Question

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A 9.5 percent semiannual coupon bond matures in 7 years. The bond has a face value...

A 9.5 percent semiannual coupon bond matures in 7 years. The bond has a face value of $1,000 and a current yield (CY) of 9.77 percent. What is the bond’s yield to maturity (YTM)?

a.

9.77%
b.

5.23%
c.

10.46%
d.

9.50%
e.

10.06%

Solutions

Expert Solution

Current yield = Annual coupon / Bond price

9.77% = (9.50% * 1000) / Bond price

Bond price = 95 / 9.77%

= 972.36

The YTM of the bond can be calculated with the help of Rate function of Excel

Inputs:

PV = 972.36

Coupon (PMT) = 1000 * 9.50%/2 = 47.50

FV = 1000

Nper = 7 * 2 = 14

The Rate function looks as follows in Excel:

=RATE(14,47.5,-972.36,1000,0,0.1)

= 0.0503

The above calculated rate represents semi annual yield

Annual YTM = Semi annual YTM * 2

= 0.0503 * 2 = 0.1006

= 10.06%

Correct choice E

jeff jeffy answered 2 years ago
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