Both Bond Bill and Bond Ted have 10.4 percent coupons, make semiannual payments,

Question

Both Bond Bill and Bond Ted have 10.4 percent coupons, make semiannual payments, and are priced at par value. Bond Bill has 5 years to maturity, whereas Bond Ted has 22 years to maturity. Requirement 1: If interest rates suddenly rise by 3 percent, what is the percentage change in the price of these bonds? (Do not round intermediate calculations. Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places (e.g., 32.16).) Percentage change in price - Bond Bill % Bond Ted % Requirement 2: If rates were to suddenly fall by 3 percent instead, what would be the percentage change in the price of these bonds? (Do not round intermediate calculations. Round your answers to 2 decimal places (e.g., 32.16).) Percentage change in price - Bond Bill % Bond Ted %

Explanation / Answer

For the bonds making semi annual ineterst payment , the price is determined by the following formula:

(C/2) x PVIFA (r/2, 2n) + M x PVIF ( r/2, 2n)

where,

C = Annual Coupon Interest

r = YTM

n = number of years to maturity

M = maturity value

As both the bonds are being sold at par value,

the YTM for both the bonds = Coupon rate of interest = 10.4 %

If interest rate suddenly rise by 3%

The price of the Bond Bill is given by,

= (104/2) x PVIFA (13.4%/2, 10) + M x PVIF ( 13.4%/2, 10)   [ r = 10.4 % + 3% = 13.4%]

= 51 x 7.122 + 1000 x 0.523

= $886.22

Percentage change in price = [(886.22 - 1000)/1000] x 100 = -11.38 %

Price will be reduced by 11.38%

The price of the Bond Ted is given by,

= (104/2) x PVIFA (13.4%/2, 44) + M x PVIF ( 13.4%/2, 44)

= 51 x 14.065 + 1000 x 0.058

= $775.32

Percentage change in price = [(775.32 - 1000)/1000] x 100 = -22.47 %

Price will be reduced by 22.47%

If interest rate suddenly fall by 3%

The price of the Bond Bill is given by,

= (104/2) x PVIFA (7.4%/2, 10) + M x PVIF ( 7.4%/2, 10)    [ r = 10.4 % - 3% = 7.4% ]

= 51 x 8.233 + 1000 x 0.695

= $1114.88

Percentage change in price = [(1114.88 - 1000)/1000] x 100 = 11.49 %

Price will be increased by 11.49 %

The price of the Bond Ted is given by,

= (104/2) x PVIFA (7.4%/2, 44) + M x PVIF ( 7.4%/2, 44)

= 51 x 21.563 + 1000 x 0.202

= $1301.71

= $775.32

Percentage change in price = [(1301.73- 1000)/1000] x 100 = 30.17 %

Price will be increased by 30.17 %

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