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

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 16 years to maturity. (a) If interest rates suddenly rise by 3 percent, what is the percentage change in the price of Bond Sam? (b) If interest rates suddenly rise by 3 percent, what is the percentage change in the price of Bond Dave? (a) If rates were to suddenly fall by 3 percent instead, what would the percentage change in the price of Bond Sam be then? (b) If rates were to suddenly fall by 3 percent instead, what would the percentage change in the price of Bond Dave be then?

Explanation / Answer

If interest rates suddenly rise by 3 percent

a)

PSam= $40(PVIFA5.5%,6) + $1,000(PVIF5.5%,6)= $925.07

The percentage change in price is calculated as:

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

PSam%= ($925.07 – 1,000) / $1,000 = –7.50%

b)

PDave= $40(PVIFA5.5%,32) + $1,000(PVIF5.5%,32)= $776.44

PDave%= ($776.43 – 1,000) / $1,000 = – 22.36%

If rates were to suddenly fall by 3 percent

a)

PSam= $40(PVIFA2.5%,6) + $1,000(PVIF2.5%,6)= $1082.62

The percentage change in price is calculated as:

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

PSam%= ($1082.62 – 1,000) / $1,000 = 8.26%

b)

PDave= $40(PVIFA2.5%,32) + $1,000(PVIF2.5%,32)= $1327.74

PDave%= ($1327.74 – 1,000) / $1,000 = 32.77%

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