Question

1.

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.)

   

Requirement 1:

(a)	If interest rates suddenly rise by 4 percent, what is the percentage change in the price of Bond Sam?
	(Click to select)11.22%10.07%-9.81%-10.91%-9.83%

    

(b)	If interest rates suddenly rise by 4 percent, what is the percentage change in the price of Bond Dave?
	(Click to select)34.59%-29.67%-29.69%-42.23%52.90%

    

Requirement 2:

(a)	If rates were to suddenly fall by 4 percent instead, what would the percentage change in the price of Bond Sam be then?
	(Click to select)-9.78%11.18%11.20%10.07%11.25%

    

(b)	If rates were to suddenly fall by 4 percent instead, what would the percentage change in the price of Bond Dave be then?
	(Click to select)52.93%-29.64%52.88%52.86%34.59%

Answer 1

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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