Question

Aziz works for a broker. One of his clients is offered to buy a bond at $1,050. It is a 10%, 15-year bond with a par value of $1,000 and a call price of $1,100. (The bonds first call date is in five years). Coupon payments are made semiannually.
Find the current yield, YTM and YTC on this issue. Which of these yields is the highest? Which is the lowest? Which yield would Aziz use to value this bond? Explain.                  (4 marks)
Assume that the price of the bond declines to $875. Now which yield is the highest? Which is the lowest? Which yield would Aziz use to value this bond? Explain.                            (3.5 marks)

Answer 1

Given,

Par Value= $1,000. Coupon rate= 10%.

Hence Interest per year= Par Value*Coupon Rate= $1000*10%= $$100

Case (i). Price to buy= $1,050.

Current Yield= (Yearly interest/Buying Price)*100 = (100/1,050)*100 = 9.52381%

Using RATE function of Excel,

Yield to Maturity (YTM) =9.439415% per year

Yield to Call (YTC) = 10.276130% per year

Yield to Call (YTC) is the highest and Yield to Maturity (YTM) is the lowest.

YTM and YTC presume that the periodical interest payments generate interest at the same rate. Holding this assumption good, Aziz shall use YTC for valuing the bond which is beneficial and shorter in term. Current yield does not take the compounding of interest into consideration and hence is not a perfect tool for valuation.

Case (ii). Price to buy= $875.

Current Yield= (Yearly interest/Buying Price)*100 = (100/875)*100 = 11.42857143%

Using RATE function of Excel,

Yield to Maturity (YTM) = 11.622143% per year

Yield to Call (YTC) = 15.05879% per year

Yield to Call (YTC) is the highest and Current Yield is the lowest.

As in the previous case, Aziz shall use YTC for valuing the bond which is beneficial and shorter in term. Current yield does not take the compounding of interest into consideration and hence is not a perfect tool for valuation.