coupon rates

4. Coupon Rates – Rhiannon corporation has bonds on the market with 13.5 years to maturity, a YTM of 7.6 percent, and a current price of $1,175. The bonds make semiannual payments. What must the coupon rate be on these bonds?

Answer:

t= 13.5 years – semiannual payments = 2 x 13.5 = 27 times

r= 7.6% - semiannual rate = 7.6% / 2 = 3.8 %

P = $1,175

Financial Calculator:

P=$1,175 = C (PVIFA_{3,8%, 27}) + $1,000 (PVIF_{3,8%, 27})

Note:

PVIFA = Present Value Interest Factor of Annuity

PVIF = Present Value Interest Factor

Solving for the coupon payment, we get:

C = $48.48

Formula:

Bond Price = (par value / 1+ r^t ) + C (1 – 1/1+r^t)/r

$1,175 = (1000/1.038²⁷ ) + C (1- 1/1.038²⁷)/0.038

$1,175 = (1000/2.635) + C (16.342)

$1,175 = 379.50 + 16.342 C

16.342 C = 795.5

C = $ 48.67 – semiannual payment

Since this is semiannual payment, the annual coupon payment is:

C = $48.67 x 2 = $ 96.96

And the coupon rate is the annual coupon payment divided by par value, so:

Coupon rate = $96.96 / $ 1000 = 0.09696 = 9.7%

Note: C  >  R , bond sells at premium (greater than par).

reference: Chapter 8, Corporate Finance Book, Stephen A.Ross, Randolph W.Westerfield and Jeffrey Jaffe, Ninth Edition.