The default-free yield curve on zero-coupon U.S. Government Treasury securities

Question

The default-free yield curve on zero-coupon U.S. Government Treasury securities is given below.

Maturity (in years) Rate

1 .01

2 .015

3 .02

4 .025

5 .0275

6 .03

Currently you can buy a corporate bond sold by a company that has some chance of defaulting in the future. This corporate bond matures in 5 years, pays a 5 percent coupon once a year, and has a face value of $1000.

a. If there is no change of default what would be the price of this corporate bond? Hint: if there is no chance of default, then the required rates of return for money at various horizons is given by the Treasury zero yield curve above. Given these rates, what would be the price of the corporate bond?

b. If there was a default-free bond with the same cash flows as the corporate bond described above, what would its price be? What would its yield to maturity be? Hint: Use goal seek to figure out the single rate YTM when applied to the cash flows implied a present value equal to the price you just derived.

c. The current price of the corporate bond with default risk is $1075 per $1000 in face value. What is the YTM on this bond? What is the annualized default risk premium on this bond (that is, what is the extra return per annum that this bond would return over a default free bond with the same payment stream)?

Explanation / Answer

a) The price of such a bond would be $1107.26

b) The YTM would be in this case 2.6793% For this use the above table only, just instead of using different rates, type 1 in an independent cell and give its reference to all the cells of column3 of the above table. Then using goal seek set the price of the bond equal to 1107.263 by changing that cell with entry one and you will get a table like this

1107.263

That independent cell as shown above will become 0.026793 which is your YTM

c) If the price is 1075 then again use the same thing, just instead of setting value to 1107.263 set it to 1075 and the YTM you will get is 3.3461% For your reference the table will look like this

year CF Rate df PV(CF) 1 50 0.01 0.990099 49.50495 2 50 0.015 0.970662 48.53309 3 50 0.02 0.942322 47.11612 4 50 0.025 0.905951 45.29753 5 1050 0.0275 0.873154 916.8117 1107.263

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