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    -22

1-9 12

10 22

The project's beta is 2.8. Assume rf = 10% and E (rM ) = 19%.

(a) What is the net present value of the project? (Enter your answer in millions. Round your answer to 2 decimal places.)

Net present value _____million

(b) What is the highest possible beta estimate for the project before its NPV becomes negative? (Round your answer to 3 decimal places.)

Highest possible beta estimate_____

Answer 1

a). The appropriate discount rate for the company’s equity is:

E(r) = rf + β[E(rM) - rf] = 10% + [2.8 x (19% - 10%)] = 10% + 25.20% = 35.20%

NPV = -$22 + $12/(1.352) + $12/(1.352)² + $12/(1.352)³ + … + $12/(1.352)⁹ + $22/(1.352)¹⁰

  = $10.91 million

b). NPV > 0 if IRR > discount rate.

To calculate the highest possible β estimate (and therefore the highest possible discount rate) for a positive NPV, calculate the projects IRR. (Note that we can do this since the CFs do not change signs).

Use the calculator’s CF register or use Excel:

CF0 = -22, CF1 = 12, N1 = 9, CF2 = 22, N2 = 1; IRR = 54.15

So the highest β before the hurdle rate exceeds the IRR is:

E(r) = rf+ β[E(rM ) – rf ]

β = [E(r) – rf]/[E(rM ) – rf ]

β = [0.5415 - 0.10]/[0.19 - 0.10] = 0.4415 / 0.09 = 4.91