Question

You are a consultant to a large manufacturing corporation considering a project with the following net after-tax cash flows (in millions of dollars):

YEARS FROM NOW	After-Tax CF
0 1-9 10	-20 10 20

The project’s beta is 1.7. Assuming r _f = 9% and E ( r _M ) = 19%, what is the net present value of the project? What is the highest possible beta estimate for the project before its NPV becomes negative?

Short answer

The correct answer would be $15.64 million and 4.055

Step-by-step solution

Given information

The cash flows for the project comprise a 10-year annuity of $10 million per year plus an additional payment in the tenth year of $10 million (so that the total payment in the tenth year is $20 million).

Solution

The appropriate discount rate for the project is:

r_f +βE(r_M) – r_f ] = 9% + 1.7(19% – 9%) = 26%

Using this discount rate:

NPV = -20 + $\sum _{t=1}^{10}\frac{10}{1.{26}^t}+\frac{10}{1.{26}^{10}}$

= -20 + [10 x Annuity factor (26%, 10 years)] + [10 x PV factor (26%, 10 years)]

=15.64

Solution for the highest value of β

The internal rate of return on the project is 49.55%.

The highest value that beta can take before the hurdle rate exceeds the IRR is determined by:

49.55% = 9% +β(19% – 9%)

β = 40.55/10 = 4.055