Question

Both Bond Sam and Bond Dave have 7.3 percent coupons, make semiannual payments, and are priced at par value. Bond Sam has three years to maturity, whereas Bond Dave has 20 years to maturity. If interest rates suddenly rise by 2 percent, what is the percentage change in the price of Bond Sam and Bond Dave? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g.,32.16.) Percentage change in price of Bond Sam Percentage change in price of Bond Dave If rates were to suddenly fall by 2 percent instead, what would be the percentage change in the price of Bond Sam and Bond Dave? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g. 32.16.) Percentage change in price of Bond Sam Percentage change in price of Bond Dave

Answer 1

Answer:

Sam change:   -5.13%

Dave change -18.01%

Explanation:

If interest rate increase by 2%

then the YTM of the bond will be 9.3%

We need eto calcualte the present value of  the coupon and maturity of the bond at this new rate:

For the coupon payment we use the formula for ordinary annuity

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

Coupon payment: 1,000 x 7.3% / 2 payment per year: 36.50

time 6 (3 years x 2 payment per year)

YTM seiannual: 0.0465 (9.3% annual /2 = 4.65% semiannual)

$36.5 \times \frac{1-(1+0.0465)^{-6} }{0.0465} = PV$

PV $187.3546

For the maturity we calculate usign the lump sum formula:

$\frac{Maturity}{(1 + rate)^{time} } = PV$  

Maturity: $ 1,000.00

time: 6 payment

rate: 0.0465

$\frac{1000}{(1 + 0.0465)^{6} } = PV$  

PV   761.32

Now, we add both together:

PV coupon $187.3546 + PV maturity  $761.3154 = $948.6700

now we calcualte the change in percentage:

948.67/1,000 - 1 = -0.051330026 = -5.13

For Dave we do the same:

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C 36.50

time 40

rate 0.0465

$36.5 \times \frac{1-(1+0.0465)^{-40} }{0.0465} = PV$

PV $657.5166

$\frac{Maturity}{(1 + rate)^{time} } = PV$  

Maturity   1,000.00

time   40.00

rate  0.0465

$\frac{1000}{(1 + 0.0465)^{40} } = PV$  

PV   162.34

PV c $657.5166

PV m  $162.3419

Total $819.8585

Change:

819.86 / 1,000 - 1 = -0.180141521 = -18.01%