Question

Both Company A and Company B have 9 percent coupons, make semiannual payments, and are priced at par value. Company A has 3 years to maturity, whereas Company B has 17 years to maturity.

	A) If interest rates suddenly rise by 2 percent, what is the percentage change in the price of Company A?
	B) If interest rates suddenly rise by 2 percent, what is the percentage change in the price of Company B? C) If rates were to suddenly fall by 2 percent instead, what would the percentage change in the price of Company A be then? D) If rates were to suddenly fall by 2 percent instead, what would the percentage change in the price of Company B be then?

Answer 1

Company A:

Face Value = $1,000

Annual Coupon Rate = 9.00%
Semiannual Coupon Rate = 4.50%
Semiannual Coupon = 4.50% * $1,000
Semiannual Coupon = $45

Time to Maturity = 3
Semiannual Period to Maturity = 6

If bond is selling at par, then current interest rate is equal to the coupon rate

So, current interest rate is 9.00%

If interest rate increases by 2%:

Annual Interest Rate = 11.00%
Semiannual Interest Rate = 5.50%

Price of Bond = $45 * PVIFA(5.50%, 6) + $1,000 * PVIF(5.50%, 6)
Price of Bond = $45 * (1 - (1/1.055)^6) / 0.055 + $1,000 / 1.055^6
Price of Bond = $950.04

Percentage Change in Price = ($950.04 - $1,000) / $1,000
Percentage Change in Price = -5.00%

If interest rate decreases by 2%:

Annual Interest Rate = 7.00%
Semiannual Interest Rate = 3.50%

Price of Bond = $45 * PVIFA(3.50%, 6) + $1,000 * PVIF(3.50%, 6)
Price of Bond = $45 * (1 - (1/1.035)^6) / 0.035 + $1,000 / 1.035^6
Price of Bond = $1,053.29

Percentage Change in Price = ($1,053.29 - $1,000) / $1,000
Percentage Change in Price = 5.33%

Company B:

Face Value = $1,000

Annual Coupon Rate = 9.00%
Semiannual Coupon Rate = 4.50%
Semiannual Coupon = 4.50% * $1,000
Semiannual Coupon = $45

Time to Maturity = 17
Semiannual Period to Maturity = 34

If bond is selling at par, then current interest rate is equal to the coupon rate

So, current interest rate is 9.00%

If interest rate increases by 2%:

Annual Interest Rate = 11.00%
Semiannual Interest Rate = 5.50%

Price of Bond = $45 * PVIFA(5.50%, 34) + $1,000 * PVIF(5.50%, 34)
Price of Bond = $45 * (1 - (1/1.055)^34) / 0.055 + $1,000 / 1.055^34
Price of Bond = $847.63

Percentage Change in Price = ($847.63 - $1,000) / $1,000
Percentage Change in Price = -15.24%

If interest rate decreases by 2%:

Annual Interest Rate = 7.00%
Semiannual Interest Rate = 3.50%

Price of Bond = $45 * PVIFA(3.50%, 34) + $1,000 * PVIF(3.50%, 34)
Price of Bond = $45 * (1 - (1/1.035)^34) / 0.035 + $1,000 / 1.035^34
Price of Bond = $1,197.01

Percentage Change in Price = ($1,197.01 - $1,000) / $1,000
Percentage Change in Price = 19.70%