Question & Answer: Janice V. bought a 5% $1000 20-year bond for $875. She received a semiannual dividend for 8 years, then sold it immedi…..

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%

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