Janice V. bought a 5% $1000 20-year bond for $875. She received a semiannual dividend for 8 years, then sold it immediately after the sixteenth dividend for $950. What rate of return did she make per semiannual period, and per year (nominal)? The rate of return that she made per semiannual period is %. The rate of return that she made per year is [ ] %.

## Expert Answer

For computing the semi annual rate of return, we need to use trail and error technique………….

(1) so let us assume 4% return semi annually.

CF = Cash flow = 1000 * 5% * 1/2 = 25

DF = Discounting factor ……….For 1 – 16 periods we take sum of all discounting factors. But for 16th period maturity value only that years DF is taken.

PV = CF * DF

Int Periods | CF | DF | PV |

1 to 16 | 25 | 11.6523 | 291.3074 |

16 | 950 | 0.533908 | 507.2128 |

798.5202 |

This present value of 798.52 is less than the 875. So let us decrease the discount rate to 3%

Int Periods | CF | DF | PV |

1 to 16 | 25 | 12.5611 | 314.0276 |

16 | 950 | 0.623167 | 592.0086 |

906.0361 |

Thus the required rate of return is between 3% and 4%. We use simple interpolation to find the rate which equals 875.

3 | 906 | ||

x | 875 | ||

4 | 799 | ||

(x -3) / (4 -3) = (875 – 906) / (799 – 906) | |||

x – 3 = – 31 / – 107 | |||

x – 3 = 0.29 | |||

X = 3.29 |

a) Thus semi annual rate of return **= 3.29%**

b) Effective annual rate = ( 1.0329)^{2} – 1 **= 0.0669 or 6.69%**