Arnot Internatioanl\'s bonds have a current market price of $1200. The bonds hav

Question

Arnot Internatioanl's bonds have a current market price of $1200. The bonds have an 11% annual coupon payment, a $1000 face value and 10 years left until maturity. The bonds may be called in 5 years at 109% of face value. (call price = $1090)
a) what is the yeild to maturity?
b) what is the yeild to call if they are called in 5 years?
c)Which yeild might investors expect to earn on these bonds and why?
d)The bond's indenture indicates that the call provision gives the firm to right to call them at the end of each year begining in Year 5. In year 5, they may be called at 109% of face value, but in each of the next 4 years thecaall percentage will decline by 1 percentage point. If the yeild curve is horizontal and interest rates remain at their current level, when is the latest that investors might expect the firm to call the bonds?

Explanation / Answer

We have nper = 10 Yrs, Present Value of Bond PV = $1200, Maturity valueFV = $1000
PMT = 11%*$1000 = $110
We have YTM = Rate(nper,PMT,PV,FV)
YTM = RATE(10,110,-1200,1000) = 8.02%......Ans (1)

For YTC at Y5, We have nper = 5 Yrs, Present Value of Bond PV = $1200, Maturity valueFV = $1000*1.09 = $1090
PMT = 11%*$1000 = $110
We have YTC = Rate(nper,PMT,PV,FV)
YTC = RATE(5,110,-1200,1090) = 7.59%......Ans (2)

For YTC at Y6, We have nper = 4 Yrs, Present Value of Bond PV = $1200, Maturity valueFV = $1000*1.08 = $1080
PMT = 11%*$1000 = $110
We have YTC = Rate(nper,PMT,PV,FV)
YTC = RATE(4,110,-1200,1080) = 6.91%......Ans (3)

For YTC atY7, We have nper = 3 Yrs, Present Value of Bond PV = $1200, Maturity valueFV = $1000*1.07 = $1070
PMT = 11%*$1000 = $110
We have YTC = Rate(nper,PMT,PV,FV)
YTC = RATE(3,110,-1200,1070) = 5.76%......Ans (4)

For YTC atY8, We have nper = 2 Yrs, Present Value of Bond PV = $1200, Maturity valueFV = $1000*1.06 = $1060
PMT = 11%*$1000 = $110
We have YTC = Rate(nper,PMT,PV,FV)
YTC = RATE(2,110,-1200,1060) = 3.43%......Ans (5)

For YTC at Y9, We have nper = 1 Yrs, Present Value of Bond PV = $1200, Maturity valueFV = $1000*1.05 = $1050
PMT = 11%*$1000 = $110
We have YTC = Rate(nper,PMT,PV,FV)
YTC = RATE(1,110,-1200,1050) = -3.33%......Ans (6)

The true yield of a callable bond at any given price is usually lower than its yield to maturity because the call provisions limit the bond's potential price appreciation -- when interest rates fall, the price of a callable bond will not go any higher than its call price. This is because the issuer should act in the best interests of the company and call the bond as soon as it is favorable to do so.

As a result, investors usually consider the lower of the yield to call and the yield to maturity as the more realistic indication of the return an investor will actually receive on a callable bond. Some investors go a step further and calculate the yield to call not just for the first call date, but for all possible call dates. Then the investor compares all the calculated yields to call and yields to maturity and relies on the lowest of them, called the yield to worst. So here the Firm may call the bond in 9th year.

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