Question

A 10% coupon bond matures in twenty years and sells for $500. Which of the following will be the highest?

A. The annual yield to maturity if there are semi-annual payments

B. The annual yield to maturity if there are annual payments

C. The effective annual rate if there are semi-annual payments

D. The effective annual rate if there are annual payments

E. “A” and “D” will be the highest.

F. “B” and “C” will be the highest

Answer 1

Note- It is assumed that Bond are mature on its par value.

A. Annual Return to Maturity- [Interest+(Maturity Value-Net Proceeds)/n]/(Maturity Value+Net Proceeds)/2

=[50+(500-500)/2]/(500+500)/2

= 10%

Semi-annually Payment Made= 10%/2 = 5%

B. Annual Return to Maturity- [Interest+(Maturity Value-Net Proceeds)/n]/(Maturity Value+Net Proceeds)/2

=[50+(500-500)/2]/(500+500)/2

= 10%

C. Effective Semi-Annually Rate = (1+r/m)^m-1

= (1+0.1/2)²-1

= 10.25%

D. Effective Annual Rate = (1+r/m)^m-1

=(1+0.1/1)²-1

= 10%

E. Effective Annual Rate is higher than Annual return because effective annual rate give higher return to the company,

F. Effective Annual Rate is higher than Annual return because effective annual rate give higher return to the company,So it is be.tter for the company to adopt effective annual rate to taken more return to the company