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 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

As per CAPM

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

Expected return% = 4 + 1.5 * (12 - 4)

Expected return% = 16

Discount rate	16.000%
Year	0	1	2	3	4	5	6	7	8	9	10
Cash flow stream	-36	12	12	12	12	12	12	12	12	12	24
Discounting factor	1.000	1.160	1.346	1.561	1.811	2.100	2.436	2.826	3.278	3.803	4.411
Discounted cash flows project	-36.000	10.345	8.918	7.688	6.627	5.713	4.925	4.246	3.660	3.155	5.440
NPV = Sum of discounted cash flows
NPV Project =	24.72
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor

b

IRR is the rate at which NPV =0
IRR	31.91%
Year	0	1	2	3	4	5	6	7	8	9	10
Cash flow stream	-36.000	12.000	12.000	12.000	12.000	12.000	12.000	12.000	12.000	12.000	24.000
Discounting factor	1.000	1.319	1.740	2.295	3.028	3.994	5.268	6.949	9.167	12.092	15.950
Discounted cash flows project	-36.000	9.097	6.896	5.228	3.963	3.005	2.278	1.727	1.309	0.992	1.505
NPV = Sum of discounted cash flows
NPV Project =	0.001
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
IRR=	31.91%

As per CAPM

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

31.91 = 4 + Beta * (12 - 4)

Beta = 3.49