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 | –50 |

1–10 | 16 |

The project's beta is 1.1.

**a.** Assuming that *r _{f}* = 7%
and

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

Answer #1

Required rate of return from the project using CAPM = risk free rate + beta*(market return - risk free return)

= 7% + 1.1*(15%-7%)

= 15.8%

NPV = -50 +16*PVAF(15.8%, 10 years)

= -50+16*4.869

= 27.904

B let the return at which NPV = 0 be X

0 = -50 + 16*PVAF(X%, 10 Years)

PVAF (x%, 10 years) = 3.125

PVAF(29%, 10 years) = 3.178

PVAF(30%, 10 years) = 3.092

Using interpolation, X = 29% + (3.178-3.125)/(3.178-3.092)

= 29.62%

29.62 = 7% + beta(15%-7%)

Beta = 2.8275

Or 2.83

Hence, highest possible beta = 2.83

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