Question

Arjay purchases a bond, newly issued by Amalgamated Corporation for $1000. The bond pays $60 to its holder at the end of the first and second years and pays $1060 upon its maturity at the end of the third year.

Principal amount $1000

Term 3 years

Coupon rate 6%
Coupon payment $60

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?

What are the expected prices for the bond at:

1. 3% $
2. 8% $
3. 10% $

Answer 1

The expected sale price of Arjay's bond after receiving the second coupon payment depends on the market interest rate, with calculations showing expected prices of $1,029.13 at 3%, $981.48 at 8%, and $963.64 at 10%.

Step-by-step explanation:

Arjay can expect different prices for his bond at the end of the second year depending on the current market interest rates. To calculate the expected price of the bond, we use the present value of future cash flows, which includes the final coupon payment and the principal repayment. The formula to calculate present value (PV) is PV = Cash Flow / (1 + r)^n, where r represents the market interest rate, and n represents the number of periods until the cash flow will be received.

• At a market interest rate of 3%, the bond's expected payment one year from now is $1,060. The price can be estimated as $1,060 / (1 + 0.03) = $1,029.13.
• At a market interest rate of 8%, the expected price would be $1,060 / (1 + 0.08) = $981.48.
• At a market interest rate of 10%, the expected price would be $1,060 / (1 + 0.10) = $963.64.

If the bond's interest rate is lower than the market interest rate, the bond will generally sell for less than its face value, as investors can find more attractive rates elsewhere. The formula provided assists in calculating the discounted value of the bond's expected payments to determine its current sale price in the market.