MACROECON MAJORS HELp!!!what is the highest price someone will be willing to pay for your bond?

Question

Suppose that you purchase a 3-year government bond with a principal amount of $1,000 and a coupon rate of 4%. Coupons are paid at the end of each year.

Suppose that after two years you decide to sell your bond in the used bond market. If the prevailing market interest rate is 5%, what is the highest price someone will be willing to pay for your bond? Round to two decimal places.

A. $40.00

B. $990.48

C. $1,000.00

D. $1,009.62

Suppose that instead of waiting two years to sell the bond, you decide to sell the bond after one year, at which point the prevailing market interest rate is again 5%. What is the highest price that someone will be willing to pay for your bond? Round to two decimal places.

A. $1,000.00

B. $990.48

C. $1,040.00

D. $981.41

Answer 1

The correct answer in the first cases is : B. $990.48

In the first case: At the ernd of the  third year, the buyer of the  old bond will get $1040. This is approximately equal to what he would have got by investing $990.48 at the new market rate of interest of 5% ($990.48 + 5% of $990.48 = $990.48 + $49.70 = $1040.18) at the end of the third year..

In the second case, the purchaser of the old bond will get  $40 from at the end of second year and $1040 at the end of the third year. To determine the price of the used bond at the end of first year trherefore we have to equate the price of the bond to the present value of the two cash flows of $40 after one year and $1040 after two years discounted at an interest of 5%. This is approximately equalt to $981.41. So the correct answer in the second case is:

D. $981.41

Answer 2

Simplest NPV method should be used in both cases taking into account relevant number of year till due.

1:

B. $990.48

Solution is simple: 1000*1.04/1.05=990.4762 ≈990.48

2:

D. $981.41

Solution: 1000*1.04²/1.05² ≈ 981

Answer 3

First question is B, since the prevailing rate is higher than the coupon rate, you'll have to discount it.

Since you are tying up the money in a below market coupon bond for two years instead of one, you'll have to discount a bit more, so the answer will be close to but less than the answer in the first question, or D in this case.