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	–24
1–9	10
10	20

The project's beta is 1.8. Assuming r_f = 4% and E(r_M) = 14%

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.)

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.)

Answer 1

Discount rate=risk free rate+(beta*(market return-risk free rate))=4%+(1.8*(14%-4%))=4%+18%=22%

Net present value has to be calculated using NPV function in EXCEL

=NPV(rate,Year1 to Year10 cashflows)-Year0 cashflow

=NPV(22%,Year1 to Year10 cashflows)-24

NPV=$16.60 million

discount rate	22%
	Cashflows (Millions)
Year0	-24
Year1	10
Year2	10
Year3	10
Year4	10
Year5	10
Year6	10
Year7	10
Year8	10
Year9	10
Year10	20
NPV	16.60

b. Now we have to rate at which NPV (Net present value) becomes Zero. Below that NPV becomes negative. Internal rate of return (IRR) is the rate at which NPV becomes zero.

To find IRR use IRR function in EXCEL
=IRR(Year0 to Year10 cashflows)

IRR=40.87%

	Cashflows (Millions)
Year0	-24
Year1	10
Year2	10
Year3	10
Year4	10
Year5	10
Year6	10
Year7	10
Year8	10
Year9	10
Year10	20
IRR	40.87%

Now use above formula of discount rate to find the maximum beta

Discount rate=risk free rate+(beta*(market return-risk free rate))

40.87%=4%+(beta*10%)

beta=(40.87%-4%)/10%=36.87%/10%=3.69

The highest possible beta estimate for the project before its NPV becomes negative=3.69

==>If you want to check the answer by increasing 0.1 decimal of beta becoming 3.70

discount rate=4%+(3.7*10%)=41%

No calculate the NPV, it becomes negative

=NPV(41%,Year1 to Year10 cashflows)-24

NPV=-0.07 million

discount rate	41%
	Cashflows (Millions)
Year0	-24
Year1	10
Year2	10
Year3	10
Year4	10
Year5	10
Year6	10
Year7	10
Year8	10
Year9	10
Year10	20
NPV	-0.07