# Chapter 9 Fundamentals of Capital Budgeting

Problem 5

Kokomochi is considering the launch of an advertising campaign for its latest dessert product, the Mini Mochi Munch. Kokomochi plans to spend $5 million on TV, radio, and print advertising this year for the campaign. The ads are expected to boost sales of the Mini Mochi Munch by $9 million this year and by $7 million next year. In addition, the company expects that new consumers who try the Mini Mochi Munch will be more likely to try Kokomochi’s other products. As a result, sales of other products are expected to rise by $2 million each year.

Kokomochi’s gross profit margin for the Mini Mochi Munch is 35%, and its gross profit margin averages 25% for all other products. The company’s marginal corporate tax rate is 35% both this year and next year. What are the incremental earnings associated with the advertising campaign?

Problem 11

Castle View Games would like to invest in a division to develop software for video games. To evaluate this decision, the firm first attempts to project the working capital needs for this operation. Its chief financial officer has developed the following estimates (in millions of dollars):

Assuming that Castle View currently does not have any working capital invested in this division, calculate the cash flows associated with changes in working capital for the first five years of this investment.

Problem 17

Beryl’s Iced Tea currently rents a bottling machine for $50,000 per year, including all maintenance expenses. It is considering purchasing a machine instead and is comparing two options:

a. Purchase the machine it is currently renting for $150,000. This machine will require $20,000 per year in ongoing maintenance expenses.

b. Purchase a new, more advanced machine for $250,000. This machine will require $15,000 per year in ongoing maintenance expenses and will lower bottling costs by $10,000 per year. Also, $35,000 will be spent upfront in training the new operators of the machine.

Suppose the appropriate discount rate is 8% per year and the machine is purchased today. Maintenance and bottling costs are paid at the end of each year, as is the rental of the machine. Assume also that the machines will be depreciated via the straight-line method over seven years and that they have a 10-year life with a negligible salvage value. The marginal corporate tax rate is 35%. Should Beryl’s Iced Tea continue to rent, purchase its current machine, or purchase the advanced machine?

We can use Eq. 7.5 to evaluate the free cash flows associated with each alternative. Note that we only need to include the components of free cash flows that vary across each alternative. For example, since NWC is the same for each alternative, we can ignore it.

The spreadsheet below computes the relevant FCF from each alternative. Note that each alternative has a negative NPV—this represents the PV of the costs of each alternative. We should choose the one with the highest NPV (lowest cost), which in this case is purchasing the existing machine.

a. See spreadsheet

b. See spreadsheet

Problem 22

Home Builder Supply, a retailer in the home improvement industry, currently operates seven retail outlets in Georgia and South Carolina. Management is contemplating building an eighth retail store across town from its most successful retail outlet. The company already owns the land for this store, which currently has an abandoned warehouse located on it. Last month, the marketing department spent $10,000 on market research to determine the extent of customer demand for the new store. Now Home Builder Supply must decide whether to build and open the new store.

Which of the following should be included as part of the incremental earnings for the proposed new retail store?

a. The original purchase price of the land where the store will be located.

b. The cost of demolishing the abandoned warehouse and clearing the lot.

c. The loss of sales in the existing retail outlet, if customers who previously drove across town to shop at the existing outlet become customers of the new store instead.

d. The $10,000 in market research spent to evaluate customer demand.

e. Construction costs for the new store.

f. The value of the land if sold.

g. Interest expense on the debt borrowed to pay the construction costs.

a. No, this is a sunk cost and will not be included directly. (But see (f) below.)

b. Yes, this is a cost of opening the new store.

c. Yes, this loss of sales at the existing store should be deducted from the sales at the new store to determine the incremental increase in sales that opening the new store will generate for HBS.

d. No, this is a sunk cost.

e. This is a capital expenditure associated with opening the new store. These costs will, therefore, increase HBS’s depreciation expenses.

f. Yes, this is an opportunity cost of opening the new store. (By opening the new store, HBS forgoes the after-tax proceeds it could have earned by selling the property. This loss is equal to the sale price less the taxes owed on the capital gain from the sale, which is the difference between the sale price and the book value of the property. The book value equals the initial cost of the property less accumulated depreciation.)

g. While these financing costs will affect HBS’s actual earnings, for capital budgeting purposes we calculate the incremental earnings without including financing costs to determine the project’s unlevered net income.

