Question

Kiss the Sky Enterprises has bonds on the market making annual payments, with 15 years to maturity, and selling for $950. At this price, the bonds yield 10.0 percent. What must the coupon rate be on the bonds?

Answer 1

Answer:-

The formula for Coupon Rate is given by:-

Coupon Rate = Annual payment / Face Value

The following information is given in the question:-

Time (n) = 15 years

Bond price = $ 950

Yield to Maturity = 10% = 0.1

Face Value = 1000

Here, first we want to calculate the annual coupon payment from the equation of bond price.

The formula for Price of the Bond is given by:

  

Where, C = Coupon Payment

YTM  = Yeild to maturity

n = Maturity year

FV = Face Value

5

                                                          

                                            950 = C (7.606) + 239.392

                                                                 

C = 93.43%

So, Annual Coupon payment  = 93.43%

Nominal Coupon Rate = Annual coupon payment / Face value

= 93.43% /1000

= 0.0934 = 9.34%

Therefore , the coupon rate on the bond is 9.43%

Another method using excel for calculating Coupon rate

STEP 1

For calculating Coupon rate , first we want to find out PMT or Coupon Payment.

We can calculate it through excel using the formula

= PMT( rate,nper,pv,fv)

where, rate represent as the yield

nper is the time or year to maturity

pv is the present value

fv is the future value

Coupon Payment = PMT( 0.1,15,-950,1000)

= $ 93.43

STEP 2

Coupon rate = Annual payment / face value

= $ 93.43 /1000

= 0.09343

= 9.34 %