Question

​(Bond valuation​) Flora​ Co.'s bonds, maturing in 9 ​years, pay 7 percent interest on a $1,000 face value.​ However, interest is paid semiannually. If your required rate of return is 9 percent, what is the value of the​ bond? How would your answer change if the interest were paid​ annually?

a. If the interest is paid​ semiannually, the value of the bond is ​$ . ​(Round to the nearest​ cent.)

Answer 1

a. The value of the bond is computed as shown below:

Coupon payment is computed as follows:

= 7% / 2 x $ 1,000 (since interest payments are semi annually, hence divided by 2)

= $ 35

YTM will be as follows:

= 9% / 2 (since interest payments are semi annually, hence divided by 2)

= 4.5% or 0.045

N will be as follows:

= 9 x 2 (since interest payments are semi annually, hence multiplied by 2)

= 18

So the price of the bond will be:

= $ 35 / 1.045¹ + $ 35 / 1.045² + $ 35 / 1.045³ + $ 35 / 1.045⁴ + $ 35 / 1.045⁵ + $ 35 / 1.045⁶ + $ 35 / 1.045⁷ + $ 35 / 1.045⁸ + $ 35 / 1.045⁹ + $ 35 / 1.045¹⁰ + $ 35 / 1.045¹¹ + $ 35 / 1.045¹² + $ 35 / 1.045¹³ + $ 35 / 1.045¹⁴ + $ 35 / 1.045¹⁵ + $ 35 / 1.045¹⁶ + $ 35 / 1.045¹⁷ + $ 35 / 1.045¹⁸ + $ 1,000 / 1.045¹⁸

= $ 878.40 Approximately

b. The value of the bond is computed as shown below:

Coupon payment is computed as follows:

= 7% x $ 1,000

= $ 70

YTM will be as follows:

= 9% or 0.09

N will be as follows:

= 9

So the price of the bond will be:

= $ 70 / 1.09¹ + $ 70 / 1.09² + $ 70 / 1.09³ + $ 70 / 1.09⁴ + $ 70 / 1.09⁵ + $ 70 / 1.09⁶ + $ 70 / 1.09⁷ + $ 70 / 1.09⁸ + $ 70 / 1.09⁹ + $ 1,000 / 1.09⁹

= $ 880.10 Approximately

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