Question

GEM, Inc., has two bonds outstanding in the market. Both Bond X and Bond Y have 7 percent coupons, make semiannual payments, and are priced at par value. Bond X has 20 years to maturity, whereas Bond Y has 5 years to maturity.

1. If interest rates suddenly rise by 2 percent (percentage points), what is the percentage change in the price of the two bonds?

2. If rates were to suddenly fall by 2 percent (percentage points) instead, what would be the percentage change in the price of the two bonds?

USING EXCEL FORMULAS PLEASE

Answer 1

Bond X

When coupon rate and market interest rate is same, the current price of bond and face value is same

Years to maturity * semi annual frequency 20 * 2 = 40 (n or NPER)

Semi annual Coupon payment (PMT) = 1000 * (7% / 2) = 35

A rise of 2% percent would mean 7% + 2% = 9%; semi annual rate or r is (9%/ 2)

You can use the PV function in excel to find the bond price

PV(rate,NPER,PMT,FV,TYPE)

PV(9%/2,40,35,1000)

$815.98

Percentage change = ((Ending price - Beginning price) / Beginning Price) *100

Percentage change = ((815.98 - 1000) / 1000) *100

Percentage change = (-184.02 / 1000) * 100

Percentage change = -18.40%

Bond Y

When coupon rate and market interest rate is same, the current price of bond and face value is same

Years to maturity * semi annual frequency 5 * 2 = 10 (n or NPER)

Semi annual Coupon payment (PMT) = 1000 * (7% / 2) = 35

A rise of 2% percent would mean 7% + 2% = 9%; semi annual rate or r is (9%/ 2)

You can use the PV function in excel to find the bond price

PV(rate,NPER,PMT,FV,TYPE)

PV(9%/2,10,35,1000)

$920.87

Percentage change = ((Ending price - Beginning price) / Beginning Price) *100

Percentage change = ((920.87- 1000) / 1000) *100

Percentage change = (-79.13 / 1000) * 100

Percentage change = -7.91%

Bond X

When coupon rate and market interest rate is same, the current price of bond and face value is same

Years to maturity * semi annual frequency 20 * 2 = 40 (n or NPER)

Semi annual Coupon payment (PMT) = 1000 * (7% / 2) = 35

A fall of 2% percent would mean 7% - 2% = 5%; semi annual rate or r is (5%/ 2)

You can use the PV function in excel to find the bond price

PV(rate,NPER,PMT,FV,TYPE)

PV(5%/2,40,35,1000)

1251.03 Bond sells at a premium when coupon rate is more than the market rate

Percentage change = ((Ending price - Beginning price) / Beginning Price) *100

Percentage change = ((1251.03 - 1000) / 1000) *100

Percentage change = (251.03 / 1000) * 100

Percentage change = 25.10%

Bond Y

When coupon rate and market interest rate is same, the current price of bond and face value is same

Years to maturity * semi annual frequency 5 * 2 = 10 (n or NPER)

Semi annual Coupon payment (PMT) = 1000 * (7% / 2) = 35

A fall of 2% percent would mean 7% - 2% = 5%; semi annual rate or r is (5%/ 2)

You can use the PV function in excel to find the bond price

PV(rate,NPER,PMT,FV,TYPE)

PV(5%/2,10,35,1000)

1087.52 Bond sells at a premium when coupon rate is more than the market rate

Percentage change = ((Ending price - Beginning price) / Beginning Price) *100

Percentage change = ((1087.52 - 1000) / 1000) *100

Percentage change = (87.52 / 1000) * 100

Percentage change = 8.75%