Question

You are evaluating two similar bonds. Both mature in four years, both have a K1,000 par value, and both pay a coupon rate of 10 percent. However, one bond pays that coupon in annual installments, whereas the other makes semiannual payments. Suppose you require a 10 percent return on either bond. Should these bonds sell at identical prices or should one be worth more than the other? What prices do you obtain for these bonds? Can you explain the apparent paradox?

Answer 1

We shall compute the present value of both bonds as follows:

Bond one present value is computed as shown below:

= K100 / 1.10¹ + K100 / 1.10² + K100 / 1.10³ + K100 / 1.10⁴ + K1,000 / 1.10⁴

= K1,000

Bond two present value is computed as shown below:

Coupon payments will be:

= K1,000 x 10% / 2

= K50

N = 4 x 2

= 8

YTM = 10% / 2

= 5%

= K50 / 1.05¹ + K50 / 1.05² + K50 / 1.05³ + K50 / 1.05⁴ + K50 / 1.05⁵ + K50 / 1.05⁶ + K50 / 1.05⁷ + K50 / 1.05⁸ + K1,000 / 1.05⁸  

= K1,000

As we can see that both these bonds sells at identical prices irrespective of the fact that whether the coupon payments are being made annually or semi annually

This concludes that whenever the bond's coupon rate is equal to the bond's yield to maturity, it will always be equal to its par value.

Feel free to ask in case of any query relating to this question