Question

Consider two corporate bonds. Both bonds pay annual interest and have face values of $1000. Bond X matures in 10 years, has 5% annual coupons and currently has 5% YTM. Bond Y matures in 15 years, had 5% annual coupons, and currently had 5% YTM. If the market rate of interest drops unexpectedly to 4%, what will happen to the prices of the bonds?

A. The price of both bonds will rise by the same dollar

B. The price of both bonds will rise and Bond X will rise by a larger amount

C. The price of both bonds will rise and Bond Y will rise by a larger amount

D. The price of both bonds will rise but only one of them will rise above $1000

Answer 1

Answer : Correct Option is (C.) The price of both bonds will rise and Bond Y will rise by a larger amount

Reason :

Calculation of Price of Bond before market rate of interest drops

Price of Bond X will be 1000 as the coupon rate and market interest rate both are equal because when the coupon rate and market interest rate are equal price of the bond will be equal to its face value.

Price of Bond Y will also be 1000 as the coupon rate and market interest rate both are equal because when the coupon rate and market interest rate are equal price of the bond will be equal to its face value.

Calculation of Price of Bond X when market interest drops to 4 % :

Price of the bond can be calculated using PV function of Excel

=PV(rate,nper,pmt,fv)

where

rate is the market rate of interest i.e 4%

nper is the number of years to maturity i.e 10

pmt is the annual coupon payment i.e 50 (1000 * 5%)

fv is the face value i.e 1000

=PV(4%,10,-50,-1000)

The price of Bond X will be 1081.11

Rise in Price = $1081.11 - $1000 = $81.11

Calculation of Price of Bond Y when market interest drops to 4 % :

Price of the bond can be calculated using PV function of Excel

=PV(rate,nper,pmt,fv)

where

rate is the market rate of interest i.e 4%

nper is the number of years to maturity i.e 15

pmt is the annual coupon payment i.e 50 (1000 * 5%)

fv is the face value i.e 1000

=PV(4%,15,-50,-1000)

The price of Bond Y will be 1111.81

Rise in Price = $1111.81 - $1000 = $111.81

Therefore The price of both bonds will rise and Bond Y will rise by a larger amount