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 -38

1-9 12

10 24

The project's beta is 1.4. Assuming rf = 6% and E(rM) = 16% 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

1)

As per CAPM

expected return = risk-free rate + beta * (expected return on the market - risk-free rate)

Expected return% = 6 + 1.4 * (16 - 6)

Expected return% = 20

Discount rate	20.000%
Year	0	1	2	3	4	5	6	7	8	9	10
Cash flow stream	-38	12	12	12	12	12	12	12	12	12	24
Discounting factor	1.000	1.200	1.440	1.728	2.074	2.488	2.986	3.583	4.300	5.160	6.192
Discounted cash flows project	-38.000	10.000	8.333	6.944	5.787	4.823	4.019	3.349	2.791	2.326	3.876
NPV = Sum of discounted cash flows
NPV A =	14.25
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor

2)

A
IRR is the rate at which NPV =0
IRR	29.97%
Year	0	1	2	3	4	5	6	7	8	9	10
Cash flow stream	-38.000	12.000	12.000	12.000	12.000	12.000	12.000	12.000	12.000	12.000	24.000
Discounting factor	1.000	1.300	1.689	2.196	2.854	3.709	4.820	6.265	8.143	10.583	13.755
Discounted cash flows project	-38.000	9.233	7.104	5.466	4.205	3.236	2.489	1.915	1.474	1.134	1.745
NPV = Sum of discounted cash flows
NPV A =	0.000
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
IRR=	29.97%

As per CAPM

expected return = risk-free rate + beta * (expected return on the market - risk-free rate)

29.97 = 6 + Beta * (16 - 6)

Beta = 2.4