Question

Assets, Inc., plans to Issue $7 million of bonds with a coupon rate of 10 percent, a par value of $1,000, semiannual coupons, and 15 years to maturity. The current market Interest rate on these bonds is 9 percent. In one year, the Interest rate on the bonds will be either 12 percent or 6 percent with equal probability. Assume Investors are risk- neutral. 0.5 points 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.) Price of the bonds Print References b. b. If the bonds are callable one year from today at $1,060, will their price be greater or less than the price you computed In part (a)?

a. Lesser b. Greater

Answer 1

Answer: To calculate the price of the bonds today, we can use the present value of future cash flows. Given that the bonds have a coupon rate of 10%, a par value of $1,000, semiannual coupons, and 15 years to maturity, we can break down the calculation into several steps.

Step 1: Calculate the coupon payment:

The coupon payment is the coupon rate multiplied by the par value, divided by the number of periods per year:

Coupon Payment = (Coupon Rate × Par Value) / 2

Coupon Payment = (0.10 × $1,000) / 2

Coupon Payment = $50

Step 2: Determine the discount rate:

The discount rate is the current market interest rate. In this case, it is 9% or 0.09.

Step 3: Calculate the present value of the coupon payments:

Since the bonds have semiannual coupons, we need to calculate the present value of 30 coupon payments (15 years × 2 semiannual periods per year):

Present Value of Coupon Payments = Coupon Payment × [1 - (1 + Discount Rate)^(-Number of Periods)] / Discount Rate

Present Value of Coupon Payments = $50 × [1 - (1 + 0.09)^(-30)] / 0.09

Step 4: Calculate the present value of the face value:

Since the bonds have a par value of $1,000, we need to calculate the present value of the face value at maturity:

Present Value of Face Value = Par Value / (1 + Discount Rate)^(Number of Periods)

Present Value of Face Value = $1,000 / (1 + 0.09)^(30)

Step 5: Calculate the price of the bonds today:

The price of the bonds today is the sum of the present value of coupon payments and the present value of the face value:

Price of the Bonds = Present Value of Coupon Payments + Present Value of Face Value

By plugging in the values and performing the calculations, we can determine the price of the bonds today.

Regarding part (b), if the bonds are callable one year from today at $1,060, the price of the bonds will be lower than the price computed in part (a) because the option to call the bonds gives an advantage to the issuer. The callable feature allows the issuer to redeem the bonds before maturity if it becomes favorable for them to do so, which reduces the value of the bond to the investor.

Please note that the precise calculations involve more steps and specific assumptions that may not be provided in the given information.

Step-by-step explanation: