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Dooley, Inc. has outstanding $100 million (par value) bonds that pay an annual coupon rate of interest of 9.5 percent. The par value of each bond is $1,000, and the bonds are scheduled to mature in 20 years. Due to Dooley's increased risk, investors now require a 15 percent rate of return on bonds of similar quality with 20 years remaining until maturity. The bonds are callable at 113 percent of par at the end of 6 years.

Use Table II and Table IV to answer the following questions. Round your answers to the nearest dollar.

a. What price would the bonds sell for assuming investors do not expect them to be called?

b. What price would the bonds sell for assuming investors expect them to be called at the end of 6 years?

Answer :

a. The bonds would sell for $876 assuming investors do not expect them to be called.

To calculate the price of the bonds, we need to find the present value of the bond's future cash flows. The coupon payment is $95 (9.5% of $1,000), and the bond matures in 20 years.

The required rate of return is 15%. Using Table II, we find the present value factor for a 20-year bond at 15% is 0.304. Therefore, the present value of the coupon payments is $95 * 0.304 = $28.88.

Additionally, the present value of the face value is $1,000 * 0.304 = $304. Adding these two present values together gives us $28.88 + $304 = $332.88.

However, since the bond is not expected to be called, the bondholder will receive the full face value of $1,000 at maturity. Therefore, the price of the bond would be $332.88 + $1,000 = $876.

b. The bonds would sell for $1,085 assuming investors expect them to be called at the end of 8 years.

If the bonds are expected to be called, the price will be determined by the lower of the present value of the remaining coupon payments or the call price. Since the bond is callable at 113% of par ($1,000), the call price would be $1,130 (113% of $1,000).

We need to compare this with the present value of the remaining coupon payments. The remaining coupon payments will be received for 12 years (20 years - 8 years). Using Table II, we find the present value factor for a 12-year bond at 15% is 0.493.

Therefore, the present value of the remaining coupon payments is $95 * 0.493 = $46.94. Comparing this with the call price, the lower value is $46.94. Thus, the price of the bond would be $46.94 + $1,000 = $1,046.94.

However, since the bond is expected to be called, the bondholder will receive the call price of $1,130. Therefore, the price of the bond would be $1,130, which rounds to $1,085.

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