Both Bond Sam and Bond Dave have 9 percent coupons, make semiannual payments, an

Question

Both Bond Sam and Bond Dave have 9 percent coupons, make semiannual payments, and are priced at par value. Bond Sam has six years to maturity, whereas Bond Dave has 17 years to maturity.

A.

If interest rates suddenly rise by 2 percent, what is the percentage change in the price of Bond Sam and Bond Dave?

B.

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?

If interest rates suddenly rise by 2 percent, what is the percentage change in the price of Bond Sam and Bond Dave?

B.

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?

Explanation / Answer

. Both bonds sell at par, so the initial YTM on both bonds is the coupon rate, 9 percent. If the YTM suddenly rises to 11 percent:

          P   SAM    = $45(PVIFA 5.5% ,6     5.5%,6) + $1,000(PVIF 5.5% ,6)       = $950.04

   P DAVE = $45(PVIFA 5.5% ,40         ) + $1,000(PVIF 5.5% ,40 )     = $839.54

                        Percentage change in price = (New price – Original price) / Original price

                        DPSam%            = ($950.04 – 1,000) / $1,000 = – 5.00%

                        DPDave%           = ($839.54 – 1,000) / $1,000 = – 16.05%

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