Both Bond Sam and Bond Dave have 7 percent coupons, make semiannual payments, an
ID: 2626055 • Letter: B
Question
Both Bond Sam and Bond Dave have 7 percent coupons, make semiannual payments, and are priced at par value. Bond Sam has three years to maturity, whereas Bond Dave has 16 years to maturity. [Instructor's note: we aren't covering this in this class but when a bond is priced at par, it costs $1000 and the 6-month discount rate is the same as the 6-month coupon rate, which is the annual coupon rate divided by two.] If interest rates suddenly rise by 2 percentage points (New YTM=Old YTM + 2.00%) , what is the percentage change in the price of Bond Sam and Bond Dave? (Negative amounts should be indicated by a minus sign. Round your answers 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 percentage points instead, what would be the percentage change in the price of Bond Sam and Bond Dave? (Round your answers to 2 decimal places. (e.g., 32.16)) Percentage change in price of Bond Sam % Percentage change in price of Bond Dave
Explanation / Answer
If interest rates suddenly rise by 2 percentage points
Bond Sam :
Value of Bond= pv(rate,nper,pmt,fv)
where,
rate = (7 + 2)/2 = 4.5%
nper = 3*2 = 6
PMT = 1000*7%*1/2 = $ 35
Fv =1000
Now,
Value of Bond= pv(4.5%,6,35,1000)
Value of Bond= $ 948.42
Change In Price = 948.42 - 1000 = -$ 51.52
Percentage Change in the price of Bond Sam = -51.52/1000
Percentage Change in the price of Bond Sam = -5.15%
Bond Dave :
Value of Bond= pv(rate,nper,pmt,fv)
where,
rate = (7 + 2)/2 = 4.5%
nper = 16*2 = 32
PMT = 1000*7%*1/2 = $ 35
Fv =1000
Now,
Value of Bond= pv(4.5%,32,35,1000)
Value of Bond= $ 932.95
Change In Price = 932.95 - 1000 = -$ 67.05
Percentage Change in the price of Bond Sam = -67.05/1000
Percentage Change in the price of Bond Sam = -6.71%
If interest rates suddenly fall by 2 percentage points
Bond Sam :
Value of Bond= pv(rate,nper,pmt,fv)
where,
rate = (7 - 2)/2 = 2.5%
nper = 3*2 = 6
PMT = 1000*7%*1/2 = $ 35
Fv =1000
Now,
Value of Bond= pv(2.5%,6,35,1000)
Value of Bond= $ 1055.08
Change In Price = 1055.08 - 1000 = $ 55.08
Percentage Change in the price of Bond Sam = 55.08/1000
Percentage Change in the price of Bond Sam = 5.51%
Bond Dave :
Value of Bond= pv(rate,nper,pmt,fv)
where,
rate = (7 - 2)/2 = 2.5%
nper = 16*2 = 32
PMT = 1000*7%*1/2 = $ 35
Fv =1000
Now,
Value of Bond= pv(2.5%,32,35,1000)
Value of Bond= $ 1218.49
Change In Price = 1218.49 - 1000 = 218.49
Percentage Change in the price of Bond Sam = 218.49/1000
Percentage Change in the price of Bond Sam = 21.85 %
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