Question

The Treasury bill rate is 5% and the market risk premium is 8%.

Project	Beta			Internal Rate of Return, %
P		0.95		14
Q		0.00		12
R		2.00		21
S		0.35		13
T		1.60		23

a. What are the project costs of capital for new ventures with betas of 0.70 and 1.59? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.)

b. Which of the capital investments shown above have positive (non-zero) NPV's? (You may select more than one answer. Single click the box with the question mark to produce a check mark for a correct answer and double click the box with the question mark to empty the box for a wrong answer.)      

Answer 1

Sol:

a) Cost of capital = Risk free rate + Beta x Market risk premium

Cost of capital = Risk free rate + Beta x Market risk premium

Now cost of capital for new venture with beta of 0.70

= 5% + 0.70 x 8% = 10.60%

Costs of capital for new venture with beta of 1.59

= 5% + 1.59 x 8% = 17.72%

b) To determine which of the capital investments have positive (non-zero) NPV's we have to find cost of capital for each project. If a project IRR (Internal rate of return) is higher than its cost of capital, it will have positive NPV.

Cost of capital = risk free rate + beta x market risk premium

Project	Risk free rate	Beta	Market risk premium	Output
P	5%	0.95	8%	12.60%
Q	5%	0.00	8%	5.00%
R	5%	2.00	8%	21.00%
S	5%	0.35	8%	7.80%
T	5%	1.60	8%	17.80%

The entire projects have higher IRR than its cost of capital, except for project R. Therefore project P, Q, S and T will have positive NPV.

Workings