Question

A 6-year 7.2% annual coupon bond is selling to yield 6.5%. The bond pays interest annually. The par value of the bond is $100.

a. What is the price of the 6-year 7.2% coupon bond selling to yield 6.5%?

b. What is the price of this bond one year later assuming the yield is unchanged at 6.5%?

c. Suppose that one year later the yield of the bond decreases to 6.3%. What is the price change attributable to moving to maturity assuming no change in the discount rate? What is the price change attributable to a decrease in the discount rate from 6.5% to 6.3%? What is the total price change?

Answer 1

No of periods = 6 years

Coupon per period = (Coupon rate / No of coupon payments per year) * Par value

Coupon per period = (7.2% / 1) * $100

Coupon per period = $7.2

a)

Bond Price = Coupon / (1 + YTM)^period + Par value / (1 + YTM)^period

Bond Price = $7.2 / (1 + 6.5%)¹ + $7.2 / (1 + 6.5%)² + ...+ $7.2 / (1 + 6.5%)⁶ + $100 / (1 + 6.5%)⁶

Using PVIFA = ((1 - (1 + Interest rate)^{- no of periods}) / interest rate) to value coupons

Bond Price = $7.2 * (1 - (1 + 6.5%)^-6) / (6.5%) + $100 / (1 + 6.5%)⁶

Current Bond Price at YTM (6.5%) = $103.3887

b)

Price of bond 1 year later at YTM = 6.5%

Bond Price = Coupon / (1 + YTM)^period + Par value / (1 + YTM)^period

Bond Price = $7.2 / (1 + 6.5%)¹ + $7.2 / (1 + 6.5%)² + ...+ $7.2 / (1 + 6.5%)⁵ + $100 / (1 + 6.5%)⁵

Using PVIFA = ((1 - (1 + Interest rate)^{- no of periods}) / interest rate) to value coupons

Bond Price = $7.2 * (1 - (1 + 6.5%)^-5) / (6.5%) + $100 / (1 + 6.5%)⁵

Bond Price 1 year later at YTM(6.5%) = $102.9090

c)

Price change attributable to moving to maturity assuming no change in the discount rate

Price Change = Bond Price 1 year later at YTM(6.5%) - Current Bond Price at YTM(6.5%) = $103.3887

Price Change = $102.9090 - $103.3887

Price Change = -$0.4797

Percentage price change = Price Change / Current Bond Price at YTM(6.5%)

Percentage price change = -$0.4797 / $103.3887

Percentage price change = -0.4640%

Price of bond 1 year later at YTM = 6.3%

Bond Price = Coupon / (1 + YTM)^period + Par value / (1 + YTM)^period

Bond Price = $7.2 / (1 + 6.3%)¹ + $7.2 / (1 + 6.3%)² + ...+ $7.2 / (1 + 6.3%)⁵ + $100 / (1 + 6.3%)⁵

Using PVIFA = ((1 - (1 + Interest rate)^{- no of periods}) / interest rate) to value coupons

Bond Price = $7.2 * (1 - (1 + 6.3%)^-5) / (6.3%) + $100 / (1 + 6.3%)⁵

Bond Price 1 year later at YTM(6.3%) = $103.7604

Price change attributable to a decrease in the discount rate from 6.5% to 6.3%

Price change = Bond Price 1 year later at YTM(6.3%) - Bond Price 1 year later at YTM(6.5%)

Price change = $103.7604 - $102.9090

Price change = $0.8514

Percentage price change = Price Change / Current Bond Price at YTM(6.5%)

Percentage price change = $0.8514 / $102.9090

Percentage price change = 0.8273%

Total price change = Price change attributable to moving to maturity assuming no change in the discount rate + Price change attributable to a decrease in the discount rate from 6.5% to 6.3%

Total price change = -$0.4797 + $0.8514

Total price change = $0.3717

Percentage Total price change = Percentage Price change attributable to moving to maturity assuming no change in the discount rate + Percentage Price change attributable to a decrease in the discount rate from 6.5% to 6.3%

Percentage Total price change = -0.4640% + 0.8273%

Percentage Total price change = 0.3633%