Question

A $5,000 bond with a coupon rate of 6.7% paid semiannually has five years to maturity and a yield to maturity of 8.7%. If interest rates rise and the yield to maturity increases to 9%, what will happen to the price of the bond? O A. rise by $56.41 OB. fall by $67.69 OC. fall by $56.41 OD. The price of the bond will not change.

Answer 1

Case 1: YTM = 8.7%

Face value of the bond = FV = $5000

Bond pays semiannual coupons

Semi annual time period = 5*2 = 10

Semiannual coupon rate = 6.7%/2 = 3.35%

Semiannual coupon payment = 3.35%*5000 = 167.5

Semiannual YTM = 8.7%/2 = 4.35%

Price of the bond calculation using ba ii plus calculator

N = 10, I/Y = 4.35, PMT = 167.5, FV = 5000

CPT -> PV (Press CPT and then press PV)

We get, price of the bond = PV₁ = 4601.429948

Case 2: YTM = 9%

Semi-annual YTM = 9%/2 = 4.5%

Using ba ii plus calculator to compute the price of the bond

N = 10, I/Y = 4.5, PMT = 167.5, FV = 5000

CPT -> PV

We get the new price of the bond = 4545.018705

New PV = PV₂ = 4545.018705

Therefore, change in PV = PV₂-PV₁ = 4545.018705 - 4601.429948 = -56.41124318

We see that the price has fallen by $56.41

Answer -> fall by $56.41