Question

You are working for the CFO of a small manufacturing company and are thinking about investing in new equipment. The cost of the project is 9,500 today and it pays of 15,000 in ten years. Your beta is 0.2 and the market risk premium is 5%.

1. What is the NPV of the project if the 10-year Treasury (risk-free) rate is 2.6%?

2. What is the NPV if the 10-year Treasury rate is 3.1%?

Answer 1

1

As per CAPM expected return = risk-free rate + beta * (Market risk premium) Expected return% = 2.6 + 0.2 * (5) Expected return% = 3.6

Project
Discount rate	0.036
Year	0	1	2	3	4	5	6	7	8	9	10
Cash flow stream	-9500	0	0	0	0	0	0	0	0	0	15000
Discounting factor	1	1.036	1.073296	1.111935	1.1519643	1.193435	1.236399	1.280909	1.327022	1.374795	1.424287
Discounted cash flows project	-9500	0	0	0	0	0	0	0	0	0	10531.58
NPV = Sum of discounted cash flows
NPV Project =	1031.58
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor

2

As per CAPM

expected return = risk-free rate + beta * (Market risk premium)

Expected return% = 3.1 + 0.2 * (5)

Expected return% = 4.1

Project
Discount rate	0.041
Year	0	1	2	3	4	5	6	7	8	9	10
Cash flow stream	-9500	0	0	0	0	0	0	0	0	0	15000
Discounting factor	1	1.041	1.083681	1.128112	1.1743645	1.222513	1.272637	1.324815	1.379132	1.435676	1.494539
Discounted cash flows project	-9500	0	0	0	0	0	0	0	0	0	10036.54
NPV = Sum of discounted cash flows
NPV Project =	536.54
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor