Question

Consider a 30-year bond that has a face value of $10,000 and a coupon rate of 9% with quarterly coupon payments. The yield to maturity (YTM) of the bond is 4%.

a. What is the maximum price would you be willing to pay for this bond right now?

b. What is the maximum price would you be willing to pay for this bond right after its 14thcoupon payment?

c. What is the maximum price would you be willing to pay for this bond right after its 14thcoupon payment if YTM at the time is expected to be 11%?

Answer 1

a).

Current price of the bond is sum of PV of all coupons and face value.

Coupon = 2.25% of 10000 = $225 every quarter for a period of 30 years.

n = 30*4 = 120

YTM = 4%

Face value = $10000

using financial calculator,

with n=120

I/Y = 1%

FV = 10000

PMT = 225

we get PV = $18712.57

the maximum price for this bond right now = $18712.57

b).

after 14th coupon,

total period remaining = 120-14 = 106 quarters,

rest all same, PV using financial calculator = $18146.44

the maximum price for this bond right after its 14th coupon payment is $18146.44

c).

new YTM = 11%

so using I/Y = 11/4 = 2.75

n=106

we get from financial calculator, PV = $8284.33

the maximum price for this bond right after its 14th coupon payment when, YTM at the time is expected to be 11% is $8284.33