify product lines.
                • • Individual investors do not pay extra to companies that are diversified or less to companies that are not diversified.
                  • • Individual investors do not pay extra to companies that are diversified or less to companies that are not diversified.
                • • A company’s value neither increases nor decreases based on its degree of diversification. The value of a company is the sum of its parts, no more no less (Brealey & Myers, 2003).
                  • • A company’s value neither increases nor decreases based on its degree of diversification. The value of a company is the sum of its parts, no more no less (Brealey & Myers, 2003).
                • o Dividend payments do not affect a company’s taxes
                  • o Dividend payments do not affect a company’s taxes
                • o Have limited liability for stockholders; claims made against the corporation cannot include a stockholder’s personal assets
                  • o Have limited liability for stockholders; claims made against the corporation cannot include a stockholder’s personal assets
                • o Generally viewed as perpetuities; do not have maturity dates
                  • o Generally viewed as perpetuities; do not have maturity dates
                • o Dividends are promised rather than guaranteed to preferred stockholders (Parrino et al., 2012)
                  • o Dividends are promised rather than guaranteed to preferred stockholders (Parrino et al., 2012)
                • o Method 1: Capital Asset Pricing Model (CAPM)
                  • o Method 1: Capital Asset Pricing Model (CAPM)
                • o Method 2: Constant-Growth Dividend Model
                  • o Method 2: Constant-Growth Dividend Model
          • • Diversification can nearly eliminate unique risk to individual assets, but the risk common to all assets in the market remains.
            • • Diversification can nearly eliminate unique risk to individual assets, but the risk common to all assets in the market remains.
          • • Risk that cannot be diversified away is non-diversifiable, or systematic risk. This is the risk inherent in the market or economy (Brealey & Myers, 2003).
            • • Risk that cannot be diversified away is non-diversifiable, or systematic risk. This is the risk inherent in the market or economy (Brealey & Myers, 2003).
      • Back to Table of Contents
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      • Risk and Diversification
      • Diversification eliminates unique risk but not market risk.
      • Figure
      • Diversification: Individuals vs Companies
      • Equity Securities
      • Common stock and preferred stock—two types of ownership interest in a corporation; the most prevalent types of equity securities
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      • Estimating the Cost of Equity
      • Market information is used to estimate the cost of equity. There are two other methods for estimating the cost of common stock:
      • The most appropriate method depends on the availability and reliability of information (Parrino et al., 2012)
      • Method 1: Capital Asset Price Model (CAPM)
      • Expected Return of an asset can be broken down into risk- free rate and compensation to investors for taking more risk: ( )= + [ ( )− ]
      • • Expected Return = Risk Free Rate + Beta × Market Risk
        • • Expected Return = Risk Free Rate + Beta × Market Risk
          • • Expected Return = Risk Free Rate + Beta × Market Risk
        • • Beta measures the risks of a stock relative to its market
          • • Beta measures the risks of a stock relative to its market
            • • Beta measures the risks of a stock relative to its market
            • o Beta > 1: The stock is more volatile than the market
              • o Beta > 1: The stock is more volatile than the market
                • o Beta > 1: The stock is more volatile than the market
              • o Beta < 1: The stock is less volatile than the market
                • o Beta < 1: The stock is less volatile than the market
        • • Betas by sector and the companies included in each industry are available online (Damodaran, 2021)
          • • Betas by sector and the companies included in each industry are available online (Damodaran, 2021)
            • • Betas by sector and the companies included in each industry are available online (Damodaran, 2021)
            • o Identify a “comparable” company with publicly traded stock that is in the same business and that has a similar amount of debt
              • o Identify a “comparable” company with publicly traded stock that is in the same business and that has a similar amount of debt
                • o Identify a “comparable” company with publicly traded stock that is in the same business and that has a similar amount of debt
              • o use an average of the betas for the public firms in the same industry
                • o use an average of the betas for the public firms in the same industry
              • o Levered beta is the market beta, considering the capital structure of the firm as is.
                • o Levered beta is the market beta, considering the capital structure of the firm as is.
              • o Unlevered beta removes the influence of debt, enabling comparison between companies.
                • o Unlevered beta removes the influence of debt, enabling comparison between companies.
