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 simple annual rate of 16 percent,but you expect the market to require a 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?
A) $842.00
B) $1,115.81
C) $1,359.26
D) $966.99
E) $731.85

Question

Quizplus · Accepted Answer

We can begin by calculating the present value of the bond, which is the sum of the present values of its future cash flows (interest payments and principal repayment). Since the bond pays semi-annual interest of $70, the present value of each interest payment can be calculated using:

PV = C / (1 + r/n)^(n*t)
where C is the cash flow ($70), r is the annual interest rate (16% or 0.16), n is the number of compounding periods per year (2 for semi-annual payments), and t is the time in years. For the first interest payment:

PV1 = 70 / (1 + 0.16/2)^(2*0.5)
    = 61.13

Similarly, for the second interest payment:

PV2 = 70 / (1 + 0.16/2)^(2*1)
    = 53.34

And so on, for a total of 20 interest payments (10 years * 2 payments per year). The present value of the principal payment can be calculated as:

PVp = 1000 / (1 + 0.16/2)^(2*10)
    = 322.61

Therefore, the total present value of the bond is:

PVB = PV1 + PV2 + ... + PV20 + PVp
    = 61.13 + 53.34 + ... + 14.87 + 322.61
    = 947.98

This represents the fair price of the bond if the market requires a simple annual rate of 16%. However, we expect the market to require only 12% when we sell the bond in 5 years. We can calculate the future value of the bond at that time using:

FV = PVB * (1 + r)^(n*t)
where r is the interest rate (12%), n is the number of compounding periods per year (2), and t is the time in years (5). Therefore:

FV = 947.98 * (1 + 0.12/2)^(2*5)
   = 1,359.26

This represents the amount we expect to receive when we sell the bond in 5 years. To find the present value of this future cash flow, we can discount it back to the present using the 12% rate:

PV = FV / (1 + r)^t
   = 1,359.26 / (1 + 0.12)^5
   = 731.85

Therefore, the maximum price we should be willing to pay for the bond is $731.85. The closest answer choice is D, which is the correct answer.

Assume That You Are Considering the Purchase of a $1,000