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Capital Budgeting-30 questions

Please assist me with the following problems relating to discounted payback, NPV, investments and more.

1. Haig Aircraft is considering a project which has an up-front cost paid today at t = 0. The project will generate positive cash flows of $60,000 a year at the end of each of the next five years. The project's NPV is $75,000 and the company's WACC is 10 percent. What is the project's simple, regular payback?

2. Lloyd Enterprises has a project which has the following cash flows:

Year Cash Flow
0 -$200,000
1 50,000
2 100,000
3 150,000
4 40,000
5 25,000

The cost of capital is 10 percent. What is the project's discounted payback?

3. Davis Corporation is faced with two independent investment opportunities. The corporation has an investment policy which requires acceptable projects to recover all costs within 3 years. The corporation uses the discounted payback method to assess potential projects and utilizes a discount rate of 10 percent. The cash flows for the two projects are:

Project A Project B
Year Cash Flow Cash Flow
0 -$100,000 -$80,000
1 40,000 50,000
2 40,000 20,000
3 40,000 30,000
4 30,000 0

Which investment project(s) does the company invest in?

4. You are considering the purchase of an investment that would pay you $5,000 per year for Years 1-5, $3,000 per year for Years 6-8, and $2,000 per year for Years 9 and 10. If you require a 14 percent rate of return, and the cash flows occur at the end of each year, then how much should you be willing to pay for this investment?

5. Shannon Industries is considering a project which has the following cash flows:

Year Cash Flow
0 ?
1 $2,000
2 3,000
3 3,000
4 1,500

The project has a payback of 2.5 years. The firm's cost of capital is 12 percent. What is the project's net present value NPV?

6. Below are the returns of Nulook Cosmetics and "the market" over a three-year period:

Year Nulook Market
1 9% 6%
2 15 10
3 36 24

Nulook finances internally using only retained earnings, and it uses the Capital Asset Pricing Model with a historical beta to determine its cost of equity. Currently, the risk-free rate is 7 percent, and the estimated market risk premium is 6 percent. Nulook is evaluating a project which has a cost today of $2,028 and will provide estimated cash inflows of $1,000 at the end of the next 3 years. What is this project's MIRR?

7. Two projects being considered by a firm are mutually exclusive and have the following projected cash flows:

Project A Project B
Year Cash Flow Cash Flow
0 ($100,000) ($100,000)
1 39,500 0
2 39,500 0
3 39,500 133,000

Based only on the information given, which of the two projects would be preferred, and why?

8. Genuine Products Inc. requires a new machine. Two companies have submitted bids, and you have been assigned the task of choosing one of the machines. Cash flow analysis indicates the following:

Machine A Machine B
Year Cash Flow Cash Flow
0 -$2,000 -$2,000
1 0 832
2 0 832
3 0 832
4 3,877 832

What is the internal rate of return for each machine?

9. A company is analyzing two mutually exclusive projects, S and L, whose cash flows are shown below:

Years 0 1 2 3 4

S -1,100 900 350 50 10
L -1,100 0 300 500 850

The company's cost of capital is 12 percent, and it can get an unlimited amount of capital at that cost. What is the regular IRR (not MIRR) of the better project? (Hint: Note that the better project may or may not be the one with the higher IRR.)

10. Your company is planning to open a new gold mine which will cost $3 million to build, with the expenditure occurring at the end of the year three years from today. The mine will bring year-end after-tax cash inflows of $2 million at the end of the two succeeding years, and then it will cost $0.5 million to close down the mine at the end of the third year of operation. What is this project's IRR?

11. Belanger Construction is considering the following project. The project has an up-front cost and will also generate the following subsequent cash flows:

t = 1 $400
t = 2 500
t = 3 200

The project's payback is 1.5 years, and it has a cost of capital of 10 percent. What is the project's modified internal rate of return (MIRR)?