      • Estimating Beta
      • To estimate beta for a non-publicly traded firm
      • Levered vs unlevered beta
      • Market-Risk Premium (Rm − Rf)
      • • Market-risk premium cannot be observed: the rate of return investors expect is unknown
        • • Market-risk premium cannot be observed: the rate of return investors expect is unknown
          • • Market-risk premium cannot be observed: the rate of return investors expect is unknown
        • • Market-risk premium usually estimates the average risk premium investors have earned in the past as an indication of the risk premium they might require today
          • • Market-risk premium usually estimates the average risk premium investors have earned in the past as an indication of the risk premium they might require today
            • • Market-risk premium usually estimates the average risk premium investors have earned in the past as an indication of the risk premium they might require today
            • o From 1926 through 2015, the US stock market exceeded actual returns on long-term US government bonds by an average of 5.92% per year
              • o From 1926 through 2015, the US stock market exceeded actual returns on long-term US government bonds by an average of 5.92% per year
                • o From 1926 through 2015, the US stock market exceeded actual returns on long-term US government bonds by an average of 5.92% per year
              • o If a financial analyst believes that the market-risk premium in the past is a reasonable estimate of the risk premium today, then he or she might use a similar percentage as the market risk premium for the future (Parrino et al., 2012)
                • o If a financial analyst believes that the market-risk premium in the past is a reasonable estimate of the risk premium today, then he or she might use a similar percentage as the market risk premium for the future (Parrino et al., 2012)
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      • Assumptions of CAPM
      • The following assumptions underlie the capital asset pricing model (CAPM):
      • • Many investors who are all price takers, i.e., financial markets, are competitive.
        • • Many investors who are all price takers, i.e., financial markets, are competitive.
          • • Many investors who are all price takers, i.e., financial markets, are competitive.
        • • All investors plan to invest over the same time horizon.
          • • All investors plan to invest over the same time horizon.
        • • There are no distortionary taxes or transaction costs.
          • • There are no distortionary taxes or transaction costs.
        • • All investors can borrow and lend at same risk-free rate.
          • • All investors can borrow and lend at same risk-free rate.
        • • Investors care only about their expected return (like) and variance (dislike).
          • • Investors care only about their expected return (like) and variance (dislike).
        • • All investors have same information and beliefs about the distribution of returns.
          • • All investors have same information and beliefs about the distribution of returns.
        • • The market portfolio that determines beta consists of all publicly traded assets (Parrino et al., 2012).
          • • The market portfolio that determines beta consists of all publicly traded assets (Parrino et al., 2012).
      • Method 2: Constant-Growth Dividend Model
      • The constant-growth dividend model is useful for a company that pays dividends that will grow at a constant rate—such as an electric utility—rather than a fast-growing high-tech firm.
      • • Present Value of Perpetuity: 0=
        • • Present Value of Perpetuity: 0=
          • • Present Value of Perpetuity: 0=
        • • Value of stocks with fixed dividend level: 0=
          • • Value of stocks with fixed dividend level: 0=
        • • Value of stocks with dividend growing at the rate of g: 0= 1 −
          • • Value of stocks with dividend growing at the rate of g: 0= 1 −
        • • The equation above can be rearranged to solve for the required rate of return (R), which is also the cost of common stock (KCS)
          • • The equation above can be rearranged to solve for the required rate of return (R), which is also the cost of common stock (KCS)
      • = 1 0+
      • In practice, most people use the CAPM to estimate the cost of equity if the result is going to be used in the discount rate for evaluating a project (Parrino et al., 2012).
      • Bank Loans and Corporate Bonds
      • • Investors’ required rate of return is often not directly observable.
        • • Investors’ required rate of return is often not directly observable.
          • • Investors’ required rate of return is often not directly observable.
        • • The market value (price) of securities is often used to estimate the required rate of return.
          • • The market value (price) of securities is often used to estimate the required rate of return.
        • • To estimate the cost of debt, long-term debt (i.e., maturity longer than one year) is of particular interest; long-term debt can be considered permanent, since companies often issue new debt to pay off the old (Parrino et al., 2012).
          • • To estimate the cost of debt, long-term debt (i.e., maturity longer than one year) is of particular interest; long-term debt can be considered permanent, since companies often issue new debt to pay off the old (Parrino et al., 2012).
