Cb Practice

Capital budgeting practice problems. 1. Evaluation of Cash Flows. Below are the cash flows for two mutually exclusive

projects. year 0 1 2 3 4

CFX (5,000) 2,085 2,085 2,085 2,085

CFY (5,000) 0 0 0 9,677

a. Calculate the payback for both projects. b. Initially, the cost of capital is uncertain, so construct NPV profiles for the two projects (on the same graph) to assist in the analysis. The profiles cross at what cost of capital? What is the significance of that? c. It is now determined that the cost of capital for both projects is 14%. Which project should be selected? Why? d. Calculate the MIRR for both projects, using the 14% cost of capital.  Answers: a. 2.4 yrs, 4 yrs; yrs; b. 10%; c. X; d. MIRR X = 19.69% 2. More practice with Cash Flow Evaluation. Cash flows for two mutually exclusive

projects are shown below: year 0 1 2 3

CFM (100) 10 60 80

CFN (100) 70 50 20

Both projects have a cost of capital of 10%. a. Calculate the payback for both projects. b. Calculate the NPV for both projects. c. Calculate the IRR for both projects. d. Calculate the MIRR for both projects.  Answers: a. 2.4 yrs, 1.6 1.6 yrs; b. $18.78, $19.98; c. c. 18.1%, 23.56%; d. 16.5%, 16.5%, 16.9%;

3. Expansion Project. A machine has a cost of $180. It will have a life of 3 years, and

will be depreciated straight line to zero salvage value. It will result in sales revenue of  $200 per year and cash operating costs of $110 per year. Use of the machine will require an increase in working capital of $70 for the 3 years, beginning at year 0. The appropriate discount rate is 8% and the firm’s tax rate is 40%. a. b. c. d.

Calculate the initial cash flow at time 0. Calculate the annual operating cash flows (they are identical each year). Calculate the relevant terminal cash flows at the end of year 3. What is the NPV for the machine?

 Answers: a. -250; b. 78; c. 70; d. $6.58 4. Inflation adjustment : A project requires an initial investment of $8,000, has a 4-year 

life and provides expected cash flows as follows, based on year 1 prices and costs: annual revenue = $5,000 annual cash operating costs = $2,000 annual depreciation = $2,000 terminal cash flow = 0 cost of capital = 14% T = 30% a. Calculate the annual operating cash flows without adjusting for inflation. (Are these cash flows real or nominal?) Calculate the associated NPV. b. Adjust the cash flows to reflect the effects of inflation, which is expected to affect sales revenue and cash operating expenses at the rate of 4% annually. (Are these cash flows real or nominal?) Calculate the associated NPV. c. Which NPV is the correct one for evaluating the project? a. -$133; b. $202 5. Mutually Exclusive Projects with Unequal Lives . Murray’s Coffee House is trying

to choose between two new coffee bean roasters. The required rate of return for either  machine is 10%. Shown below are the after-tax cash flows associated with each machine: year 0 1 2 3 4

CFX (50,000) 20,000 20,000 20,000 20,000

CFY (30,000) 20,000 20,000

a. Calculate the replacement chain NPV for each project. b. Calculate the equivalent annual annuity for each project. c. Which project should be selected? Why?  Answers: a. RCNPVX = $13,397, RCNPVY = $8,604; b. EAA X = $4,226, EAAY = $2,714

6. Risk Adjustment and Project Selection. Acme Mfg is considering two projects, A &

B, with cash flows as shown below: period 0 1 2 3 4

CF A -50,000 20,000 20,000 20,000 20,000

CFB -100,000 60,000 25,000 25,000 25,000

The opportunity cost of capital for A is 14 percent. The opportunity cost of capital for B is 10 percent. a. Calculate the NPV for each project. b. Calculate the IRR for each project. c. Which project(s) should be accepted in each of the following situations: (1) The projects are mutually exclusive and there is no capital constraint. (2) The projects are independent and there is no capital constraint. (3) The projects are independent and there is a total of $100,000 of financing for  capital outlays in the coming period. d. Explain why the cost of capital for A might be higher than for B.  Answers: a. NPV A = $8,274, NPVB = $11,065; b. IRR A = 21.86%, IRR B = 16.08% 7. Cost of Capital. Delta, Inc. has a stock price of $50. In the fiscal year just ended,

dividends were $2.00. Earnings per share and dividends are expected to increase at an annual rate of 8 percent. The risk-free rate is 4 percent, the market risk premium is 6.4 percent and the beta on Delta’s stock is 1.25. Delta’s target capital structure is 40% debt and 60% common equity. Delta’s tax rate is 40 percent. New common stock can be sold to net $40 per share after flotation costs. Delta can sell bonds that mature in 25 years with a par value of $1,000 and an 8% coupon rate paid annually for $960. a. Calculate the before-tax interest rate on new debt financing. b. Calculate the after-tax cost of debt financing. c. Calculate the required return on the firm’s stock using CAPM. d. Calculate the required return on the firm’s stock using the discounted cash flow approach. e. Calculate the cost of financing from the sale of common stock. f. Calculate the WACC if equity financing is from retained earnings. g. Calculate the WACC if equity financing is from the sale of common stock.  Answers: a. 8.39%; b. 5.03%; c. 12%; d. 12.3%; e. 13.4%; f. 9.3%; g. 10%

8. Replacement project: Existing machine was purchased 2 years ago at a cost of 

$3,200. It is being depreciated straight line over its 8 year life. It can be sold now for  $3,000 or used for 6 more years at which time it will be sold for an estimated $500. It provides revenue of $5,000 annually and cash operating costs of $2,000 annually.  A replacement machine can be purchased now for $7,800. It would be used for 6 years, and depreciated straight line. It will result in additional sales revenue of $1,500 annually, but because of its increased efficiency it would reduce cash operating costs by $600 per  year. The new machine would require additional inventories of $700, and accounts receivable would increase by $300. Its expected salvage value in 6 years is $2,000. The tax rate is 40% and the required rate of return is 13%. Should the old machine be replaced? a. Calculate the incremental cash flow at time 0. b. Calculate the incremental annual operating cash flows that result from the new machine. c. Calculate the incremental terminal cash flow. d. Show the incremental CFs in the table below. Year 0 1 2 3 4

Cash Flow ________   ________   ________   ________   ________  

e. Calculate the NPV for this project.  Answers: a. –$6,040; b. $1,620; c. 1,900; e. 1,349 9. Capital Budgeting Scenario Analysis

 Acme Mfg. is considering a project that requires initial investment of $9,600 and has a 4year life. Acme’s corporate weighted average cost of capital (WACC) is 10%. The probability distribution of annual operating cash flows (over its 4-year life) is shown below. There are no other cash flows associated with the project. Scenario

prob

Ann CF

Worst Case Most Likely Best Case

.3 .4 .3

$2,500 3,000 4,000

NPV @ that Ann CF -$1,675 -90 $3,079

a. Calculate the expected NPV. b. Calculate the standard deviation of NPV. c. Calculate the coefficient of variation (CV) of NPV.  Acme classifies projects into high, average, or low risk according to the CV of NPV as shown below:

CV Below 2 Between 2 and 3  Above 3

risk low average high

To determine the risk-adjusted discount rate (RADR) for each project, Acme adds or  subtracts 2% to the corporate WACC based on the CV. d. What is the RADR for this project? e. Calculate the expected NPV using the RADR. f. Should the project be accepted or rejected? State what your decision is based on.  Answers: a. $385.08; b. $1,881.65; c. 4.89; e. -$32.35