The Following Bonds Have A Par Value Of 1000 And The Required Rate O
The following bonds have a par value of $1,000 and the required rate of return is 10%. Bond XY: 5¼ percent coupon, with interest paid annually for 20 years Bond AB: 14 percent coupon, with interest paid annually for 20 years What is each bond's current market price? Bond XY Bond AB Rate 5% 14% Nper 20 20 PMT $47.50 $140.00 FV $1,000.00 $1,000.00 Type 0 0 PV ($1,000.00) ($1,000.00) If current interest rates are 9%, which bond would you expect to be called? Explain.
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The valuation of bonds involves calculating their current market prices based on coupon payments, face value, remaining periods, and current market interest rates. In this analysis, we evaluate two bonds—Bond XY and Bond AB—by determining their present values and assessing which bond might be called if interest rates decrease to 9%.
Initially, both bonds are described with a par value of $1,000, a maturity of 20 years, and interest payments derived from their coupon rates. Bond XY offers a 5¼ percent coupon rate, translating into annual coupon payments of $47.50, while Bond AB has a 14 percent coupon, resulting in annual payments of $140. Assume a required rate of return of 10%, which, when used as the discount rate, yields the current market prices of about $1,000 for both bonds. This reflects that at a 10% discount rate, both bonds are valued close to their par value, indicating they are fairly priced under the initial rate assumption.
The calculation of each bond's present value (PV) employs standard bond valuation formulas, which discount each coupon payment and the face value to today's dollars. The present value of an bond is the sum of the present values of all future coupons plus the present value of the face value. Using the formula:
PV = (PMT × [1 - (1 + r)^-n] / r) + (FV / (1 + r)^n)
where:
- PMT is the annual coupon payment, - r is the discount rate or yield, - n is the total number of periods,
- FV is the face value.
For Bond XY:
- Coupon rate: 5.25%
- PMT: $47.50
- n: 20 years
- FV: $1,000
- Discount rate: 9% (current market interest rate)
Calculations show that with a lower current rate (9%) than the coupon rate (5.25%), Bond XY’s market price would rise above its face value, indicating a premium. Conversely, for Bond AB:
- Coupon rate: 14%
- PMT: $140
- n: 20 years
- FV: $1,000
- Discount rate: 9%
Since the coupon rate exceeds the prevailing market rate of 9%, Bond AB would also be valued above face value, but the degree differs.
Adjusting for the lower market interest rate (9%), the premium on Bond XY would be less pronounced because its fixed coupon rate is relatively low, offering less attraction compared to current rates. Bond AB’s coupon rate exceeds the current market rate significantly, making it even more attractive and likely to trade at a substantial premium.
Regarding the callability of bonds, issuers typically call or redeem bonds when interest rates decline, allowing them to refinance at lower rates. The bond most likely to be called is the one offering the higher coupon rate, which in this case is Bond AB with 14%. Since current interest rates are now 9%, significantly lower than the coupon rate on Bond AB, the issuer has an economic incentive to call this bond to reissue debt at a lower cost, thus saving interest expenses in the future. By calling the higher-coupon bond, the issuer can replace the existing debt with new bonds issued at current lower interest rates, reducing their overall debt servicing costs.
In conclusion, although both bonds would have increased market values due to the decrease in market
interest rates from the original required rate of 10%, Bond AB, with its higher coupon, would be more attractive for redemption. The issuer would likely call Bond AB to exploit the lower current interest environment, confirming that bonds with higher coupons are more probable to be called when interest rates fall below their coupon rates (Mishkin & Eakins, 2018).
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