Question

Problem #5: A 10-year bond has face value (redemption value) $450,000 and quarterly coupons of 2.5%. Consider the time right after the 12th coupon has been paid, when the yield is 4.4%. (a) What is the price of the bond? (b) Compute the price of the bond if the yield were to increase by 1 basis point (a basis point is 1/100 of 1%). What is the absolute value of the difference between that price, and your answer to part a)? (c) Would the yield have to increase or decrease in order for the bond to increase in value by $1261.38? (d) Based only on your answer to b), approximately how many basis points (bp) would the yield have to move in order for the bond to increase in value by $1261.38? (Answer as a positive integer.)

Answer 1

a.

Calculating Price of Bond,

Using TVM Calculation,

PV = [FV = 450,000, PMT = 11,250, N = 28, I = 0.044/4]

PV = $601,112.80

b.

Calculating Price after 1 BP change in Yield,

Using TVM Calculation,

PV = [FV = 450,000, PMT = 11,250, N = 28, I = 0.0441/4]

PV = $600,791.54

c.

As bond price is inversely proportional to change in interest rates, so interest rate needs to be decreased for bond price to increase.

d.

New Bond Price = 601,112.80 + 1,261.38 = $602,374.18

Calculating Yield,

Using TVM Calculation,

I = [PV = -602,374.18, FV = 450,000, N = 28, PMT = 11,250]

I = 4.36%