        • • The interest rate (or historical interest rate determined when the debt was issued) the firm is paying on its outstanding debt does not necessarily reflect its current cost of debt.
          • • The interest rate (or historical interest rate determined when the debt was issued) the firm is paying on its outstanding debt does not necessarily reflect its current cost of debt.
        • • The current cost of long-term debt is the appropriate cost of debt for weighted average cost of capital (WACC) calculations; WACC is the opportunity cost of capital for the firm’s investors as of today.
          • • The current cost of long-term debt is the appropriate cost of debt for weighted average cost of capital (WACC) calculations; WACC is the opportunity cost of capital for the firm’s investors as of today.
        • • Use yield to maturity (YTM) to determine the cost of debt and adjust for the tax deductibility of interest on debt (Parrino et al., 2012).
          • • Use yield to maturity (YTM) to determine the cost of debt and adjust for the tax deductibility of interest on debt (Parrino et al., 2012).
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      • Yield to Maturity (YTM)
      • Yield to maturity is the internal rate of return (IRR) of a bond investment if the investor holds the bond to maturity and all payments are made as scheduled.
      • • YTM accounts for the time value of money (TVM) and the bond purchase price.
        • • YTM accounts for the time value of money (TVM) and the bond purchase price.
          • • YTM accounts for the time value of money (TVM) and the bond purchase price.
        • • The current YTM of a bond reflects the required rate of return for the bondholder.
          • • The current YTM of a bond reflects the required rate of return for the bondholder.
        • • YTM is used to estimate the cost of debt to a company (Parrino et al., 2012).
          • • YTM is used to estimate the cost of debt to a company (Parrino et al., 2012).
      • Taxes and the Cost-of-Debt Equation
      • The after-tax cost of interest payments equals the pre-tax cost times 1, minus the tax rate (Parrino et al., 2012): − = − ×(1− )
      • Weighted Average Cost of Capital (WACC)
      • • After-tax weighted-average cost of capital equation:
        • • After-tax weighted-average cost of capital equation:
          • • After-tax weighted-average cost of capital equation:
      • = (1− )+ +
      • • Use market values, not book values, to calculate WACC.
        • • Use market values, not book values, to calculate WACC.
          • • Use market values, not book values, to calculate WACC.
        • • A l
          • • A l
            • • A l
            • ist of estimated WACC per industry in the US is at https://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/wacc.htm
            • 1. The level of systematic risk for the project is the same as that of the portfolio of projects that currently comprise the firm.
              • 1. The level of systematic risk for the project is the same as that of the portfolio of projects that currently comprise the firm.
                • 1. The level of systematic risk for the project is the same as that of the portfolio of projects that currently comprise the firm.
              • 2. The project uses the same financing mix—proportions of debt, preferred shares, and common shares—as the firm as a whole.
                • 2. The project uses the same financing mix—proportions of debt, preferred shares, and common shares—as the firm as a whole.
      • Limitations of WACC
      • WACC can be used as a discount rate for evaluating projects under the following conditions (Parrino et al., 2012):
      • Alternatives to WACC
      • • Using a public company in a similar, or pure-play comparable business (often difficult to find)
        • • Using a public company in a similar, or pure-play comparable business (often difficult to find)
          • • Using a public company in a similar, or pure-play comparable business (often difficult to find)
        • • Classifying projects into categories based on their systematic risks and specifying a discount rate for each
          • • Classifying projects into categories based on their systematic risks and specifying a discount rate for each
            • • Classifying projects into categories based on their systematic risks and specifying a discount rate for each
            • Source: Parrino et al. (2012)
              • Source: Parrino et al. (2012)
      • Category
        • Category
          • Category
            • Category
              • Category
            • Discount Rate
              • Discount Rate
        • Speculative ventures
          • Speculative ventures
            • Speculative ventures
              • Speculative ventures
            • 30%
              • 30%
          • New products
            • New products
              • New products
            • 20%
              • 20%
          • Expansion of existing business
            • Expansion of existing business
              • Expansion of existing business
            • 15%
              • 15%
          • Cost Improvement, known technology
            • Cost Improvement, known technology
              • Cost Improvement, known technology
            • 10%
              • 10%
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      • Problems/Exercises
      • What to Do
      • Complete all the practice exercises from the book and the custom exercise that follows to gain the knowledge and skills to complete the final Project 5 deliverable. The answers are provided, so you can check your work.
