Question

You are a consultant to a large manufacturing corporation that is considering a project with the following net after-tax cash flows.

• Initial Cash Flow = -$40
• Cash Flow in Year 1 = $100

The project’s beta is 1.8. Assuming that the risk-free rate offers a return of 8% and expected return of market portfolio is 16%, what is the highest possible beta estimate for the project before its NPV becomes negative?

Answer 1

NPV at Zero = Present value of Cash inflow plus initial cash outflow will be equal to zero

There fore present value of cash iflow will be equal to 40 that is 100* Pvf @ Ke % at year 1 = 40

pvf (ke, 1) = 40/100 = 0.40

Pvf ( Ke , 1 ) = 1/ (1+Ke)^1 = 0.40

(1+Ke) = 1/0.40 = 2.5

Ke = 2.5-1 = 1.5 That is 150%

At this Ke Beta will be =

Ke = Rf + Beta * (Rm-Rf)

150 = 8 + Beta * (16 - 8)

150 = 8 + 8 beta

Beta = (150-8)/8 = 17.75

Therefore highest possible beta = 17.75