ABC's bonds are selling today at $77

Finance Oct 17, 2020

ABC's bonds are selling today at $77.10 discount based on a face value of $1000. They have a 6% coupon rate, pay semi annual coupons and will mature in seven years. If ABC were to issue similar bonds today, what will be it's coupon rate if they are sold at par and mature in 7 years?

Expert Solution

We can calculate the yield to maturity by using the following formula in excel:-

=rate(nper,pmt,-pv,fv)

Here,

Rate = Yield to maturity (semiannual)

Nper = 7*2 = 14 periods (semiannual)

Pmt = Coupon payment = $1,000*6%/2 = $30

PV = $771

FV = $1,000

Substituting the values in formula:

= rate(14,30,-771,1000)

= 5.37%

Yield to maturity = Rate * 2

= 5.37%*2

= 10.74%

When the bond is selling at par the coupon rate is equal to yield to maturity.

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