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West Corp. issued 10-year bonds two years ago at a coupon rate of 8.1 percent. The bonds make semiannual payments. If these bonds currently sell for 102 percent of par value, what is the YTM? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

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Answer:

7.82%

Explanation:

Given the following :

Par value = 102%

Coupon rate = 8.1%

Period (n) = 10 years

Yield to maturity (YTM) =?

with a face value (F) of $1000

The current price (P) of bond will be:

102% * $1000 = (1.02 * $1000) = $1020

Annual coupon payment = $1000 * 8.1% = $1000 * 0.081 = $81

The YTM formula is given by:

YTM = [ C +( F - P) / n] / [(F + P) / 2)]

YTM= [(81 + (1000 - 1020) / 10] / [(1000 + 1020)/2)]

YTM = [(81 +(-20/10)] / (2020/2)

YTM = [(81 - 2) / 1010]

YTM = 79 / 1010

YTM = 0.078217

YTM =0.078217 * 100

YTM = 7.82%

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