      • Self Study Problems
      • • Chapter 7 Self Study problems (all)
        • • Chapter 7 Self Study problems (all)
          • • Chapter 7 Self Study problems (all)
        • • Chapter 10 Self Study problems (all)
          • • Chapter 10 Self Study problems (all)
        • • Chapter 13 Self Study problems (all)
          • • Chapter 13 Self Study problems (all)
      • Advanced Problems and Questions 10.36
      • 10.36 Quasar Tech Co. is investing $6 million in new machinery to produce next-generation routers. Sales will amount to $1.75 million for the next three years and increase to $2.4 million for the three years after that. The project is expected to last six years. Operating costs, excluding depreciation, will be $898,620 annually. The machinery will be depreciated to a salvage value of $0 over 6 years using the straight-line method. The company’s tax rate is 30 percent, and the cost of capital is 16 percent.
      • A. What is the payback period?
        • A. What is the payback period?
          • A. What is the payback period?
        • B. What is the average accounting return (ARR)?
          • B. What is the average accounting return (ARR)?
        • C. Calculate the project NPV.
          • C. Calculate the project NPV.
        • D. What is the IRR for the project?
          • D. What is the IRR for the project?
      • Solution to Problem 10.36
      • A.
        • A.
          • A.
      • Table
        • THead
          • TR
            • TH
              • P
                • Span
              • Year
            • TH
              • P
                • Span
              • Net Income
            • TH
              • P
                • Span
              • Depreciation
            • Project 1 Cash Flows
              • Project 1 Cash Flows
            • Cumulative CF
              • Cumulative CF
        • 0
          • 0
            • 0
              • 0
            • $(6,000,000)
              • $(6,000,000)
            • $(6,000,000)
              • $(6,000,000)
          • 1
            • 1
              • 1
            • $(104,034)
              • $(104,034)
            • $1,000,000
              • $1,000,000
            • 895,966
              • 895,966
            • (5,104,034)
              • (5,104,034)
          • 2
            • 2
              • 2
            • $(104,034)
              • $(104,034)
            • $1,000,000
              • $1,000,000
            • 895,966
              • 895,966
            • (4,208,068)
              • (4,208,068)
          • 3
            • 3
              • 3
            • $(104,034)
              • $(104,034)
            • $1,000,000
              • $1,000,000
            • 895,966
              • 895,966
            • (3,312,102)
              • (3,312,102)
          • 4
            • 4
              • 4
            • 350,966
              • 350,966
            • $1,000,000
              • $1,000,000
            • 1,350,966
              • 1,350,966
            • (1,961,136)
              • (1,961,136)
          • 5
            • 5
              • 5
            • 350,966
              • 350,966
            • $1,000,000
              • $1,000,000
            • 1,350,966
              • 1,350,966
            • (610,170)
              • (610,170)
          • 6
            • 6
              • 6
            • 350,966
              • 350,966
            • $1,000,000
              • $1,000,000
            • 1,350,966
              • 1,350,966
            • 740,796
              • 740,796
      • PB = Years before cost recovery + (Remaining cost to recover/ Cash flow during the year) = 5 + ($610,170 / $1,350,966) = 5.45 years
      • Back to Table of Contents
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      • B.
