Suppose a portfolio manager is considering the purchase of a bond, a 12-year, 8% non-callable bond selling at $1050 per $1000 of par value. Assume also that the portfolio manager’s investment horizon is 5 years. The portfolio manager believes the reinvestment rate range can vary from 3% to 6% and the discount rate at the end of the investment horizon from 4% to 6%. Use 50 bps grids to compute the various return scenarios. Identify all the scenarios that generate less than 4% annualized return.
Sample Solution
When a portfolio manager is considering the purchase of a bond, there are many factors that must be taken into consideration. In this case, the portfolio manager is considering purchasing a 12-year, 8% non-callable bond selling at $1050 per $1000 of par value with an investment horizon of 5 years. The portfolio manager also believes the reinvestment rate range can vary from 3% to 6%, and the discount rate at the end of the investment horizon can vary from 4% to 6%. As such, we will use 50 bps grids to compute various return scenarios.
Sample Solution
When a portfolio manager is considering the purchase of a bond, there are many factors that must be taken into consideration. In this case, the portfolio manager is considering purchasing a 12-year, 8% non-callable bond selling at $1050 per $1000 of par value with an investment horizon of 5 years. The portfolio manager also believes the reinvestment rate range can vary from 3% to 6%, and the discount rate at the end of the investment horizon can vary from 4% to 6%. As such, we will use 50 bps grids to compute various return scenarios.
First, we need to calculate the current yield on the bond. To do this, we take (8 x 1000) / 1050 = 7.619047619%. This is our current yield for both our low and high reinvestment rates; however, since our reinvestment rate can range from 3%-6%, these numbers may change depending on what percentages are chosen.
Next, we need to calculate our total cashflows over 5 years in order determine all possible outcomes each respective scenario . Starting with lowest discount rate 4% ,we know that net present value (NPV) equation as follows: NPV= CF1/(1+r) + CF2/(1+r)^2 + … CFn/(1+ r )^n where r equal discount rate selected . Then plugging relevant variables obtain following cash flows : Year 1 = 85 Year 2 = 86 Year3 = 87 Year4 = 88 Year5 = 925 .
Now let us begin analyzing different scenarios based upon given criteria . If choose lowest reinvestment 3% coupled highest discount 6 % then npv equation looks like this : 85/1.06 +86/1.1296 +87/ 1….4941 +88/ 1…555635 +925/ (1..06)…5 or approximately 844 using calculator resulting annunalized return 844 /50 or 16.88 % which greater than required threshold 4 % Therefore if choose same parameters again higher returns expected
However if decide select lower reinvestment 3% combined lower discount 2 % then npv equation changes slightly 917 /(1..02).05 or approximately 1041 meaning annualized return would drop 1041/50 2083 % still above minimum required by portfolio manager Under these conditions it would appear prudent move forward with purchase Bond as long able keep invested period specified generate positive returns customer even potentially sizable profits depending specific circumstances any given situation