12. The following cash flows are estimated for two mutually exclusive projects:

Project A Project B
Year Cash Flow Cash Flow
0 -$100,000 -$110,000
1 60,000 20,000
2 40,000 40,000
3 20,000 40,000
4 10,000 50,000

When is Project B more lucrative than Project A? (That is, over what range of costs of capital (r) does Project B have a higher NPV than Project A?)

13. Martin Fillmore is a big football star who has been offered contracts by two different teams. The payments (in millions of dollars) he receives under the two contracts are listed below:

Team A Team B
Year Cash Flow Cash Flow
0 $8.0 $2.5
1 4.0 4.0
2 4.0 4.0
3 4.0 8.0
4 4.0 8.0

Fillmore is committed to accepting the contract which provides him with the highest net present value (NPV). At what discount rate would he be indifferent between the two contracts?

14. Your company is considering two mutually exclusive projects, X and Y, whose costs and cash flows are shown below:

Project X Project Y
Year Cash Flow Cash Flow
0 -$2,000 -$2,000
1 200 2,000
2 600 200
3 800 100
4 1,400 75

The projects are equally risky, and the firm's cost of capital is 12 percent. You must make a recommendation, and you must base it on the modified IRR (MIRR). What is the MIRR of the better project?

15. A company's balance sheets show a total of $30 million long-term debt with a coupon rate of 9 percent. The yield to maturity on this debt is 11.11 percent, and the debt has a total current market value of $25 million. The balance sheets also show that that the company has 10 million shares of stock; the total of common stock and retained earnings is $30 million. The current stock price is $7.5 per share. The current return required by stockholders, rS, is 12 percent. The company has a target capital structure of 40 percent debt and 60 percent equity. The tax rate is 40%. What weighted average cost of capital should you use to evaluate potential projects?

16. A company has determined that its optimal capital structure consists of 40 percent debt and 60 percent equity. Given the following information, calculate the firm's weighted average cost of capital.

rd = 6%
Tax rate = 40%
P0 = $25
Growth = 0%
D0 = $2.00

(The following information applies to the next six problems.)

Rollins Corporation is estimating its WACC. Its target capital structure is 20 percent debt, 20 percent preferred stock, and 60 percent common equity. Its bonds have a 12 percent coupon, paid semiannually, a current maturity of 20 years, and sell for $1,000. The firm could sell, at par, $100 preferred stock which pays a 12 percent annual dividend, but flotation costs of 5 percent would be incurred. Rollins' beta is 1.2, the risk-free rate is 10 percent, and the market risk premium is 5 percent. Rollins is a constant-growth firm which just paid a dividend of $2.00, sells for $27.00 per share, and has a growth rate of 8 percent. The firm's policy is to use a risk premium of 4 percentage points when using the bond-yield-plus-risk-premium method to find rs. The firm's marginal tax rate is 40 percent.

17. What is Rollins' component cost of debt?

18. What is Rollins' cost of preferred stock?

19. What is Rollins' cost of common stock (rs) using the CAPM approach?

20. What is the firm's cost of common stock (rs) using the DCF approach?

21. What is Rollins' cost of common stock using the bond-yield-plus-risk-premium approach?

22. What is Rollins' WACC?

23. Allison Engines Corporation has established a target capital structure of 40 percent debt and 60 percent common equity. The firm expects to earn $600 in after-tax income during the coming year, and it will retain 40 percent of those earnings. The current market price of the firm's stock is P0 = $28; its last dividend was D0 = $2.20, and its expected growth rate is 6 percent. Allison can issue new common stock at a 15 percent flotation cost. What will Allison's marginal cost of equity capital (not the WACC) be if it must fund a capital budget requiring $600 in total new capital?

24. Hamilton Company's 8 percent coupon rate, quarterly payment, $1,000 par value bond, which matures in 20 years, currently sells at a price of $686.86. The company's tax rate is 40 percent. Based on the nominal interest rate, not the EAR, what is the firm's component cost of debt for purposes of calculating the WACC?

