Question

A $1000 bond with a coupon rate of 6.2% paid semi annually has eight years to maturity and a yield to maturity of 8.3%. If interest rates rise and the yield to maturity increases to 8.6% what will happen to the price of the bond?
A) the price of the bond will rise by $15.78,

B) the price of the bond will fall by $18.93,

C) the price of the bond will fall by $15.78,

D) the price of the bond will not change

Answer 1

Answer:

Correct option is (C)

Explanation:

Given:

Face value of bond (FV) = $1,000

Coupon rate = 6.2% annual and 6.2 / 2 = 3.1% semi annual

Coupon payment (pmt) = 0.031 × 1,000 = $31

Maturity period (nper) = 8×2 = 16 periods

Rate = 8.3% annual or 8.3 / 2 = 4.15%

Present value of bond can be computed using spreadsheet function =PV(rate,nper,pmt,FV)

Present value of bond when yield is 8.3% is $878.99

If ytm increases to 8.6% annual or 8.6 / 2 = 4.3% semi annual, then present value of bond will be $863.22 (using spreadsheet function again)

It can be seen that as ytm increased from 8.3% to 8.6%, price of bond fell by $15.77 approximately (878.99 - 863.22)