Question

Suppose you have purchased a 30-year, 4.99% coupon bond pays interest annually. The bond has a face value of $1,000. What is the change in the price of this bond if the market yield to maturity declines to 5.15% from the current rate of 5.90%? Please show all the calculations by which you came up with the final answer. Why did the 30-year bond price change? Please explain your reasoning.

Answer 1

Case 1

Nper = 30 years

Face value (FV) = 1000

Annual coupon(PMT) = 4.99% * 1000 = $ 49.9

YTM of the bond(rate) = 5.9%

Price of the bond(PV) =
=pv(5.9%,30,49.9,1000 PV(rate, nper, pmt, [fv], [type])
= $ 873.39

Case 2

Rate = 5.15%

Price of the bond (PV) =
=PV(5.15%,30,49.9,1000) PV (rate, nper, pmt, [fv], [type])
= $ 975.82

Change in Price = $ 975.82 - $ 873.39 = $ 102.43

Bond Prices are inversely proportional to its yield to maturity ie when YTM increases, the price decreases and when YTM decreases, Price increases. In other words, the Price of the bond is the future cash flows provided by the bond to its investors discounted at the YTM rate.