Question

Bettanin Corporation recently issued 20-year bonds. The bonds have a coupon rate of 8 percent and pay interest semiannually. Also, the bonds are callable in 6 years at a call price equal to 115 percent of par value of $1,000. The par value of the bonds is $1,000. If the yield to maturity is 7 percent, what is the yield to call?

Answer 1

First calculate the bond price:

F = Face value =	$1,000.00
C = Coupon rate = Semi-annual = Coupon /2 = 8%/2 =	4.00%
R = Rate = Required rate of return = Yield semi-annual = Yield / 2 = 7%/2 =	3.50%
Number of coupon payments till maturity = N =	40
PV or Price of Bond = (C x F x ((1-((1+R)^-N)) / R) + (F/(1+R)^N)
Price of the bond =4%*1000*(1-(1+3.5%)^-40)/3.5%+1000/(1+3.5%)^40
Price of the bond =	$1,106.78

Now calculate the yield to call:

Alternate methods:

Using excel function (accurate):

=RATE(12,-40,1106.78,-1150)*2

Yield to call = 7.75%

Or

This is manual method which will give approximate answer:

Call price = CP =	$1,150.00
Bond price = PV =	$1,106.78
Coupon = C =	$40.00
Total number of payment remaining to call = n =	12
Yield to call calculation = Yield = (C+(CP-PV)/n) / ((CP+PV)/2)
Yield =(40+(1150-1106.78))/((1150+1106.78)/2)	7.38% (approx.)

Or

Using BA II plus calculator:

FV = Call value

PV = Present Value or Price of the bond

I/Y = Rate or yield

N = Total number of compounding periods

PMT = Coupon Payment

12= N ; -40 = PMT ; 1106.78 = PV ; -1150 = FV; CPT > I/Y = 3.8758 (semi-annual)

Converting to annual yield = 3.8758% x 2 = 7.75%