Question

Consider a bond selling at par ($100) with a coupon rate of 6% and 10 years to maturity. (a) What is the price of this bond if the required yield is 15%?

(b) What is the price of this bond if the required yield increases from 15% to 16%, and by what percentage did the price of this bond change?

(c) What is the price of this bond if the required yield is 5%?

(d) What is the price of this bond if the required yield increases from 5% to 6%, and by what percentage did the price of this bond change?

Answer 1

Answer a.

Par Value = $100

Annual Coupon Rate = 6%
Annual Coupon = 6% * $100
Annual Coupon = $6

Time to Maturity = 10 years

If yield to maturity is 15%:

Annual YTM = 15%

Price of Bond = $6 * PVIFA(15%, 10) + $100 * PVIF(15%, 10)
Price of Bond = $6 * (1 - (1/1.15)^10) / 0.15 + $100 / 1.15^10
Price of Bond = $54.83

Answer b.

If yield to maturity is 16%:

Annual YTM = 16%

Price of Bond = $6 * PVIFA(16%, 10) + $100 * PVIF(16%, 10)
Price of Bond = $6 * (1 - (1/1.16)^10) / 0.16 + $100 / 1.16^10
Price of Bond = $51.67

Percentage Change in Price = ($51.67 - $54.83) / $54.83
Percentage Change in Price = -0.0576 or -5.76%

Answer c.

If yield to maturity is 5%:

Annual YTM = 5%

Price of Bond = $6 * PVIFA(5%, 10) + $100 * PVIF(5%, 10)
Price of Bond = $6 * (1 - (1/1.05)^10) / 0.05 + $100 / 1.05^10
Price of Bond = $107.72

Answer d.

If yield to maturity is 6%:

Annual YTM = 6%

Price of Bond = $6 * PVIFA(6%, 10) + $100 * PVIF(6%, 10)
Price of Bond = $6 * (1 - (1/1.06)^10) / 0.06 + $100 / 1.06^10
Price of Bond = $100.00

Percentage Change in Price = ($100.00 - $107.72) / $107.72
Percentage Change in Price = -0.0717 or -7.17%