25. The Target Copy Company is contemplating the replacement of its old printing machine with a new model costing $60,000. The old machine, which originally cost $40,000, has 6 years of expected life remaining and a current book value of $30,000 versus a current market value of $24,000. Target's corporate tax rate is 40 percent. If Target sells the old machine at market value, what is the initial after-tax outlay for the new printing machine?

26. Real Time Systems Inc. is considering the development of one of two mutually exclusive new computer models. Each will require a net investment of $5,000. The cash flow figures for each project are shown below:

Period Project A Project B
1 $2,000 $3,000
2 2,500 2,600
3 2,250 2,900

Model B, which will use a new type of laser disk drive, is considered a high-risk project, while Model A is of average risk. Real Time adds 2 percentage points to arrive at a risk-adjusted cost of capital when eval┬Čuating a high-risk project. The cost of capital used for average-risk projects is 12 percent. Find the NPV of Model A and Model B.

27. Klott Company encounters significant uncertainty with its sales volume and price in its primary product. The firm uses scenario analysis in order to determine an expected NPV, which it then uses in its budget. The base case, best case, and worse case scenarios and probabilities are provided in the table below. What is Klott's expected NPV, standard deviation of NPV, and coefficient of variation of NPV?

Probability Unit Sales Sales NPV
of Outcome Volume Price (In Thousands)
Worst case 0.30 6,000 $3,600 -$6,000
Base case 0.50 10,000 4,200 +13,000
Best case 0.20 13,000 4,400 +28,000

28. Pierce Products is deciding whether it makes sense to purchase a new piece of equipment. The equipment costs $100,000 (payable at t = 0). The equipment will provide before-tax cash inflows of $45,000 a year at the end of each of the next four years (t = 1, 2, 3, 4). The equipment can be depreciated according to the following schedule:
t = 1: 0.33
t = 2: 0.45
t = 3: 0.15
t = 4: 0.07

At the end of four years the company expects to be able to sell the equipment for a salvage value of $10,000 (after-tax). The company is in the 40 percent tax bracket. The company has an after-tax cost of capital of 11 percent. Since there is more uncertainty about the salvage value, the company has chosen to discount the salvage value at 12 percent. What is the net present value of purchasing the equipment?

29. Your company is considering a machine that will cost $1,000 at Time 0 and which can be sold after 3 years for $100. To operate the machine, $200 must be invested at Time 0 in inventories; these funds will be recovered when the machine is retired at the end of Year 3. The machine will produce sales revenues of $900/year for 3 years; variable operating costs (excluding depreciation) will be 50 percent of sales. Operating cash inflows will begin 1 year from today (at Time 1). The machine will have depreciation expenses of $500, $300, and $200 in Years 1, 2, and 3, respectively. The company has a 40 percent tax rate, enough taxable income from other assets to enable it to get a tax refund from this project if the project's income is negative, and a 10 percent cost of capital. Inflation is zero. What is the project's NPV?

30. The Unlimited, a national retailing chain, is considering an investment in one of two mutually exclusive projects. The discount rate used for Project A is 12 percent. Further, Project A costs $15,000, and it would be depreciated using MACRS. It is expected to have an after-tax salvage value of $5,000 at the end of 6 years and to produce after-tax cash flows (including depreciation) of $4,000 for each of the 6 years. Project B costs $14,815 and would also be depreciated using MACRS. B is expected to have a zero salvage value at the end of its 6-year life and to produce after-tax cash flows (including depreciation) of $5,100 each year for 6 years. The Unlimited's marginal tax rate is 40 percent. What risk-adjusted discount rate will equate the NPV of Project B to that of Project A?

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1 Haig Aircraft is considering a project which has an up-front cost paid today at t = 0. The project will generate positive cash flows of $60,000 a year at the end of each of the next five years. The project's NPV is $75,000 and the company's WACC is 10 percent. What is the project's simple, regular payback?