            • Year 1
              • Year 1
            • Year 2
              • Year 2
            • Year 3
              • Year 3
            • Year 4
              • Year 4
            • Year 5
              • Year 5
            • Year 6
              • Year 6
        • Sales
          • Sales
            • Sales
              • Sales
            • $ 1,750,000
              • $ 1,750,000
            • $ 1,750,000
              • $ 1,750,000
            • $ 1,750,000
              • $ 1,750,000
            • $ 2,400,000
              • $ 2,400,000
            • $ 2,400,000
              • $ 2,400,000
            • $ 2,400,000
              • $ 2,400,000
          • Expenses
            • Expenses
              • Expenses
            • 898,620
              • 898,620
            • 898,620
              • 898,620
            • 898,620
              • 898,620
            • 898,620
              • 898,620
            • 898,620
              • 898,620
            • 898,620
              • 898,620
          • Depreciation
            • Depreciation
              • Depreciation
            • 1,000,000
              • 1,000,000
            • 1,000,000
              • 1,000,000
            • 1,000,000
              • 1,000,000
            • 1,000,000
              • 1,000,000
            • 1,000,000
              • 1,000,000
            • 1,000,000
              • 1,000,000
          • EBIT
            • EBIT
              • EBIT
            • $(1,48,620)
              • $(1,48,620)
            • $(1,48,620)
              • $(1,48,620)
            • $(1,48,620)
              • $(1,48,620)
            • $ 501,380
              • $ 501,380
            • $ 501,380
              • $ 501,380
            • $ 501,380
              • $ 501,380
          • Taxes (30%)
            • Taxes (30%)
              • Taxes (30%)
            • 44,586
              • 44,586
            • 44,586
              • 44,586
            • 44,586
              • 44,586
            • (150,414)
              • (150,414)
            • (150,414)
              • (150,414)
            • (150,414)
              • (150,414)
          • Net income
            • Net income
              • Net income
            • $ (104,034)
              • $ (104,034)
            • $ (104,034)
              • $ (104,034)
            • $ (104,034)
              • $ (104,034)
            • $ 350,966
              • $ 350,966
            • $ 350,966
              • $ 350,966
            • $ 350,966
              • $ 350,966
          • Beginning BV
            • Beginning BV
              • Beginning BV
            • 6,000,000
              • 6,000,000
            • 5,000,000
              • 5,000,000
            • 4,000,000
              • 4,000,000
            • 3,000,000
              • 3,000,000
            • 2,000,000
              • 2,000,000
            • 1,000,000
              • 1,000,000
          • Less: Depreciation
            • Less: Depreciation
              • Less: Depreciation
            • 1,000,000
              • 1,000,000
            • 1,000,000
              • 1,000,000
            • 1,000,000
              • 1,000,000
            • 1,000,000
              • 1,000,000
            • 1,000,000
              • 1,000,000
            • 1,000,000
              • 1,000,000
          • Ending BV
            • Ending BV
              • Ending BV
            • $ 5,000,000
              • $ 5,000,000
            • $ 4,000,000
              • $ 4,000,000
            • $ 3,000,000
              • $ 3,000,000
            • $ 2,000,000
              • $ 2,000,000
            • $ 1,000,000
              • $ 1,000,000
            • $ 0
              • $ 0
      • Average after-tax income = $123,466
      • Average book value of equipment = $3,000,000
      • Accounting rate of return = Average after-tax income = $123,466 = 4.1%
      • Artifact
      • Average book value $3,000,000
      • Artifact
      • C.
        • C.
          • C.
      • Cost of this project = $6,000,000
      • Required rate of return = k =16%
      • Length of project = n = 6 years
      • =∑ (1+ ) =0=−$6,000,000+$895,966×[1−1(1.16)30.16]+$1,350,966×[1−1(1.16)30.16]×1(1.16)3=−$6,000,000+$2,012,241+$1,943,833=−$2,043,927
        • =∑ (1+ ) =0=−$6,000,000+$895,966×[1−1(1.16)30.16]+$1,350,966×[1−1(1.16)30.16]×1(1.16)3=−$6,000,000+$2,012,241+$1,943,833=−$2,043,927
      • Back to Table of Contents
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          • Back to Table of Contents
      • D.
        • D.
          • D.
      • To compute the IRR, try rates lower than 16 percent. Try IRR = 3%.
      • =0=∑ (1+ ) =00=−$6,000,000+$895,966×[1−1(1.03)30.03]+$1,350,966×[1−1(1.03)30.03]×1(1.03)3=−$6,000,000+$2,534,340+$3,497,084=$31,424
        • =0=∑ (1+ ) =00=−$6,000,000+$895,966×[1−1(1.03)30.03]+$1,350,966×[1−1(1.03)30.03]×1(1.03)3=−$6,000,000+$2,534,340+$3,497,084=$31,424
      • Try IRR = 3.1%.
