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 –65

1–10 15

The project's beta is 1.6.

a. Assuming that rf = 6% and E(rM) = 13%, what is the net present value of the project?

b. What is the highest possible beta estimate for the project before its NPV becomes negative?

Answer 1

As per CAPM

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

Expected return% = 6 + 1.6 * (13 - 6)

Expected return% = 17.2

a
Project A
Discount rate	0.172
Year	0	1	2	3	4	5	6	7	8	9	10
Cash flow stream	-65	15	15	15	15	15	15	15	15	15	15
Discounting factor	1	1.172	1.373584	1.60984	1.886733	2.211251	2.591586	3.037339	3.559761	4.17204	4.889631
Discounted cash flows project	-65	12.79863	10.92034	9.317694	7.9502505	6.78349	5.787961	4.938533	4.213766	3.595363	3.067716
NPV = Sum of discounted cash flows
NPV Project A =	4.37
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
b
Project A
IRR is the rate at which NPV =0
IRR	0.190372039
Year	0	1	2	3	4	5	6	7	8	9	10
Cash flow stream	-65	15	15	15	15	15	15	15	15	15	15
Discounting factor	1	1.190372	1.416986	1.68674	2.0078482	2.390086	2.845092	3.386718	4.031454	4.79893	5.712513
Discounted cash flows project	-6500.00%	12.6011	10.58585	8.892894	7.4706844	6.275924	5.272237	4.429067	3.720742	3.125697	2.625815
NPV = Sum of discounted cash flows
NPV Project A =	1.41909E-05
Where
Discounting factor =	(1 + IRR)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
IRR=	19.04%

As per CAPM

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

19.04 = 6 + Beta * (13 - 6)

Beta = 1.86