1. Both Bond Sam and Bond Dave have 8 percent coupons, make semiannual payments,

ID: 2816612 • Letter: 1

Question

Both Bond Sam and Bond Dave have 8 percent coupons, make semiannual payments, and are priced at par value. Bond Sam has 3 years to maturity, whereas Bond Dave has 19 years to maturity. (Do not round your intermediate calculations.)

If rates were to suddenly fall by 4 percent instead, what would the percentage change in the price of Bond Sam be then?

If rates were to suddenly fall by 4 percent instead, what would the percentage change in the price of Bond Dave be then?

Explanation / Answer

Let in the case KD = Coupon Rate. Which defines the Issued price is equal to Maturity Price.

1.a. The correct answer is -9.833%.

In the first Case when Interest rate rises by 4% in Sam then Price of Bond is changes by-

First We need to calculate Price of Bond After changes Interest rate to 12%.

Then,

Let face value or Maturity value of the bond is 100.

B0 or Price of Bond as per semi Annually = 100 * 8%/2 * PVAF (12%/2 , 3 year * 2) + 100 * PVF (6% , 6 year)

B0 = 100 * 4% * PVAF ( 6%, 6 year) + 100 * PVF (6% , 6 year)

B0 = 4 * 4.917 + 100 * 0.70496

B0 = 19.67 + 70.496

B0 = 90.166

Then change in price after changing Interest rate = (90.166 - 100)*100/100

Then change in price after changing Interest rate = -9.833%

1.b. The correct answer is -29.69%.

In the Second Case when Interest rate rises by 4% in Dave then Price of Bond is changes by-

First We need to calculate Price of Bond After changes Interest rate to 12%.

Then,

Let face value or Maturity value of the bond is 100.

B0 or Price of Bond as per semi Annually = 100 * 8%/2 * PVAF (12%/2 , 19 year * 2) + 100 * PVF (6% , 38 year)

B0 = 100 * 4% * PVAF ( 6%, 38 year) + 100 * PVF (6% , 38 year)

B0 = 4 * 14.846 + 100 * 0.10924

B0 = 59.38 + 10.924

B0 = 70.308

Then change in price after changing Interest rate = (70.308 - 100)*100/100

Then change in price after changing Interest rate = -29.69%.

1.a. The correct answer is 11.20%.

In the first Case when Interest rate fall by 4% in Sam then Price of Bond is changes by-

First We need to calculate Price of Bond After changes Interest rate to 4%.

Then,

Let face value or Maturity value of the bond is 100.

B0 or Price of Bond as per semi Annually = 100 * 8%/2 * PVAF (4%/2 , 3 year * 2) + 100 * PVF (2% , 6 year)

B0 = 100 * 4% * PVAF ( 2%, 6 year) + 100 * PVF (2% , 6 year)

B0 = 4 * 5.601 + 100 * 0.88797

B0 = 22.41 + 88.797

B0 = 111.21

Then change in price after changing Interest rate = (111.20 - 100)*100/100

Then change in price after changing Interest rate = 11.20%

2.b. The correct answer is 52.88%.

In the Second Case when Interest rate fall by 4% in Dave then Price of Bond is changes by-

First We need to calculate Price of Bond After changes Interest rate to 4%.

Then,

Let face value or Maturity value of the bond is 100.

B0 or Price of Bond as per semi Annually = 100 * 8%/2 * PVAF (4%/2 , 19 year * 2) + 100 * PVF (2% , 38 year)

B0 = 100 * 4% * PVAF ( 2%, 38 year) + 100 * PVF (2% , 38 year)

B0 = 4 * 26.441 + 100 * 0.471187

B0 = 105.76 + 47.1187

B0 = 152.88

Then change in price after changing Interest rate = (152.88 - 100)*100/100

Then change in price after changing Interest rate = 52.88%.

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1. Both Bond Sam and Bond Dave have 8 percent coupons, make semiannual payments,

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