Question

You are a consultant to a large manufacturing corporation that is considering a project with the following net after-tax cash flows (in millions of dollars):

Years from Now	After-Tax Cash Flow
0	–30
1–10	14

The project's beta is 1.6.

a. Assuming that r_f = 4% and E(r_M) = 18%, 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? (Round your answer to 2 decimal places.)

Answer 1

a

As per CAPM

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

Expected return% = 4 + 1.6 * (18 - 4)

Expected return% = 26.4

Cashflow
Discount rate	0.264
Year	0	1	2	3	4	5	6	7	8	9	10
Cash flow stream	-30	14	14	14	14	14	14	14	14	14	14
Discounting factor	1	1.264	1.597696	2.019488	2.5526325	3.226527	4.078331	5.15501	6.515933	8.236139	10.41048
Discounted cash flows project	-30	11.07595	8.762618	6.932451	5.4845341	4.33903	3.432777	2.715805	2.14858	1.699826	1.344799
NPV = Sum of discounted cash flows
NPV Cashflow =	17.94
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
b
Cashflow
IRR is the rate at which NPV =0
IRR	0.45574853
Year	0	1	2	3	4	5	6	7	8	9	10
Cash flow stream	-30	14	14	14	14	14	14	14	14	14	14
Discounting factor	1	1.455749	2.119204	3.085028	4.4910247	6.537803	9.517396	13.85494	20.1693	29.36143	42.74286
Discounted cash flows project	-30	9.617046	6.606255	4.538047	3.1173287	2.141392	1.470991	1.01047	0.694124	0.476816	0.32754
NPV = Sum of discounted cash flows
NPV Cashflow =	8.87263E-06
Where
Discounting factor =	(1 + IRR)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
IRR=	45.57%

As per CAPM

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

45.57 = 4 + Beta * (18 - 4)

Beta = 2.97