In: Finance
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?

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%