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	–23
1–9	10
10	20

The project's beta is 1.7. 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.)

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% = 6 + 1.7 * (16 - 6)

Expected return% = 23

Project
Discount rate	23.000%
Year	0	1	2	3	4	5	6	7	8	9	10
Cash flow stream	-23	10	10	10	10	10	10	10	10	10	20
Discounting factor	1.000	1.230	1.513	1.861	2.289	2.815	3.463	4.259	5.239	6.444	7.926
Discounted cash flows project	-23.000	8.130	6.610	5.374	4.369	3.552	2.888	2.348	1.909	1.552	2.523
NPV = Sum of discounted cash flows
NPV Project =	16.25
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor

b

Project
IRR is the rate at which NPV =0
IRR	42.77%
Year	0	1	2	3	4	5	6	7	8	9	10
Cash flow stream	-23.000	10.000	10.000	10.000	10.000	10.000	10.000	10.000	10.000	10.000	20.000
Discounting factor	1.000	1.428	2.038	2.910	4.155	5.932	8.469	12.091	17.263	24.646	35.187
Discounted cash flows project	-23.000	7.004	4.906	3.436	2.407	1.686	1.181	0.827	0.579	0.406	0.568
NPV = Sum of discounted cash flows
NPV Project =	0.000
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
IRR=	42.77%

As per CAPM

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

42.77 = 6 + Beta * (16 - 6)

Beta = 3.68