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%.

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

Ans:

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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