Problem 25

You are a manager at Percolated Fiber, which is considering expanding its operations in synthetic fiber manufacturing. Your boss comes into your office, drops a consultant’s report on your desk, and complains, “We owe these consultants $1 million for this report, and I am not sure their analysis makes sense. Before we spend the $25 million on new equipment needed for this project, look it over and give me your opinion.” You open the report and find the following estimates (in thousands of dollars):

All of the estimates in the report seem correct. You note that the consultants used straight-line depreciation for the new equipment that will be purchased today (year 0), which is what the accounting department recommended. They also calculated the depreciation assuming no salvage value for the equipment, which is the company’s assumption in this case. The report concludes that because the project will increase earnings by $4.875 million per year for 10 years, the project is worth $48.75 million. You think back to your glory days in finance class and realize there is more work to be done!

First, you note that the consultants have not factored in the fact that the project will require $10 million in working capital upfront (year 0), which will be fully recovered in year 10. Next, you see they have attributed $2 million of selling, general and administrative expenses to the project, but you know that $1 million of this amount is overhead that will be incurred even if the project is not accepted. Finally, you know that accounting earnings are not the right thing to focus on!

a. Given the available information, what are the free cash flows in years 0 through 10 that should be used to evaluate the proposed project?

b. If the cost of capital for this project is 14%, what is your estimate of the value of the new project?

a. Free Cash Flows are:

0 1 2 … 9 10

= Net income 4,875 4,875 4,875 4,875

+ Overhead (after tax at 35%) 650 650 650 650

+ Depreciation 2,500 2,500 2,500 2,500

– Capex 25,000

– Inc. in NWC 10,000 –10000

FCF –35,000 8,025 8,025 … 8,025 18,025

b.

Problem 28

Why is it that real options must have positive value?

Real options must have positive value because they are only exercised when doing so would increase the value of the investment. If exercising the real option would reduce value, managers can allow the option to go unexercised. Thus, having the option but not the obligation to act is valuable.

Chapter 13 The Cost of Capital

Problem 5

Avicorp has a $10 million debt issue outstanding, with a 6% coupon rate. The debt has semi-annual coupons, the next coupon is due in six months, and the debt matures in five years. It is currently priced at 95% of par value.

a. What is Avicorp’s pre-tax cost of debt?

b. If Avicorp faces a 40% tax rate, what is its after-tax cost of debt?

a. The pre-tax cost of debt is the YTM on the outstanding debt issue. We solve for the 6-month YTM on the bond, and then compute the EAR.

The pre-tax cost of debt is 3.6044% every 6 months, or 7.3387% per year.

b. After-tax cost of debt ?

Avicorp’s before-tax cost of debt is 7.3387% per year, while it after-tax cost of debt (reflecting the tax deductibility of interest) is 4.4032%.

Problem 12

Mackenzie Company has a price of $36 and will issue a dividend of $2 next year. It has a beta of 1.2, the risk-free rate is 5.5%, and it estimates the market risk premium to be 5%.

a. Estimate the equity cost of capital for Mackenzie.

b. Under the CGDM, at what rate do you need to expect Mackenzie’s dividends to grow to get the same equity cost of capital as in part (a)?

a. Using the Capital Asset Pricing Model,

b.

Mackenzie’s cost of equity using the CAPM is 11.5%, which would require a dividend growth rate of 5.944% to result in the same cost of equity using CGDM.

Problem 15

Growth Company’s current share price is $20 and it is expected to pay a $1 dividend per share next year. After that, the firm’s dividends are expected to grow at a rate of 4% per year.

a. What is an estimate of Growth Company’s cost of equity?

b. Growth Company also has preferred stock outstanding that pays a $2 per share fixed dividend. If this stock is currently priced at $28, what is Growth Company’s cost of preferred stock?

c. Growth Company has existing debt issued three years ago with a coupon rate of 6%. The firm just issued new debt at par with a coupon rate of 6.5%. What is Growth Company’s pre-tax cost of debt?

d. Growth Company has 5 million common shares outstanding and 1 million preferred shares outstanding, and its equity has a total book value of $50 million. Its liabilities have a market value of $20 million. If Growth Company’s common and preferred shares are priced as in parts (a) and (b), what is the market value of Growth Company’s assets?