      • =0−∑ (1+ ) =00=−$6,000,000+$895,966×[1−1(1.031)30.031]+$1,350,966×[1−1(1.031)30.031]×1(1.031)3=−$6,000,000+$2,529,475+$3,480,225=$9,700
        • =0−∑ (1+ ) =00=−$6,000,000+$895,966×[1−1(1.031)30.031]+$1,350,966×[1−1(1.031)30.031]×1(1.031)3=−$6,000,000+$2,529,475+$3,480,225=$9,700
      • The IRR of the project is approximately 3.1%.
      • Advanced Problems and Questions 10.38
      • 10.38 Trident Corp. is evaluating two independent projects. The following table lists the costs and expected cash flows. The cost of capital is 10 percent.
      • Year
        • Year
          • Year
            • Year
              • Year
            • A
              • A
            • B
              • B
        • 0
          • 0
            • 0
              • 0
            • -$312,500
              • -$312,500
            • -$395,000
              • -$395,000
          • 1
            • 1
              • 1
            • 121,450
              • 121,450
            • 153,552
              • 153,552
          • 2
            • 2
              • 2
            • 121,450
              • 121,450
            • 158,711
              • 158,711
          • 3
            • 3
              • 3
            • 121,450
              • 121,450
            • 166,220
              • 166,220
          • 4
            • 4
              • 4
            • 121,450
              • 121,450
            • 132,000
              • 132,000
          • 5
            • 5
              • 5
            • 121,450
              • 121,450
            • 122,00
              • 122,00
      • A. Calculate the projects’ NPV.
        • A. Calculate the projects’ NPV.
          • A. Calculate the projects’ NPV.
        • B. Calculate the projects’ IRR.
          • B. Calculate the projects’ IRR.
        • C. Which project should be chosen based on NPV? Based on IRR? Is there a conflict?
          • C. Which project should be chosen based on NPV? Based on IRR? Is there a conflict?
        • D. If you are the decision maker for the firm, which project or projects will be accepted? Explain your reasoning.
          • D. If you are the decision maker for the firm, which project or projects will be accepted? Explain your reasoning.
      • Back to Table of Contents
        • Back to Table of Contents
          • Back to Table of Contents
      • Solution to Problem 10.38
      • A.
        • A.
          • A.
      • Project A:
      • Cost of this project = $312,500
      • Annual cash flows = $121,450
      • Required rate of return = k = 10%
      • Length of project = n = 5 years
      • =∑ (1+ ) =0=−312,500+$121,450×[1−1(1.10)50.10]
        • =∑ (1+ ) =0=−312,500+$121,450×[1−1(1.10)50.10]
          • =∑ (1+ ) =0=−312,500+$121,450×[1−1(1.10)50.10]
          • =−$312,500+460,391
          • =$147,891
      • Project B:
      • Cost of this project = $395,000
      • Required rate of return = k = 10%
      • Length of project = n = 5 years
      • =∑ (1+ ) =0=−$395,000+$153,552(1.10)1+$158,711(1.10)2+$166,220(1.10)3+$132,000(1.10)4+$122,000(1.10)5=−395,000+$139,593+$131,166+$124,884+90,158+75,752=$166,553
        • =∑ (1+ ) =0=−$395,000+$153,552(1.10)1+$158,711(1.10)2+$166,220(1.10)3+$132,000(1.10)4+$122,000(1.10)5=−395,000+$139,593+$131,166+$124,884+90,158+75,752=$166,553
      • B.
        • B.
          • B.
      • Project A:
      • Since NPV > 0, to compute the IRR, try rates higher than 10%.
      • Try IRR = 27%.
      • =0=∑ (1+ ) =00=−312,500+$121,450×[1−1(1.27)50.27]=−$312,500+313,666≠$1,166
        • =0=∑ (1+ ) =00=−312,500+$121,450×[1−1(1.27)50.27]=−$312,500+313,666≠$1,166
      • Try IRR = 27.2%
      • =0=∑ (1+ ) =00=−312,500+$121,450×[1−1(1.272)50.272]=−$312,500+312,418=−$82≅0
        • =0=∑ (1+ ) =00=−312,500+$121,450×[1−1(1.272)50.272]=−$312,500+312,418=−$82≅0
      • The IRR of Project A is approximately 27.2 percent. Using a financial calculator, we find that the IRR is 27.187 percent.
