Suppose Hillard Manufacturing sold an issue of bonds with a 10-year maturity, a $1,000 par value,...

Suppose Hillard Manufacturing sold an issue of bonds with a 10-year maturity, a $1,000 par value, a 10% coupon rate, and semiannual interest payments.

a) Two years after the bonds were issued, the going rate of interest on bonds such as these fell to 7%. At what price would the bonds sell? Round the answer to the nearest cent.

b) Suppose that 2 years after the initial offering, the going interest rate had risen to 13%. At what price would the bonds sell? Round the answer to the nearest cent.

c) Suppose that 2 years after the issue date (as in Part a) interest rates fell to 7%. Suppose further that the interest rate remained at 7% for the next 8 years. What would happen to the price of the bonds over time? I. The price of the bond will remain the same. II. The price of the bond will rise, approaching $1,000 at the maturity date. III. The price of the bond will decline, approaching $1,000 at the maturity date.

Solutions

Expert Solution

Price of a bond is presenty value of all cash flows associated with the bond (namely coupons and face value) discounted at market interest rate. It is mathematically represented as:

where P is the price of bond with periodic coupon C, periodic market interest rate i, M as face value and n as periods to maturity.

a) We need to calculate P, when, interest rate = 7%

M = $1,000; C = $100 per year = $50 per semi-annual period, i = 7% per year = 3.5% per semi-annual period, n = 8 years = 16 semi-annual periods.

P = $1,181.4 --> Current price of bond. Bond trading at premium.

a) We need to calculate P, when, interest rate = 13%

M = $1,000; C = $100 per year = $50 per semi-annual period, i = 13% per year = 6.5% per semi-annual period, n = 8 years = 16 semi-annual periods.

P = $853.5 --> Current price of bond. Bond trading at discount.

c) Answer is iii. The price of the bond will decline, approaching $1,000 at the maturity date.

The price of a bond always approaches its par value with maturity, if the market interest rates remain constant. If the bond is trading at premium, bond price will decline to reach par value at maturity. If a bond is trading at discount, bond price will rise to reach par value at maturity.

jeff jeffy answered 1 year ago

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