Question

You are asked to choose among three bonds based on their YTM. All three bonds are selling for the same price $953.10. The first bond has a coupon rate of 8% with three years until maturity making semiannual coupon payments. The second bond has the same maturity and 8% coupon rate but it only makes annual coupon payments. Finally, the third bond has a 9% coupon rate with semiannual payments and matures in five years.

Answer 1

The YTM of each bond is calculated as below :

Bond 1

YTM is calculated using RATE function in Excel with these inputs :

nper = 3*2 (3 years to maturity with 2 semiannual coupon payments each year)

pmt = 1000 * 8% / 2 (semiannual coupon payment = face value * annual coupon rate / 2. This is a positive figure as it is an inflow to the bondholder)

pv = -953.10 (current bond price. This is a negative figure as it is an outflow to the buyer of the bond)

fv = 1000 (face value of the bond receivable on maturity. This is a positive figure as it is an inflow to the bondholder)

The RATE calculated is the semiannual YTM. To calculate the annual YTM, we multiply by 2. Annual YTM is 9.84%

A1 X Fax =RATE(3*2,1000*8%/2,-953.1, 1000)*2 | B C D E F G A 9.84%

Bond 2

YTM is calculated using RATE function in Excel with these inputs :

nper = 3 (3 years to maturity with 1 annual coupon payment each year)

pmt = 1000 * 8% (annual coupon payment = face value * annual coupon rate. This is a positive figure as it is an inflow to the bondholder)

pv = -953.10 (current bond price. This is a negative figure as it is an outflow to the buyer of the bond)

fv = 1000 (face value of the bond receivable on maturity. This is a positive figure as it is an inflow to the bondholder)

The RATE is calculated to be 9.88%. This is the YTM.

A2 foc =RATE(3,1000*8%,-953.1,1000) Xv X C B D E F G A 9.88% 2

Bond 3

YTM is calculated using RATE function in Excel with these inputs :

nper = 5*2 (5 years to maturity with 2 semiannual coupon payments each year)

pmt = 1000 * 9% / 2 (semiannual coupon payment = face value * annual coupon rate / 2. This is a positive figure as it is an inflow to the bondholder)

pv = -953.10 (current bond price. This is a negative figure as it is an outflow to the buyer of the bond)

fv = 1000 (face value of the bond receivable on maturity. This is a positive figure as it is an inflow to the bondholder)

The RATE calculated is the semiannual YTM. To calculate the annual YTM, we multiply by 2. Annual YTM is 10.22%

АЗ х v ft =RATE(5*2,1000*9%/2,-953.1,1000)*2 B C D E з A 10.22%

Bond 3 should be chosen as it has the highest YTM