      • Back to Table of Contents
        • Back to Table of Contents
          • Back to Table of Contents
      • Project B:
      • Since NPV > 0, to compute the IRR, try rates higher than 10 percent. Try IRR = 26%
      • Figure
      • The IRR of Project A is approximately 27.2 percent. Using a financial calculator, the solution reached is 27.187 percent.
      • Try IRR = 26.1%
      • =0=∑ (1+ ) =00=−$395,000+$153,552(1.261)1+$158,711(1.261)2+$166,220(1.261)3+$132,000(1.261)4+$122,000(1.261)5=−$395,000+$121,770+$99,811+$82,897+$52,205+$38,263=−$54≅0
        • =0=∑ (1+ ) =00=−$395,000+$153,552(1.261)1+$158,711(1.261)2+$166,220(1.261)3+$132,000(1.261)4+$122,000(1.261)5=−$395,000+$121,770+$99,811+$82,897+$52,205+$38,263=−$54≅0
      • The IRR of Project B is approximately 26.1 percent.
      • C.
        • C.
          • C.
      • There is no conflict between the NPV and IRR decisions. Using NPV decision criteria, both projects have positive NPVs; they are independent projects; both should be accepted. Using IRR decision criteria, both projects have IRRs greater than the cost of capital; both will be accepted.
      • D.
        • D.
          • D.
      • Based on NPV, both projects will be accepted.
      • Advanced Problems and Questions 10.39
      • 10.39 Tyler, Inc., is considering switching to a new production technology. The cost of the required equipment will be $4 million. The discount rate is 12%. The cash flows the firm expects the new technology to generate are as follows.
      • Years
        • Years
          • Years
            • Years
              • Years
            • CF
              • CF
        • 1-2
          • 1-2
            • 1-2
              • 1-2
            • 0
              • 0
          • 3-5
            • 3-5
              • 3-5
            • $ 845,000
              • $ 845,000
          • 6-9
            • 6-9
              • 6-9
            • $ 1,845,000
              • $ 1,845,000
      • A. Compute the payback and discounted payback periods for the project.
        • A. Compute the payback and discounted payback periods for the project.
          • A. Compute the payback and discounted payback periods for the project.
        • B. What is the NPV for the project? Should the firm proceed with the project?
          • B. What is the NPV for the project? Should the firm proceed with the project?
        • C. What is the IRR? Based on IRR, what would the decision be?
          • C. What is the IRR? Based on IRR, what would the decision be?
      • Back to Table of Contents
        • Back to Table of Contents
          • Back to Table of Contents
      • Solution to Problem 10.39
      • A.
        • A.
          • A.
      • Table
        • THead
          • TR
            • TH
              • P
                • Span
              • Year
            • TH
              • P
                • Span
              • Cash Flows
            • TH
              • P
                • Span
              • PVCF
            • Cumulative CF
              • Cumulative CF
            • Cumulative PVCF
              • Cumulative PVCF
        • 0
          • 0
            • 0
              • 0
            • $(4,000,000)
              • $(4,000,000)
            • $(4,000,000)
              • $(4,000,000)
            • $(4,000,000)
              • $(4,000,000)
            • $(4,000,000)
              • $(4,000,000)
          • 1
            • 1
              • 1
            • (4,000,000)
              • (4,000,000)
            • (4,000,000)
              • (4,000,000)
          • 2
            • 2
              • 2
            • (4,000,000)
              • (4,000,000)
            • (4,000,000)
              • (4,000,000)
          • 3
            • 3
              • 3
            • 845,000
              • 845,000
            • 601,454
              • 601,454
            • (3,155,000)
              • (3,155,000)
            • (3,398,546)
              • (3,398,546)
          • 4
            • 4
              • 4
            • 845,000
              • 845,000
            • 537,013
              • 537,013
            • (2,310,000)
              • (2,310,000)
            • (2,861,533)
              • (2,861,533)
          • 5
            • 5
              • 5
            • 845,000
              • 845,000
            • 479,476
              • 479,476
            • (1,465,000)
              • (1,465,000)
            • (2,382,057)
              • (2,382,057)
          • 6
            • 6
              • 6
            • 1,450,000
              • 1,450,000
            • 734,615
              • 734,615
            • (15,000)
              • (15,000)
            • (1,647,442)
              • (1,647,442)
          • 7
            • 7
              • 7
            • 1,450,000
              • 1,450,000
            • 655,906
              • 655,906
            • 1,435,000
              • 1,435,000
            • (991,536)
              • (991,536)
          • 8
            • 8
              • 8
            • 1,450,000
              • 1,450,000
            • 585,631
              • 585,631
            • 2,885,000
              • 2,885,000
            • (405,905)
              • (405,905)
          • 9
            • 9
              • 9
            • 1,450,000
              • 1,450,000
            • 522,885
              • 522,885
            • 4,335,000
              • 4,335,000
            • 116,979
              • 116,979
          • =
          • +
          • =6+$15,000$1,450,000=6.01
          • =
          • +
          • =8+$405,905$522,885=8.8
      • Back to Table of Contents
        • Back to Table of Contents
          • Back to Table of Contents
      • B.
