Question

BCC has bonds that trade frequently, pay a 8.5 percent coupon rate, and mature in Year 5. The bonds mature on March 1 in the maturity year. Suppose an investor bought this bond on March 1, Year 1, and assume interest is paid annually on March 1. Calculate the yield-to-maturity assuming the investor bought the bond at the following price, as quoted in the financial press: 100, 95, 111.

Answer 1

Yield to Maturity : It means return on bond from the date of purchase of bond till the date of maturity of bond.

Formula :

YTM = {I +[(MV-PP)/N]} / [(MV+PP)/2]

YTM = Yield to maturity

I = Interest amount

MV = Maturity Value

PP = Purchase price

N = No of year

Given :

I = 8.5

MV = Assumed 100 for every case

PP = 100 , 95, 111

N = 5

Option 1 : When Purchase Price = 100

YTM = {8.5 +[(100-100)/5]} / [(100+100)/2]

YTM = {8.5 +[(0)/5]} / [(200)/2]

YTM = {8.5 +[0]} / [(200)/2]

YTM = 8.5 / 100

YTM = 8.5 / 100

YTM = 8.5%

Option 2 : When Purchase Price = 95

YTM = {8.5 +[(100-95)/5]} / [(100+95)/2]

YTM = {8.5 +[(5)/5]} / [(195)/2]

YTM = {8.5 +[1]} / 97.5]

YTM = 9.5 / 97.5

YTM = 9.74%

Option 3 : When Purchase Price = 111

YTM = {8.5 +[(100-111)/5]} / [(100+111)/2]

YTM = {8.5 +[-11/5]} / [(211)/2]

YTM = {8.5 +[-2.2]} / 105.5]

YTM = 6.3 / 105.5

YTM = 5.97%