Question

The bonds of CEPS Group sells for OMR 1,191.53. The yield to maturity is 12 percent and

the maturity date is 9 years from today. What is the annual coupon rate of this bond if the face

value is $1,000?

Answer 1

The price of the bond is equal to present value of all future cash flows to avoid any arbitrage. Discounting of all future cash flows is done.

Price or PV (present value) = 1191.53

Yield to maturity or rate, r = 12%

Time period or nper = 9years.

Face value or FV( future value) = 1000

Let annual coupon be PMT

Thus, PV = PMT/(1+r) + PMT/(1+r)^2 +...PMT/(1+r)^9 + 1000/(1+r)^9

Or 1191.53 = PMT/(1.12) + PMT/(1.12^2) + ... PMT/(1.12^9) + 1000/(1.12^9)

Or PMT = 155.95

Excel's function =pmt can be used

=Pmt(rate,nper,pv,fv)

=Pmt(0.12,9,-1191.53,1000) = $155.95

Thuw annual coupon payment is 155.95

PV is entered as negative as it is a cash outflow but coupon and face value are cash inflow. Thus signs are opposite.

Thus coupon rate = annual coupon payment/face value= 155.95/1000 = 15.595%