You are considering buying a 10-year, $1,000 par value bond issued by IBM. The coupon rate is 8% annually, with interest being paid semiannually. If you expect to earn a 10% rate of return on this bond, what is the maximum price you should be willing to pay for this IBM bond?

Question

Quizplus · Accepted Answer

To find the maximum price you should be willing to pay for the bond, you need to calculate its present value given the desired rate of return (yield to maturity) of 10%. The bond pays semiannual interest, so the coupon payment is $40 ($1,000 * 8% / 2), and the yield per period is 5% (10% / 2). The bond has 20 periods (10 years * 2). The present value of the bond is the sum of the present value of the annuity (coupon payments) and the present value of the par value ($1,000) received at maturity. Using the present value formula for an annuity and the present value formula for a lump sum, the calculation is as follows:$$ PV = \frac{C}{r} \left(1 - \frac{1}{(1 + r)^n}\right) + \frac{F}{(1 + r)^n} $$Where:- $PV$ = present value of the bond- $C$ = semiannual coupon payment = $40- $r$ = semiannual yield = 5% or 0.05- $n$ = total number of periods = 20- $F$ = face value of the bond = $1,000$$ PV = \frac{40}{0.05} \left(1 - \frac{1}{(1 + 0.05)^{20}}\right) + \frac{1000}{(1 + 0.05)^{20}} $$$$ PV \approx 875.39 $$Therefore, the maximum price you should be willing to pay for the bond, given a 10% desired rate of return, is approximately $875.39.

You Are Considering Buying a 10-Year, $1,000 Par Value Bond