PVIFA= Present Value Interest Factor for an Annuity

n= 5
r= 10.00%

PVIFA (5 periods, 10.% rate=) 3.790787

Annual cash flow= $60,000
PV of cash flow= $227,447 =60000*3.790787

Project's NPV= $75,000

Therefore Investment in year 0= $152,447 =227447-75000

Year Cash flow Cumulative cash flow

0 (152,447) (152,447)
1 60,000 (92,447)
2 60,000 (32,447)
3 60,000 27,553 Payback period= 3 years
4 60,000 87,553 (In this year the cash flow becomes positive)
5 60,000 147,553
147553

Payback period of Project = 3 years

2 Lloyd Enterprises has a project which has the following cash flows:

Year Cash Flow
0 ($200,000)
1 50,000
2 100,000
3 150,000
4 40,000
5 25,000

The cost of capital is 10 percent. What is the project's discounted payback?
Cost of capital= Discount rate= 10%

Year Cash flow Present value factor Discounted cash flow Cumulative cash flow

0 (200,000) 1 (200,000) (200,000)
1 50,000 0.909091 45,455 (154,545)
2 100,000 0.826446 82,645 (71,900)
3 150,000 0.751315 112,697 40,797 Payback period= 3 years
4 40,000 0.683013 27,321 68,118 (In this year the discounted cash flow becomes positive)
5 25,000 0.620921 15,523 83,641

Payback period of Project = 3 years

3 Davis Corporation is faced with two independent investment opportunities. The corporation has an investment policy which requires acceptable projects to recover all costs within 3 years. The corporation uses the discounted payback method to assess potential projects and utilizes a discount rate of 10 percent. The cash flows for the two projects are:

Project A Project B
Year Cash Flow Cash Flow
0 ($100,000) ($80,000)
1 40,000 50,000
2 40,000 20,000
3 40,000 30,000
4 30,000 0

Which investment project(s) does the company invest in?

Project A
Discount rate= 10%
Project A Present value factor Discounted cash flow Cumulative cash flow
Year Cash Flow
0 ($100,000) 1 (100,000) (100,000)
1 40,000 0.909091 36,364 (63,636)
2 40,000 0.826446 33,058 (30,578)
3 40,000 0.751315 30,053 (525)
4 30,000 0.683013 20,490 19,965 Payback period= 4
(In this year the discounted cash flow becomes positive)

Payback period of Project A = 4 years

Project B
Discount rate= 10%
Project B Present value factor Discounted cash flow Cumulative cash flow
Year Cash Flow
0 ($80,000) 1 (80,000) (80,000)
1 50,000 0.909091 45,455 (34,545)
2 20,000 0.826446 16,529 (18,016)
3 30,000 0.751315 22,539 4,523 Payback period= 3
4 0 0.683013 0 4,523 (In this year the discounted cash flow becomes positive)

Payback period of Project B = 3 years

Only the Project B meets the investment criteria of recovering all the costs within 3 years
Hence the company invests in B

4 You are considering the purchase of an investment that would pay you $5,000 per year for Years 1-5, $3,000 per year for Years 6-8, and $2,000 per year for Years 9 and 10. If you require a 14 percent rate of return, and the cash flows occur at the end of each year, then how much should you be willing to pay for this investment?

Discount rate=rate of return= 14%

Year Cash flow Present value factor Discounted cash flow

1 5,000 0.877193 4,386
2 5,000 0.769468 3,847
3 5,000 0.674972 3,375
4 5,000 0.59208 2,960
5 5,000 0.519369 2,597
6 3,000 0.455587 1,367
7 3,000 0.399637 1,199
8 3,000 0.350559 1,052
9 2,000 0.307508 615
10 2,000 0.269744 539
Total=Present Value= 21,937

The Present value= 21,937
This is the upper limit of what can be paid for the investment

5 Shannon Industries is considering a project which has the following cash flows:

Year Cash Flow
0 ?
1 $2,000
2 3,000
3 3,000
4 1,500

The project has a payback of 2.5 years. The firm's cost of capital is 12 percent. What is the project's net present value NPV?

