Question

Ashes Divide Corporation has bonds on the market with 12 years to maturity, a YTM of 9.6 percent, and a current price of $1,306.50. The bonds make semiannual payments. What must the coupon rate be on these bonds?

Please explain how to do this on a financial calculator if possible.

Answer 1

Face value of the bond = $1000

The present value of the bond = $1306.50

The bond pays semiannual coupons, so we will consider semi-annual time periods and semiannual YTM

Time to maturity = 12 years

Semi-annual time period = 12*2 = 24

YTM = 9.6%

Semiannual YTM = 9.6%/2 = 4.8%

Method 1: Using financial calculator

Insert these values in ba ii plus calculator

N = 24

I/Y = 4.8

PV = -1306.5 (PV Should be negative because we pay the price of the bond)

FV = 1000

CPT -> PMT [Press CPT and then press PMT]

We get PMT = 69.78218213

Please note that this value is the semiannual coupon payment

Annual coupon payment = 69.78218213*2 = 139.5643643

Annual coupon rate = Annual coupon payment/Face value = 139.5643643/1000 = 0.1395643643 = 13.95643643%

Answer -> Coupon rate = 13.95643643%

Method 2: Using Excel

We can use the PMT function in Excel to calculate the coupons. Since, the bond pays semiannual coupons, hence we will get semi-annula coupon payments

=PMT(4.8%,24,-1306.5,1000) = 69.7821821299873

Annual coupon payments = 69.7821821299873*2 = 139.564364259975

Annual coupon rate = 139.564364259975/1000 = 13.9564364259975%

B6 X V fc =PMT(4.8%,24,-1306.5,1000) C D E F G | A 1 Rate 2 NPER 3 PV 4 FV 5 6 Semiannual coupon 7 B 4.80% 24 -1306.5 1000 69.78218213

Answer -> Coupon rate = 13.9564364259975%