Question

Consider a $1,000 par value bond with a 9% annual coupon. The bond pays interest annually. There are 20 years remaining until maturity. You have expectations that in 5 years the YTM on a 15-year bond with similar risk will be 7.5%. You plan to purchase the bond now and hold it for 5 years. Your required return on this bond is 10%. How much would you be willing to pay for this bond today

Answer 1

To determine the price you are willing to pay for the bond today, you must calculate the present value of the annual coupon payments for the next 5 years and the present value of the expected sale price in 5 years, all discounted at your required return of 10%.

Step-by-step explanation:

To price the bond you are considering purchasing today, we'll need to discount the cash flows from the bond (the annual coupon payments and the expected sale price in 5 years) back to the present using your required return of 10%. First, we calculate the present value of the annual coupon payments you would receive for the next 5 years. The bond has a 9% annual coupon on a $1,000 par value, which equals $90 per year. Next, we have to estimate the sale price of the bond in 5 years, assuming that the YTM will then be 7.5%. This is equivalent to finding the present value of the remaining cash flows (15 years of $90 coupons plus the $1,000 par value at maturity) discounted at the new YTM of 7.5%. Finally, we sum the present value of the 5 years' worth of coupon payments and the present value of the price we expect to sell the bond for after 5 years, both discounted at your required return of 10%.

To calculate this precisely requires use of the present value formula for an annuity and a complex calculation for the sale price in 5 years, which is beyond the scope of this explanation but is usually done using financial calculators or spreadsheet software.

Answer 2

The multiple choices are:

a. $1132

b. $1044

c. $ 962

d. $1153

e. $ 988

The correct option is C,$962

Step-by-step explanation:

The price a rational and prudent investor like me would be willing to pay for the bond today is the present worth of future cash inflows receivable from the bond issuer,which comprises of annual coupon interest and the face value at maturity.

=-pv(rate,nper,pmt,fv)

rate is required rate of return expected by investor of 10%

nper is 5 years since the investor intends to hold the bond for 5 years

pmt is the annual coupon interest=$1000*9%=$90

fv is the face value of $1000

=-pv(10%,5,90,1000)=$962.09

The current price is $962