Year Cash Flow
1 $2,000
2 3,000
3 3,000
4 1,500

In 2.5 years the cash flow that will accrue= $6,500 =2000+3000+3000/2

Therefore this is the initial investment

Discount rate=rate of return= 12%

Year Cash Flow Present value factor Discounted cash flow
0 ($6,500) 1 (6,500)
1 $2,000 0.892857 1,786
2 3,000 0.797194 2,392
3 3,000 0.71178 2,135
4 1,500 0.635518 953
NPV=Total= 766

Answer: NPV= 766

6 Below are the returns of Nulook Cosmetics and "the market" over a three-year period:

Year Nulook Market
1 9% 6%
2 15% 10%
3 36% 24%

Nulook finances internally using only retained earnings, and it uses the Capital Asset Pricing Model with a historical beta to determine its cost of equity. Currently, the risk-free rate is 7 percent, and the estimated market risk premium is 6 percent. Nulook is evaluating a project which has a cost today of $2,028 and will provide estimated cash inflows of $1,000 at the end of the next 3 years. What is this project's MIRR?

To calculate the value of beta for Nulook, nulook return is plotted against market return and a straight line is fitted. The slope of this straight line is beta.

Slope of this line= 1.5

This can also be seen from

Year Market Nulook
1 6% 9% =1.5*6%
2 10% 15% =1.5*10%
3 24% 36% =1.5*24%

Thus beta =β= 1.5

r = r f + β (r m - r f)

r f = 7% risk free rate
β= 1.5 beta
r m -rf = 6% market risk premium
r = cost of euity , to be calculated
Therefore
r = 16%

Cost of equity= 16%

Year Cash Flow
0 ($2,028)
1 $1,000
2 1,000
3 1,000

The terminal value of cash flows for years 1-3 invested at the rate of 16% is calculated below

Year Cash Flow Future value factor Terminal value

1 $1,000 1.3456 $1,345.60
2 1,000 1.16 $1,160.00
3 1,000 1 $1,000.00
$3,505.60

We have to discount $3,505.60 for 3 years at MIRR rate to get $2,028

Therefore MIRR= 20%

Answer: MIRR= 20%

7 Two projects being considered by a firm are mutually exclusive and have the following projected cash flows:
Project A Project B
Year Cash Flow Cash Flow
0 ($100,000) ($100,000)
1 39,500 0
2 39,500 0
3 39,500 133,000

Based only on the information given, which of the two projects would be preferred, and why?

Since cost of capital is not given we will calculate IRR (Internal rate of return )to determine which project is preferred

IRR is the rate at which the NPV of the project becomes zero. It is calculated using trial and error or using the excel function IRR

The IRR for the two projects are:
Projct A: 8.9922%
Project B: 9.97%

Project A
Discount rate= 8.9922%
Year Cash Flow Present value factor Discounted cash flow
0 ($100,000) 1 (100,000)
1 39,500 0.91749685 36,241
2 39,500 0.84180047 33,251
3 39,500 0.77234928 30,508

NPV=Total= 0.00

Project B
Discount rate= 9.9724%
Year Cash Flow Present value factor Discounted cash flow
0 ($100,000) 1 (100,000)
1 0 0.90931907 0
2 0 0.82686116 0
3 133,000 0.75188062 100,000

NPV=Total= 0.00

Thus we see that the IRR values ...

Solution Summary

The solution provides answers to 30 questions on Capital Budgeting- Discounted Payback, NPV, Investment, IRR, modified , internal rate of return (MIRR), point of indifference, WACC, risk-adjusted discount rate.

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