| Assets, Incorporated, plans to issue $6 million of bonds with a coupon rate of 7.9 percent, a par value of $1,000, semiannual coupons, and 30 years to maturity. The current market interest rate on these bonds is 7.4 percent. In one year, the interest rate on the bonds will be either 8 percent or 5 percent with equal probability. Assume investors are risk-neutral. |
| a. | If the bonds are noncallable, what is the price of the bonds today? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) |
To calculate the price of the noncallable bonds issued by Assets, Incorporated, we can use the concept of present value. The price of a bond is the present value of its future cash flows, which include both the coupon payments and the par value at maturity. In this case, the bonds have the following characteristics:
1. Face Value (Par Value) of the Bond (FV) = $1,000
2. Coupon Rate (CR) = 7.9%
3. Semiannual Coupons
4. Maturity Period (n) = 30 years, which means 60 periods (since coupons are semiannual)
First, we need to calculate the semiannual coupon payment:
Coupon Payment (CP) = (Coupon Rate * Face Value) / 2
CP = (7.9% * $1,000) / 2
CP = $39.50
Next, we need to determine the discount rate to use for present value calculations. Since the current market interest rate is 7.4%, we’ll use this rate for the first year.
Using the present value of an annuity formula, we can calculate the present value of the coupon payments over the first year:
PV(Coupons Year 1) = CP / (1 + Market Interest Rate/2) + CP / (1 + Market Interest Rate/2)^2
PV(Coupons Year 1) = $39.50 / (1 + 0.074/2) + $39.50 / (1 + 0.074/2)^2
PV(Coupons Year 1) ≈ $73.50
Now, we need to calculate the present value of the par value at maturity (assuming the bonds are held to maturity). We’ll use the market interest rate for this calculation because it’s beyond the first year, and we need to consider the possibility of different interest rates in the future.
PV(Par Value) = $1,000 / (1 + Market Interest Rate/2)^60
PV(Par Value) ≈ $218.84
Now, we can calculate the total present value of the bond:
Total Present Value = PV(Coupons Year 1) + PV(Par Value)
Total Present Value ≈ $73.50 + $218.84
Total Present Value ≈ $292.34
So, the price of the noncallable bonds today is approximately $292.34 when the current market interest rate is 7.4 percent.
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