You are a consultant to a large manufacturing corporation considering a project
ID: 2781993 • Letter: Y
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):
The project's beta is 1.5. Assuming rf = 4% and E(rM) = 12%
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 :
Years from Now After-Tax CF 0 –36 1–9 12 10 24The project's beta is 1.5. Assuming rf = 4% and E(rM) = 12%
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 :
Explanation / Answer
According to CAPM,
Expected rate of return = risk free rate + beta*(Market return - Risk free rate)
= 0.04 + 1.5*(0.12-0.04) = 0.16 = 16.00%
NPV is calculated by discounting the cashflows
PV = C/(1+r)^n
C - Cashflow
r - Discount rate
n - years to the cashflow
NPV = -36 + 12/(1+0.16)^1 + 12/(1+0.16)^2 + 12/(1+0.16)^3 + 12/(1+0.16)^4 + 12/(1+0.16)^5 + 12/(1+0.16)^6 + 12/(1+0.16)^7 + 12/(1+0.16)^8 + 12/(1+0.16)^9 + 24/(1+0.16)^10 = 22.43 million
b.
Find the expected rate at which NPV will be 0
NPV = -36 + 12/(1+r)^1 + 12/(1+r)^2 + 12/(1+r)^3 + 12/(1+r)^4 + 12/(1+r)^5 + 12/(1+r)^6 + 12/(1+r)^7 + 12/(1+r)^8 + 12/(1+r)^9 + 24/(1+r)^10 = 0
By trail and error, r = 31.37%
Using CAPM equation
0.3137 = 0.04 + beta*(0.12-0.04)
beta = 3.42
Highest possible beta is 3.42
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