Question

Whatever, Inc., has a bond outstanding with a coupon rate of 5.75 percent and semiannual payments. The yield to maturity is 4.7 percent and the bond matures in 22 years. What is the market price if the bond has a par value of $1,000?

Multiple Choice

• $1,142.07

• $1,144.77

• $1,143.01

• $1,146.28

• $1,165.87

Answer 1

The market price of the bond is computed as shown below:

Coupon payment is computed as follows:

= 5.75% / 2 x $ 1,000

= $ 28.75

YTM will be as follows:

= 4.7% / 2

= 2.35%

N will be

= 22 x 2

= 44

So the market price will be as follows:

= $ 28.75 / 1.0235¹ + $ 28.75 / 1.0235² + $ 28.75 / 1.0235³ + $ 28.75 / 1.0235⁴ + $ 28.75 / 1.0235⁵ + $ 28.75 / 1.0235⁶ + $ 28.75 / 1.0235⁷ + $ 28.75 / 1.0235⁸ + $ 28.75 / 1.0235⁹ + $ 28.75 / 1.0235¹⁰ + $ 28.75 / 1.0235¹¹ + $ 28.75 / 1.0235¹² + $ 28.75 / 1.0235¹³ + $ 28.75 / 1.0235¹⁴ + $ 28.75 / 1.0235¹⁵ + $ 28.75 / 1.0235¹⁶ + $ 28.75 / 1.0235¹⁷ + $ 28.75 / 1.0235¹⁸ + $ 28.75 / 1.0235¹⁹ + $ 28.75 / 1.0235²⁰ + $ 28.75 / 1.0235²¹ + $ 28.75 / 1.0235²² + $ 28.75 / 1.0235²³ + $ 28.75 / 1.0235²⁴ + $ 28.75 / 1.0235²⁵ + $ 28.75 / 1.0235²⁶ + $ 28.75 / 1.0235²⁷ + $ 28.75 / 1.0235²⁸ + $ 28.75 / 1.0235²⁹ + $ 28.75 / 1.0235³⁰ + $ 28.75 / 1.0235³¹ + $ 28.75 / 1.0235³² + $ 28.75 / 1.0235³³ + $ 28.75 / 1.0235³⁴ + $ 28.75 / 1.0235³⁵ + $ 28.75 / 1.0235³⁶ + $ 28.75 / 1.0235³⁷ + $ 28.75 / 1.0235³⁸ + $ 28.75 / 1.0235³⁹ + $ 28.75 / 1.0235⁴⁰ + $ 28.75 / 1.0235⁴¹ + $ 28.75 / 1.0235⁴² + $ 28.75 / 1.0235⁴³ + $ 28.75 / 1.0235⁴⁴ + $ 1,000 / 1.0235⁴⁴

= $ 1,143.01 Approximately

So the correct answer is option of $ 1,143.01

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