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Assume CAPM holds and you have the following information regarding three investment opportunities:

Project 1 has a project beta of 2.0 and you have estimated that the project’s NPV using a cost of capital of 20% equals zero. Project 2 has a project beta of 1.5 and its NPV using a cost of capital of 10% equals zero. Lastly, project 3 has a project beta of 1.0 and its NPV equals zero using a cost of capital of 6%. None of these projects are ‘scale-enhancing’ for the firm, i.e. they are different than the regular operations the firm currently maintains. As the head of the capital budgeting department you are trying to decide which projects should be accepted. The company has a levered equity beta of 0.8 and a debt-to-equity ratio of 0.5, which the company is planning to maintain for the foreseeable future. The company currently faces a 40% tax rate. Given that the expected return on the market portfolio is 8% and the risk-free rate is 3%, which projects would you accept and why? (Assume there is no capital rationing and the projects are going to be financed with 100% equity.)

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Reid Wolff
Reid WolffLv2
28 Sep 2019

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Related questions

ABC Appliance Company uses the CAPM to determine its risk-adjusted discount rate, (RADR), for each of its projects:

Rj = RF + [b * (rm – RF)]

The company is currently interested in investing in the capital project shown below. The return on market is 9.65%, the risk-free

rate is currently 8% and the project has a beta of 2.5.

Initial Investment

($3,900,000)

Year

Cash Inflow

1

1,500,000

2

1,750,000

3

2,500,000

A. Using the CAPM compute the RADR

B. Compute the Risk-Adjusted NPV of the project.

IRR, NPV, and Profitability Index. Consider two projects that your company is evaluating. Project A has cash flows of -25, +11, +12, and +10 at time-zero, one year from now, two years from now, and three years from now, respectively. Project B has cash flows of -50, +22.5, +21.5, and +20.5 at time-zero, one year from now, two years from now, and three years from now, respectively. For the risk of these projects, the appropriate discount rate is 10%.

What is the NPV and IRR of each project?

What is the Profitability Index (PI) of each project, where the appropriate discount rate (the cost of capital) is 10%? If you firm is subject to limited capital to invest (capital rationing), what does your PI suggest about which project you would likely prefer?

Now, alternatively, assume that these two projects are mutually exclusive such that your company can choose only one of the two projects. Should your company choose Project A or Project B?

Your firm is planning to invest in an automated packaging plant. Harburtin Industries is an​ all-equity firm that specializes in this business. Suppose​ Harburtin's equity beta is 0.83​, the​ risk-free rate is 5%​, and the market risk premium is 6%.

a. If your​ firm's project is​ all-equity financed, estimate its cost of capital. After computing the​ project's cost of capital you decided to look for other comparables to reduce estimation error in your cost of capital estimate. You find a second​ firm, Thurbinar​ Design, which is also engaged in a similar line of business. Thurbinar has a stock price of $18 per​ share, with 15 million shares outstanding. It also has $110 million in outstanding​ debt, with a yield on the debt of 4.4%. ​Thurbinar's equity beta is 1.00.

b. Assume​ Thurbinar's debt has a beta of zero. Estimate​ Thurbinar's unlevered beta. Use the unlevered beta and the CAPM to estimate​ Thurbinar's unlevered cost of capital.

c. Estimate​ Thurbinar's equity cost of capital using the CAPM. Then assume its debt cost of capital equals its yield and using these​ results, estimate​ Thurbinar's unlevered cost of capital.

d. Explain the difference between your estimate in part ​(b​) and part ​(c​).

e. You decide to average your results in part ​(b​) and part ​(c​), and then average this result with your estimate from part ​(a​). What is your estimate for the cost of capital of your​ firm's project?

a. If your​ firm's project is​ all-equity financed, estimate its cost of capital.

The project’s cost of capital is ?? %. (Round to two decimal places.)

b. Assume​ Thurbinar's debt has a beta of zero. Estimate​ Thurbinar's unlevered beta. Use the unlevered beta and the CAPM to estimate​ Thurbinar's unlevered cost of capital.

Thurbinar's unlevered beta is ??.

Thurbinar's unlevered cost of capital is ?? %.

c. Estimate​ Thurbinar's equity cost of capital using the CAPM. Then assume its debt cost of capital equals its yield and using these​ results, estimate​ Thurbinar's unlevered cost of capital.

Thurbinar's equity cost of capital is ??%

Thurbinar's unlevered cost of capital is ??%

d. Explain the difference between your estimate in part ​(b​) and part ​(c​).

A. The answers are actually the same; any difference is just due to rounding errors.

B. The answers are differ because we are using approximations rather than formulas that hold exactly.

C. In the first case, we assumed the debt had a beta of zero so we assumed the cost of debt was the riskless rate, while in the second case we assumed the cost of debt was the yield to debt.

D. We should have gotten the same answer, the problem is the numbers in the problem are not consistent.

e. You decide to average your results in part ​(b​) and part ​(c​), and then average this result with your estimate from part ​(a​). What is your estimate for the cost of capital of your​ firm's project?

The average unlevered cost of capital from part ​(b​) and part ​(c​) is ?? %.

The average unlevered cost of capital from part ​(b​) and part ​(c​) with part ​(a​) is ??%

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