e. Growth Company faces a 35% tax rate. Given the information in parts (a) – (d), and your answers to those problems, what is Growth Company’s WACC?

a.

b.

c. The pre-tax cost of debt is the firm’s YTM on current debt. Since the firm recently issued debt at par, then the coupon rate of that debt must be equal to the YTM of the debt. Thus, the pre-tax cost of debt is 6.5%.

d. Market value of debt ? $20 million

Market value of preferred stock ? $28 per share ? 1 million preferred shares ? $28 million

Market value of equity ? $20 per share ? 5 million shares outstanding ? $100 million

Market value of assets ? $20 ? 28 ? 100 ? $148 million

e. WACC ?

The calculation leads to a WACC of 8.003%.

Problem 17

RiverRocks, Inc., is considering a project with the following projected free cash flows:

0 1 2 3 4

-50 10 20 20 15

The firm believes that, given the risk of this project, the WACC method is the appropriate approach to valuing the project. RiverRocks’ WACC is 12%. Should it take on this project? Why or why not?

Timeline:

0 1 2 3 4

–50 10 20 20 15

Using the WACC as the discount rate and solving for NPV:

NPV is negative, RiverRocks should not take on this project.

Problem 18

RiverRocks (whose WACC is 12%) is considering an acquisition of Raft Adventured (whose WACC is 15%). What is the appropriate discount rate for RiverRocks to use to evaluate the acquisition? Why?

If RiverRocks is going to acquire Raft Adventures, then it should use a discount rate that is appropriate for the risk of Raft Adventures’ cash flows. That should be the WACC of Raft Adventures, which is 15%. So RiverRocks should use 15% as the discount rate for its evaluation of the acquisition.

Problem 19

RiverRocks’ purchase of Raft Adventured (from Problem 18) will cost $100 million, but will generate cash flows that start at $15 million in one year and then grow at 4% per year forever. What is the NPV of the acquisition?

The NPV of this acquisition is

The acquisition has a positive NPV of $36.36 million indicating that will increase the value of RiverRocks.

Chapter 9 Fundamentals of Capital Budgeting

Problem 5

Kokomochi is considering the launch of an advertising campaign for its latest dessert product, the Mini Mochi Munch. Kokomochi plans to spend $5 million on TV, radio, and print advertising this year for the campaign. The ads are expected to boost sales of the Mini Mochi Munch by $9 million this year and by $7 million next year. In addition, the company expects that new consumers who try the Mini Mochi Munch will be more likely to try Kokomochi’s other products. As a result, sales of other products are expected to rise by $2 million each year.

Kokomochi’s gross profit margin for the Mini Mochi Munch is 35%, and its gross profit margin averages 25% for all other products. The company’s marginal corporate tax rate is 35% both this year and next year. What are the incremental earnings associated with the advertising campaign?

Problem 11

Castle View Games would like to invest in a division to develop software for video games. To evaluate this decision, the firm first attempts to project the working capital needs for this operation. Its chief financial officer has developed the following estimates (in millions of dollars):

Assuming that Castle View currently does not have any working capital invested in this division, calculate the cash flows associated with changes in working capital for the first five years of this investment.

Problem 17

Beryl’s Iced Tea currently rents a bottling machine for $50,000 per year, including all maintenance expenses. It is considering purchasing a machine instead and is comparing two options:

a. Purchase the machine it is currently renting for $150,000. This machine will require $20,000 per year in ongoing maintenance expenses.

b. Purchase a new, more advanced machine for $250,000. This machine will require $15,000 per year in ongoing maintenance expenses and will lower bottling costs by $10,000 per year. Also, $35,000 will be spent upfront in training the new operators of the machine.

Suppose the appropriate discount rate is 8% per year and the machine is purchased today. Maintenance and bottling costs are paid at the end of each year, as is the rental of the machine. Assume also that the machines will be depreciated via the straight-line method over seven years and that they have a 10-year life with a negligible salvage value. The marginal corporate tax rate is 35%. Should Beryl’s Iced Tea continue to rent, purchase its current machine, or purchase the advanced machine?

