You have a planning horizon of H = 3 years and with to immunize your investment

Question

You have a planning horizon of H = 3 years and with to immunize your investment for that horizon. You attempt to do so by buying a perpetual bond that pays $100 annually and has a YTM of 20% p.a. You will reinvest the coupons throughout this 3-year period and, additionally, you will sell the bond at the end of that 3-year period. Find the total cash flow you will have 3 years from now if interest rates remain unchanged throughout your planning horizon. Give the answer with two decimals; e.g., 1,234.56. As always, do not include the dollar sign in your answer.

Explanation / Answer

The bond pays annual coupons worth $ 100 with a YTM of 20% per annum. This implies that the investor receives $100 at the end of Year 1, Year 2, Year 3, Year 4 and so on till perpetuity (as the bond is a perpetual one).

Investor Planning Horizon = 3 years

Therefore, the investor reinvests $100 (received at the end of year 1) for Year 2 and Year 3 at the YTM, reinvests $100 (received at the end of year 2) for Year 3 at the YTM and $100 received at end of Year 3 is not reinvested as the total investment planning horizon is of three years.

Total Cash Flow at the end of 3 years = $ 100 (received at the end of year 1) reinvested for Year 2 and Year 3 + $100 (received at the end of year 2) reinvested for Year 3 + $100 (received at the end of year 3) + Sale Price of the Bond = 100 x (1.2)^2 + 100 x(1.2) + 100 + Bond Sales Proceed

Bond Sale Price will be equal to the Present Value of the perpetual annual cash flows of $100 discounted at the YTM of 20%

Therefore, Bond Sale Price = 100 / 0.2 = $ 500

Total Cash Flow at the end of Year 3 = 100 x (1.44) + 100 x (1.2) + 100 + 500 = 144 + 120 + 100 + 500 = $ 864

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