Question

It is now January 1, 2015, and you are considering the purchase of an outstanding bond that was issued on January 1, 2013. It has a 9.5% annual coupon and has a 30 year maturity. (It matures on December 31, 2042.) There is a 5 years of call protection (until December 31, 2017), after which time it can be called at 109 - That is, at 109% of par, or $1,090. Interest rates have declined since it was issued, and it is now selling at 116.575% of par, or $1,165.75.

A: What is the yield to maturity? What is the yield to call?

B: If you bought this bond, which return would you actually earn? Explain your reasoning

C: Suppose the bond had been selling at a discount rather than a premium. Would the yield to maturity have been the most likely return, or would the yield to call have been most likely?

Answer 1

Part (A)

We can calculate the yield using RATE function of excel. Let's first calculate yield to maturity, YTM.

Inputs for the RATE function:

Period = Time to maturity = 30 - 2 = 28,

PMT = annual payment = coupon x Face Value = 9.5% x $ 1,000 = 95,

PV = - Current price of the bond = - 1165.75

FV = future value = face value = 1000

Hence, YTM = RATE (Period, PMT, PV, FV) = RATE (28, 95, -1165.75, 1000) = 0.08000 = 8.00%

Let's now calculate the yield to call, YTC

Inputs for the RATE function:

Period = Time to call = 5 - 2 = 3,

PMT = annual payment = coupon x Face Value = 9.5% x $ 1,000 = 95,

PV = - Current price of the bond = - 1165.75

FV = future value = 109% of face value = 109% x 1000 = 1090

Hence, YTC = RATE (Period, PMT, PV, FV) = RATE (3, 95, -1165.75, 1090) = 0.061103929 = 6.11%

Part (B)

Since interest rates have declined since the time of issuance, the Company is at loss, continuing with the bond with higher interest rate. Hence, the company will call the bond.

Hence, if I bought this bond, I would actually earn the yield to call (6.11%) on this bond.

Part (C)

If the bond is trading at discount, this means coupon rate on the bond is lower than the yield. This means the coupon, the company is paying to the holder of the bond is lower than the prevailing interest rates in the market. In such a case, the company will not call the bond. Hence, in this case I am likely to earn the yield to maturity, YTM = 8.00%