Question

Suppose you bought a 8 percent coupon bond one year ago for $1,050. The bond sells for $1,115 today.

Requirement 1: Assuming a $1,000 face value, what was your total dollar return on this investment over the past year?

Requirement 2: What was your total rate of return on this investment over the past year (in percent)?

Requirement 3: If the inflation rate last year was 5 percent, what was your total "real" rate of return on this investment? Assume that the answer for "Requirement 2" above is in "nominal" terms, and then use the Fisher Effect Formula (see Bond chapter) to find the "real" rate of return. (Do not round intermediate calculations.)

Answer 1

a.
We can find the total dollar return as a change in price plus the coupon payment as follows :-

coupon payment = 1000*8% = $80

Total dollar return = $1,115- 1,050+80
Total dollar return = $145

b.
We can calculate the nominal percentage of return of the bond as follows :-

R = ($1,115- 1,050+ 80) / $1,050
R = 0.1380, or 13.80%

c.
Using the Fisher equation, the real return can be calculated as follows :-
formula = (1 + R) / (1 + inflation rate) - 1

r = (1.1380 / 1.05) - 1
r = 0.0838, or 8.38%

If the inflation rate last year was 5 percent, our total "real" rate of return on this investment = 8.38%

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