        • B.
          • B.
      • Cost of this project = $4,000,000
      • Required rate of return = k = 12%
      • Length of project = n = 9 years
      • =∑ (1+ ) =0=−$4,000,000+0+0+$845,000×[1−1(1.12)30.12]×1(1.12)2+$1,450,000×[1−1(1.12)40.12]×1(1.12)5=−$4,000,000+0+0+$1,617,943+$2,499,037=$116,980
        • =∑ (1+ ) =0=−$4,000,000+0+0+$845,000×[1−1(1.12)30.12]×1(1.12)2+$1,450,000×[1−1(1.12)40.12]×1(1.12)5=−$4,000,000+0+0+$1,617,943+$2,499,037=$116,980
      • Since NPV > 0, the project should be accepted.
      • C.
        • C.
          • C.
      • Given a positive NPV, to compute the IRR, one should try rates higher than 12%.
      • Try IRR = 12.5%.
      • =∑ (1+ ) =0=−$4,000,000+0+0+$845,000×[1−1(1.125)30.125]×1(1.125)2+$1,450,000×[1−1(1.125)40.125]×1(1.125)5=−$4,000,000+0+0+$1,589,915+$2,418,479=$8,394
        • =∑ (1+ ) =0=−$4,000,000+0+0+$845,000×[1−1(1.125)30.125]×1(1.125)2+$1,450,000×[1−1(1.125)40.125]×1(1.125)5=−$4,000,000+0+0+$1,589,915+$2,418,479=$8,394
      • Using a financial calculator and 12.5% returns an IRR of 12.539%. The IRR exceeds the cost of capital (12%); the project should be accepted.
      • Back to Table of Contents
        • Back to Table of Contents
          • Back to Table of Contents
      • References
      • Brealey, R. A. & Myers, S. C. (2003). Principles of Corporate Finance 7th ed. McGraw-Hill.
      • Chen, J. (2020, February 3). Risk-return tradeoff. Investopedia. Retrieved August 9, 2021, from https://www.investopedia.com/terms/r/riskreturntradeoff.asp
      • Clendenen, D. (2020, March 19). 23 of the best fundraising websites for small business. LendGenius. https://www.lendgenius.com/blog/fundraising-websites/
      • Damodaran, A. (2021, January). Total betas by sector (for computing private company cost of equity)—US. Damodaran Online. Retrieved August 9, 2021, from https://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/totalbeta.html
      • Microsoft. (n.d.). Excel functions (by category). Retrieved July 22, 2021, from https://support.microsoft.com/en-us/office/excel-functions-by-category-5f91f4e9- 7b42-46d2-9bd1-63f26a86c0eb
      • Parrino, R., Kidwell, D. S., & Bates, T. W. (2012). Fundamentals of corporate finance. Wiley.
      • Zwilling, M. (2010, February 12). Top 10 sources of funding for start-ups. Forbes. Retrieved August 9, 2021, from https://www.forbes.com/2010/02/12/funding-for-startups-entrepreneurs-finance-zwilling.html?sh=46bb828b160f
      • Now that you have read this Review and Practice Guide and completed the exercises, you are ready to participate in the assignment in Step 3.
        • Now that you have read this Review and Practice Guide and completed the exercises, you are ready to participate in the assignment in Step 3.

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