Question

You are a financial analyst at a major business valuation firm. You are analyzing how a change in beta will impact the present value of corporation that is considering an investment project. The project requires an initial investment of $100 million and will generate a perpetuity of after tax cash of $15 million every year forever. The project’s beta is 2. Assume that risk free rate is 6% and the return on the market is 8%. Please answer the following questions.

What is the net present value of the project ?

What is the highest possible discount rate for the project before its NPV becomes negative ?

What is the highest possible beta estimate for the project before its NPV becomes negative ?

Answer 1

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Rf = Risk Free rate = 6%

Rm = Return on the market = 8%

Beta = 2

Discount rate = Rf + Beta * (Rm- Rf)

= 6% + 2* (8%-6%)

= 6% + 4%

= 10%

Initial Investment = 100 million

Present Value of after tax cash flows = Annual Cash Flow / Discount rate

= $15 million / 10%

= $150 million

NPV of the Project = Present Value of after tax cash flows - Initial investment

= $150 million - $100 million

= $50 million

Therefore, net present value of the project is $50 million

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At internal rate of return, the present value of future cash flows equal to Initial investment

Annual after tax cash flow / Discount rate = Initial investment

$15 million / IRR = $100 million

IRR = 0.15

IRR = 15%

Therefore, highest possible discount rate fot the project before NPV becomes negative is 15%

>>>>

Discount rate = 15%

Rf = Risk Free rate = 6%

Rm = Return on the market = 8%

Discount rate = Rf + Beta * (Rm - Rf)

15% = 6% + Beta * (8% - 6%)

15% = 6% + Beta *2%

Beta = 4.5

Therefore, the highest possible beta estimate for the project before its NPV becomes negative is 4.5