Question 2

Assume a project beta is 1.7, risk free rate is 9% and market return is 19%. The cash outflow in year zero is -20 million and cash inflow from year 1 to 9 is 10million. The cash flow in year 10 is 20 million. Calculate the net present value of the bond. What is the highest value of the beta calculated for this bond before NPV becomes negative?

Answer:

The cash flows for the project comprise a 10-year annuity of $10 million per annum and payment of $20 million at time zero. The appropriate discount rate for the project is:

  rf + β[E(rM) – rf ] = 9% + 1.7(19% – 9%) = 26%

Using this discount rate the NPV of the bond is:

                     = -20 + [10 × annuity factor (26%, 10 years)] + [10 × PV factor (26%, 10 years)]

                     = 15.2238

The internal rate of return on the bond is exactly 49.55% (doing trial and error method). The highest value that beta can take before NPV becomes negative is:

49.55% = 9% + β (19% – 9%)

Now solve for β = 40.55/10 = 4.055

my question is :

a) can u calculate how can they get NPV: 15.2238?

Using this discount rate the NPV of the bond is:

                     = -20 + [10 × annuity factor (26%, 10 years)] + [10 × PV factor (26%, 10 years)]

                     = 15.2238

b) how can they get 49.55%?

The internal rate of return on the bond is exactly 49.55% (doing trial and error method). The highest value that beta can take before NPV becomes negative is:

49.55% = 9% + β (19% – 9%)