Consider 3 Treasury bonds which pay semi-annual coupons. Bond A has 5 years rema

Question

Consider 3 Treasury bonds which pay semi-annual coupons. Bond A has 5 years remaining to maturity and a coupon rate of 10%. Bond B has 20 years remaining to maturity and a coupon rate of 10%, and Bond C has 20 years remaining to maturity and a coupon rate of 4%.

If all bonds provided a 10% return (APR, compounded semiannually) if they were purchased today and held to maturity, what is the price today of each of the bonds? Essentially, what is the price of each bond if the YTM is 10%?

What is the price of each bond if the YTM was 4%? What if it was 16%

Using Excel, create a single graph showing the price of Bonds A & B for varying YTMs. Let YTM range from 0.5% to 18% per year (compounded semi-annually) in increments of 50 basis points (1 basis point is 1/100 of a percent – thus examples of a 50 basis point change would be a change from 4.5% to 5% or 11.2% to 11.7%). Is the graph linear? If not, what shape is it? Does a change in YTM affect the price of each of the two bonds the same way? Why or why not?

Create a similar graph for Bonds B & C. Is the graph linear? If not, what shape is it? Does a change in YTM affect the price of each of the two bonds the same way? Why or why not?

Explanation / Answer

1. YTM = 10%

- Price of Bond A and Bond B will be equal, i.e., $1,000 because there coupon rate is equal to YTM
- Bond C = 20 x PVAF(5%, 40periods) + 1,000 x PVF(5%, 40periods) = $485.23

2. YTM = 4%

- In this case Bond C price will be $1,000 since coupon rate is equal to YTM.
- Bond A = 50 x PVAF(2%, 10periods) + 1,000 x PVF(2%, 10periods) = $1,269.48
- Bond B = 50 x PVAF(2%, 40periods) + 1,000 x PVF(2%, 40periods) = $1,820,67

3. YTM = 16%

- Bond A = 50 x PVAF(8%, 10periods) + 1,000 x PVF(8%, 10periods) = $798.70
- Bond B = 50 x PVAF(8%, 40periods) + 1,000 x PVF(8%, 40periods) = $642.26
- Bond C = 20 x PVAF(8%, 40periods) + 1,000 x PVF(8%, 40periods) = $284.52

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