We can use Eq. 7.5 to evaluate the free cash flows associated with each alternative. Note that we only need to include the components of free cash flows that vary across each alternative. For example, since NWC is the same for each alternative, we can ignore it.

The spreadsheet below computes the relevant FCF from each alternative. Note that each alternative has a negative NPV—this represents the PV of the costs of each alternative. We should choose the one with the highest NPV (lowest cost), which in this case is purchasing the existing machine.

a. See spreadsheet

b. See spreadsheet

Problem 22

Home Builder Supply, a retailer in the home improvement industry, currently operates seven retail outlets in Georgia and South Carolina. Management is contemplating building an eighth retail store across town from its most successful retail outlet. The company already owns the land for this store, which currently has an abandoned warehouse located on it. Last month, the marketing department spent $10,000 on market research to determine the extent of customer demand for the new store. Now Home Builder Supply must decide whether to build and open the new store.

Which of the following should be included as part of the incremental earnings for the proposed new retail store?

a. The original purchase price of the land where the store will be located.

b. The cost of demolishing the abandoned warehouse and clearing the lot.

c. The loss of sales in the existing retail outlet, if customers who previously drove across town to shop at the existing outlet become customers of the new store instead.

d. The $10,000 in market research spent to evaluate customer demand.

e. Construction costs for the new store.

f. The value of the land if sold.

g. Interest expense on the debt borrowed to pay the construction costs.

a. No, this is a sunk cost and will not be included directly. (But see (f) below.)

b. Yes, this is a cost of opening the new store.

c. Yes, this loss of sales at the existing store should be deducted from the sales at the new store to determine the incremental increase in sales that opening the new store will generate for HBS.

d. No, this is a sunk cost.

e. This is a capital expenditure associated with opening the new store. These costs will, therefore, increase HBS’s depreciation expenses.

f. Yes, this is an opportunity cost of opening the new store. (By opening the new store, HBS forgoes the after-tax proceeds it could have earned by selling the property. This loss is equal to the sale price less the taxes owed on the capital gain from the sale, which is the difference between the sale price and the book value of the property. The book value equals the initial cost of the property less accumulated depreciation.)

g. While these financing costs will affect HBS’s actual earnings, for capital budgeting purposes we calculate the incremental earnings without including financing costs to determine the project’s unlevered net income.

Problem 25

You are a manager at Percolated Fiber, which is considering expanding its operations in synthetic fiber manufacturing. Your boss comes into your office, drops a consultant’s report on your desk, and complains, “We owe these consultants $1 million for this report, and I am not sure their analysis makes sense. Before we spend the $25 million on new equipment needed for this project, look it over and give me your opinion.” You open the report and find the following estimates (in thousands of dollars):

All of the estimates in the report seem correct. You note that the consultants used straight-line depreciation for the new equipment that will be purchased today (year 0), which is what the accounting department recommended. They also calculated the depreciation assuming no salvage value for the equipment, which is the company’s assumption in this case. The report concludes that because the project will increase earnings by $4.875 million per year for 10 years, the project is worth $48.75 million. You think back to your glory days in finance class and realize there is more work to be done!

First, you note that the consultants have not factored in the fact that the project will require $10 million in working capital upfront (year 0), which will be fully recovered in year 10. Next, you see they have attributed $2 million of selling, general and administrative expenses to the project, but you know that $1 million of this amount is overhead that will be incurred even if the project is not accepted. Finally, you know that accounting earnings are not the right thing to focus on!

a. Given the available information, what are the free cash flows in years 0 through 10 that should be used to evaluate the proposed project?

b. If the cost of capital for this project is 14%, what is your estimate of the value of the new project?

a. Free Cash Flows are:

0 1 2 … 9 10

= Net income 4,875 4,875 4,875 4,875

+ Overhead (after tax at 35%) 650 650 650 650

+ Depreciation 2,500 2,500 2,500 2,500

– Capex 25,000

– Inc. in NWC 10,000 –10000

FCF –35,000 8,025 8,025 … 8,025 18,025

b.

Problem 28

Why is it that real options must have positive value?

Real options must have positive value because they are only exercised when doing so would increase the value of the investment. If exercising the real option would reduce value, managers can allow the option to go unexercised. Thus, having the option but not the obligation to act is valuable.

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