Question

A 11​-year bond pays interest of $28.30 ​semiannually, has a face value of 1,000 , and is selling for 738.53. What are its annual coupon rate and yield to​ maturity?

Answer 1

Given a 11-year bond

where Interest payment = Coupon Payment = CPN = $28.30

Number of Coupon Payments per year = 2 (Semiannually)

Number of Coupon Payments for a 11-year bond = N= (11)*(Number of Coupon Payments per year) = 11*2 = 22

Face Value = $1,000

Present Value = PV = $738.53

a) To find out the Annual Coupon Rate we need to substitute the above values in the following formula,

CPN = (Annual Coupon Rate x FV)/ Number of Coupon Payments per year

Rearranging the above equation, we get

Annual Coupon Rate = (CPN X Number of Coupon Payments per year)/ FV

Annual coupon Rate = (28.30 x 2)/ 1000

= 56.60/ 1000

= 0.0566 or 5.66%

Therefore, Annual coupon Rate = 5.66%

b) We know that YTM of a coupon bond is given by the following equation,

PV = CPN* (1/y)*(1-(1/(1+y)^N)) + FV/ (1+y)^N

Where

PV = Present Value

CPN = Coupon payment

y = YTM (Semiannual)

N = no. of coupon payments for n-year bond

FV = Face Value

We can solve by either using trail and error method or by using the RATE formula in Excel,

The rate formula in Excel is given by ,   

=RATE(NPER,PMT,PV,FV)

Where NPER = N = 22

PMT = CPN = 28.30

PV = -738.53

FV = 1000

We get

	Nper	Rate	PV	PMT	FV	Excel Formula
Given	22		-738.53	28.3	1000
Solve for PV		4.78%				=RATE(NPER,PMT,PV,FV)

Therefore, y = 4.78% because bond pays semi annually, this yield is for a six month period.

In order to convert it into annual rate we need to multiply by the number of coupon payments per year.

Therefore, this 11-year bond has an Yield to Maturity (YTM) = 4.78*2 = 9.56% Annual rate

Therefore, Annual YTM = 9.56%