Question

Bond #1: US Treasury note with a 2% coupon due in 5 years issued at a price of par ($100).
Bond #2: ABC Corp note with a 4% coupon issued at a yield to maturity of 4.2%. ABC’s credit is rated BBB.

 Both bonds were issued and will mature on the same date.
 Coupons on both bonds are stated in annual terms above, but paid semi-annually.
 The Fed Funds rate is 0.75%.
 Below is the “benchmark” US Treasury “on-the-run” Yield Curve on date of issuance:

1y 1.00% 2y 1.25% 3y 1.50% 5y 2.00% 7y 2.50% 10y 3.00%

1. What is the Yield to Maturity of Bond #1?

2. Was Bond #2 issued (sold) at a par, premium or discount price? (You can answer this without knowing

   the specific price.)

3. What do bond market participants call the “difference” between the yields to maturity of Bond #2 and

   Bond #1?

4. What type of risk is most likely the largest component of this “yield difference?”

1. 2%
2. Discount price
3. Spread
4. Default Risk

Assume you purchased Bond #1 and held it for 3 years and the treasury yield curve is unchanged (rates are exactly the same as those listed above), and answer the following questions (36 points): a. What is the new number of years to maturity for bond #1? b. How many cash flow payment dates are left? c. What is the discount rate we should use to value Bond #1 in this new environment? d. Using the same Present Value of Future Cash Flows Model shown above to compute the new price of Bond #1 (show your work).

Answer 1

1. Since the bond #1 was issued at at a price at par, Yield to Maturity (YTM) is equal to the coupon rate ie., 2%

YTM is the discount rate with which sum of present values of future cash flows become equal to the price paid. It has to be calculated by iteration. Using the Excel Program for IRR, YTM is calculated at 1% per half year which is equal to 2% per year. Detailed working as follows:

2. Since YTM is higher than the coupon rate, bond #2 was issued at a discount

3. Difference between the YTMs of two debt instruments, different in term to maturity or risk profile (in the instant case, bond #1 and bond #2), is called 'Yield Spread'

4. The largest component of the "yield difference" between bond #1 and bond #2 is Default Risk. Because, Bond #1 is treasury bond and risk free. Bond #2, on the other hand, is a corporate debt, bearing only a moderate credit rating of BBB.

5. After holding bond #1 for 3 years:

(a) New number of years to maturity= Original term minus 3 years = 5-3 = 2 years.

(b) Since the bond pays interest semiannually, number of cash flow payments left is remaining years to maturity multiplied by 2. Hence the answer is 2*2= 4

(c) Even after completion of 3 years since issue of the bond, yield curve remains unchanged. Spot rate of all treasury instruments continue as before. The remaining term to maturity is 2 years and the spot rate for 2 year treasury bonds is 2%. Hence the discount rate to be used for valuing the bond#1 in the new environment is 2%.

(d) Since the coupon rate and discount rate are same, value of the bond #1 is equal to face value ie. $100. Working of the price using Present Value method is appended below: