Question

Q1: You have been asked to evaluate the yield of maturity AAPL 6.25 maturing at 15th of November 2049 with a price at 127.676 of its par that pays annually, semi-annually, and quarterly coupons. Annual coupons Semanal respons Quarterly 1/1/2018 1/1/2049 Settlement date Maturity date Annual coupon rate Bond price Redemption value of face value) Coupon payments per year 1/1/2018 1/1/2018 1/1/2009 1/1/04 6.3% 127.676127675 127.676 Yield to maturity (decimal) 4.564% 4.571% 4.57% 02:Based on your evaluation, What is the relationship the number of coupon payment per year and the veild to maturity?

Answer 1

Coupon Rate is same in all 3 situations.

Except number of times coupon is paid, everything is same.

Situation 1: 1 time and YTM 4.564%

Situation 2: 2 times and YTM 4.571%

Situation 3: 4 times and YTM 4.575%

Effective Coupon Rate = [1+(i/n)]ⁿ - 1

where, i = Annual Interest Rate and n = Number of times coupon is paid in a year

It is clear from above that As Number of times Coupons are paid is increasing i.e. As EFECTIVE COUPON RATE is increasing(because all othe factors are same), the YTM also increases. If the number of times coupon paid is increased but Annual Coupon Rate is reduced then EFFECTIVE COUPON RATE might come down. Therefore, Annual Coupon Rate or Number of times coupon is paid in a year, INDIVIDUALLY does not have any relationship with YTM. But, Effective Coupon Rate is the rate that is related. There is direct relationship between Effective Coupon Rate and YTM(provided Redemption Value is same)

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