Question

Arjay purchases a bond, newly issued by Amalgamated Corporation, for $12,000. The bond pays $600 to its holder at the end of the first few years and pays $12,600 upon its maturity at the end of the 3 years. a. What are the principal amount, the term, the coupon rate, and the coupon payment for Arjay's bond? Instructions: Enter your responses as whole numbers. Principal amount: \$ Term: years Coupon rate: % Coupon payment: \$ b. After receiving the second coupon payment (at the end of the second year), Arjay decides to sell his bond in the bond market. What price can he expect for his bond if the one-year interest rate at that time is 3 percent? 8 percent? 10 percent? Instructions: Enter your responses as whole numbers. Expected price for the bond at: 3 percent: $ 8 percent: $ 10 percent: $

Answer 1

a. Principal amount: $12,000

Term: 3 years

Coupon rate: 5%

Coupon payment: $600

b. When the one-year interest rate is 3%, Arjay can expect the bond to be priced at approximately $12,527. At an 8% one-year interest rate, the expected bond price would be approximately $11,757. For a 10% one-year interest rate, the expected price would be approximately $11,578.

Step-by-step explanation:

a. The principal amount of Arjay's bond is the amount he paid initially, which is $12,000. The bond's term is 3 years, signifying the duration until maturity. The coupon rate, calculated as the annual coupon payment divided by the principal amount, is 5%. The coupon payment, which is the periodic interest payment the bondholder receives, is $600, calculated as 5% of $12,000.

b. To calculate the bond price under different one-year interest rates, we use the bond pricing formula. At a 3% one-year interest rate, the expected bond price is approximately $12,527. When the one-year interest rate rises to 8%, the bond's expected price drops to about $11,757. At a higher one-year interest rate of 10%, the bond price further decreases to around $11,578. These calculations involve discounting the future cash flows (coupon payments and face value) at the respective interest rates to find the present value of the bond.

The bond price moves inversely to prevailing interest rates; as interest rates increase, bond prices tend to decrease, and vice versa. When the one-year interest rates rise, the bond's fixed coupon payments become less attractive relative to the higher rates available in the market, causing the bond price to decline to align with the market's new interest rate.