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.) Net present value 24.72 million 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.) Highest possible beta value

Answer 1

a) Here rf ( Risk free rate of return) = 4% and E(rM)( Market rate) =12%, beta =1.5

Thus required rate of return = Rf +beta(Rm -Rf)

Rf = Risk free rate of return

Rm =Market rate

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

=4% +1.5(8%)

=4% +12%

=16%

Statement showing NPV

Particulars	0	1	2	3	4	5	6	7	8	9	10	NPV
Cash flow	-36	12	12	12	12	12	12	12	12	12	24
PVIF @ 16%	1	0.8621	0.7432	0.6407	0.5523	0.4761	0.4104	0.3538	0.3050	0.2630	0.2267
Present Value	-36	10.34	8.92	7.69	6.63	5.71	4.93	4.25	3.66	3.16	5.44	24.72

B) First of all we need to find the rate at which NPV will be 0

Particulars	0	1	2	3	4	5	6	7	8	9	10	NPV
Cash flow	-36	12	12	12	12	12	12	12	12	12	24
PVIF @ 31.910458%	1	0.7581	0.5747	0.4357	0.3303	0.2504	0.1898	0.1439	0.1091	0.0827	0.0627
Present Value	-36	9.10	6.90	5.23	3.96	3.00	2.28	1.73	1.31	0.99	1.50	0.00

Hence at 31.91% NPV comes to 0

Now let us calculate beta at 31.91%

31.91% = 4%+ beta(8%)

27.91 =beta(8%)

beta = 3.49

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