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	-36
1-9	12
10	24

The project's beta is 1.5. Assuming rf = 4% and E(rm) = 12%

a. What is the net present value of the project? (Do not round intermediate calculations. Enter your answer in millions rounded to 2 decimal places)

b. What is the highest possible beta estimate for the project before its NPV becomes negative? (Do not round intermediate calculations. Round your answer to 2 decimal places).

Answer 1

We are given,

Beta = 1.5

rf = 4%

E(rm) = 12%

According to CAPM equation,

Return on Equity (r) = rf + Beta ( rm - rf)

r = 4% + 1.5 ( 12% - 4%)

r = 4% + 12% = 16%

Hence return on equity or discount rate is 16%.

Calculation of NPV

Yr	Cash Flow	Discounting factor (PV @ 16%)	PV of cashflow
0	-36	1.00000	-36.00
1	12	0.86207	10.34
2	12	0.74316	8.92
3	12	0.64066	7.69
4	12	0.55229	6.63
5	12	0.47611	5.71
6	12	0.41044	4.93
7	12	0.35383	4.25
8	12	0.30503	3.66
9	12	0.26295	3.16
10	24	0.22668	5.44
		NPV	24.72

a) Hence NPV = $24.72 million.

b) highest possible beta estimate for the project before its NPV becomes negative?

NPV > 0 if IRR > discount rate

To calculate the highest possible β estimate (and therefore the highest possible discount rate) for a positive NPV, we will calculate the project's IRR.

By using Excel

IRR

31.91%

(=IRR(All cash flows))

The highest Beta before the hurdle rate exceeds the IRR is

E(r) = rf + Beta ( rm - rf)

Beta = [0.3191 - 0.04] / [ 0.12 - 0.04] = 0.2791 / 0.08 = 3.49(approx)

Hence the highest possible beta estimate for the project before its NPV becomes negative is 3.49.

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