Question

Assuming that the current interest rate is 6 percent, compute the present value of a five-year, 5 percent coupon bond with a face value of $1,000. What happens when the interest rate goes to 7 percent? What happens when the interest rate goes to 5 percent?

Answer 1

PV when interest rate is 6% = $957.88

PV when interest rate is 7%= $918

PV when interest rate is 5%= $1,000

Step-by-step explanation:

The price of a bond is equivalent to the present value of all the cash flows that are likely to accrue to an investor once the bond is bought. These cash-flows are the periodic coupon payments that are to be paid annually and the par value of the bond that will be paid at the end of 5 years.

During the 5 years, there are 5 equal periodic coupon payments that will be made. Given a par value equal to $1,000, in each year, and a coupon rate equal to 5% the annual coupon paid will be = $50. This stream of cash-flows is an ordinary annuity.

The PV of the cash-flows = PV of the coupon payments + PV of the par value of the bond

Assuming the current interest rate is 6 percent

PV =50*PV Annuity Factor for 5 periods at 6%+ $1,000* PV Interest factor with i=6% and n =5

=
`50*([1-(1+0.06)^-^5])/(0.06)+ (1,000)/((1+0.06)^5)` = $957.88

The bond sells at a discount.

Assuming the current interest rate is 7 percent

PV =50*PV Annuity Factor for 5 periods at 7%+ $1,000* PV Interest factor with i=7% and n =5

=
`50*([1-(1+0.07)^-^5])/(0.07)+ (1,000)/((1+0.07)^5)` = $918

The bond sells at a discount.

Assuming the current interest rate is 5 percent

PV =50*PV Annuity Factor for 5 periods at 5%+ $1,000* PV Interest factor with i=5% and n =5

=
`50*([1-(1+0.05)^-^5])/(0.05)+ (1,000)/((1+0.05)^5)` = $1,000

The bond sells at par