Question

# A 20 year, 4% coupon bond has a price of \$900 and face value of \$1000....

A 20 year, 4% coupon bond has a price of \$900 and face value of \$1000. If the YTM decreases by 0.50% over the next year, what is the bond's total return over the next year?

First, we need to find the YTM, for that we need to put the following values in the financial calculator:

N = 20;

PV = -900;

PMT = 4%*1000 = 40;

FV = 1000;

Press CPT, then I/Y, which gives us 4.79

So, YTM = 4.79%

YTM after 1 year = 4.79% - 0.50% = 4.29%

Bond's Value after 1 year = PV of Coupon Payment + PV of Maturity Value

= [Periodic Coupon Payment * {(1 - (1 + r)^-n) / r}] + [Face Value / (1 + r)^n]

= [{4%*\$1,000} * {(1 - (1 + 0.0429)^-19) / (0.0429)}] + [\$1,000 / {1 + 0.0429}^19]

= [\$40 * {0.5497 / 0.0429}] + [\$1,000 / 2.2206]

= [\$40 * 12.8177] + \$450.32

= \$512.71 + \$450.32 = \$963.03

Total Return = [P1 - P0 + Coupon] / P0

= [\$963.03 - \$900 + \$40] / \$900 = \$103.03 / \$900 = 0.1145, or 11.45%

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