Question

Assume that you are considering the purchase of a $1,000 par value bond that pays interest of $70 each six months and has 10 years to go before it matures. If you buy this bond, you expect to hold it for 5 years and then to sell it in the market. You (and other investors) currently require a nominal annual rate of 16 percent, but you expect the market to require a nominal rate of only 12 percent when you sell the bond due to a general decline in interest rates. How much should you be willing to pay for this bond? $966.99

Answer 1

To calculate the value of the bond, you use the present value formula to discount the future cash flows and find the present value. In this case, the present value of the bond is approximately $966.99.

Step-by-step explanation:

When deciding how much you should be willing to pay for the bond, you need to consider the future cash flows from the bond and the required rate of return. Given that the bond pays $70 in interest every six months and matures in 10 years, you will receive 20 interest payments over the holding period. Additionally, at the end of the holding period, you will receive the final interest payment and the par value of $1,000. To calculate the present value of these cash flows, you can use the formula:

PV = (C/r) * (1 - (1 + r)^(-n)) + (F/(1 + r)^n),

Where:

• PV is the present value of the bond,
• C is the coupon payment,
• r is the required rate of return (in your case, 16% or 0.16),
• n is the number of periods remaining until maturity, and
• F is the par value of the bond.

Plugging in the values, you will find that the present value of the bond is approximately $966.99. Therefore, you should be willing to pay $966.99 for this bond.