Question

CAPM and Cost of Capital. Suppose the Treasury bill rate is 4% and the market risk premium is 7%.

a. What are the project costs of capital for new ventures with betas of .75 and 1.75?

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b. Which of the following capital investments have positive NPVs?

Project	Beta	Internal Rate of Return, %
P	1.0	14
Q	0	6
R	2.0	18
S	0.4	7
T	1.6	20

Answer 1

Capital asset pricing model (CAPM) is that model which states the theory of risk-return relationship in such a way that the expected risk premium on security or any stock is equal to beta times the market risk premium (market return less the return on risk-free securities).

a.

Project costs of capital are calculated as follows using the following information:

T-Bill rate is 4%

The market risk premium is 7%

Use CAPM to compute the project cost of capital as follows when the beta is 0.75

Where,

Rf is the return on T-Bill

The market risk premium is the difference between the return on market and return on the risk-free rate.

Beta is the measure of systematic risk.

Therefore, the project cost of capital when the beta is 0.75 is computed as 9.25%

Use CAPM to compute the project cost of capital as follows when the beta is 1.75

Therefore, the project cost of capital when the beta is 1.75 is computed as 16.25%.

It is clear from the above solutions that as beta increased to 1.75 from 0.75 returns also increased from 9.25% to 16.25%. Therefore, beta which is the measure of systematic risk increases or decreases the return from an investment with respect to the market fluctuations.

b.

Computation of cost of capital of Project P using CAPM is shown as follows:

When Beta is 1.0:

The computation of cost of capital is shown below:

Therefore, the cost of capital of project P is computed as 11%.

Computation of cost of capital of Project Q using CAPM is shown as follows:

When Beta is 0:

The computation of cost of capital is shown below:

Therefore, the cost of capital of project Q is computed as 4%.

Computation of cost of capital of Project R using CAPM is shown as follows:

When Beta is 2.0:

The computation of cost of capital is shown below:

Therefore, the cost of capital of project R is computed as 18%.

Computation of cost of capital of Project S using CAPM is shown as follows:

When Beta is 0.4: The computation of cost of capital is shown below:

Therefore, the cost of capital of project S is computed as 6.8%.

Computation of cost of capital of Project T using CAPM is shown as follows:

When Beta is 1.6: The computation of cost of capital is shown below:

Therefore, the cost of capital of project T is computed as 15.2%.

Net Present Value analysis is shown in the table below:

Projects	Beta	Internal Rate of Return	Cost of Capital	NPV
P	1.0	14%	11%
Q	0	6%	4%
R	2.0	18%	18%	0
S	0.4	7%	6.8%
T	1.6	20%	15.2%

Net Present Value (NPV) is positive because the opportunity costs of capital of projects P, Q, S and T is less than the internal rate of return. This implies, if a shareholder invests elsewhere, his return would be less. In project R, NPV is zero because here the shareholder is indifferent regarding his acceptance of the project or to invest elsewhere as he would get the same return in either case.