Question

Which of the following $1,000 face value bonds has a 10% yield, assuming semiannual coupon payments of 8%?

1) a 5 year maturity bond selling for $964.54

2) a 10 year maturity bond selling for $875.39

3) a 20 year maturity bond selling for $828.36

Answer 1

a.Face value= future value= $1,000

Coupon rate= 8%/2= 4% per semi-annual period

Coupon payment= 0.04*1,000= $40

Time= 5 years*2= 10 semi-annual periods

Current price= current value= $964.54

The yield to maturity is calculated by entering the below in a financial calculator:

FV= 1,000

PV= 964.54

N= 10

PMT= 40

Press the CPT key and I/Y to compute the yield to maturity.

The value obtained is 4.4470.

Therefore, the yield to maturity is 4.4470%*2= 8.8939%.

b.Face value= future value= $1,000

Coupon rate= 8%/2= 4% per semi-annual period

Coupon payment= 0.04*1,000= $40

Time= 10 years*2= 20 semi-annual periods

Current price= current value= $875.39

The yield to maturity is calculated by entering the below in a financial calculator:

FV= 1,000

PV= -875.39

N= 20

PMT= 40

Press the CPT key and I/Y to compute the yield to maturity.

The value obtained is 4.9999.

Therefore, the yield to maturity is 4.9999%*2= 9.9998% $\rightarrow$ 10%

c. Face value= future value= $1,000

Coupon rate= 8%/2= 4% per semi-annual period

Coupon payment= 0.04*1,000= $40

Time= 20 years*2= 40 semi-annual periods

Current price= current value= $828.36

The yield to maturity is calculated by entering the below in a financial calculator:

FV= 1,000

PV= -828.36

N= 40

PMT= 40

Press the CPT key and I/Y to compute the yield to maturity.

The value obtained is 5.0003.

Therefore, the yield to maturity is 4.9999%*2= 10.0007%.

Therefore, bonds B and C have a yield of 10%.

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