A bond has a face value of $1,000, coupon of 5% (the first payment is in...

A bond has a face value of $1,000, coupon of 5% (the first payment is in a year), and maturity in two tears. The bond’s price today is $963.84. What is the bond’s yield to maturity?

Expert Solution

Face value	$1,000
Coupen annually	5%

Coupen amount	$50

Maturity	2 years

Bond Price	$963.84

YTM :

Price of bond =	Coupen * PVAF( YTM, Maturity) + Redemption value * PVF( YTM,Maturity)

963.84 =	50 * PVAF( YTM,2) + 1000* PVF(YTM,2)

Here bond price is less than face value hence YTM be more than Coupen rate
Therefore lets assume YTM be 6%

Price of bond =	50PVAF(6%,2) + 1000PVF(6%,2)
	501.8334+1000.89
	981.67

Let YTM be 7% Then:

Price of bond =	50PVAF(7%,2) + 1000PVF(7%,2)
	501.8080+1000.8734
	963.80
Therefore YTM is 7% asCalculated above

Note:
Present value Annuity Factor ( 6%, 2) =	1/(1.06)^1 + 1/1.06)^2
Present valueFactor(6%,2) =	1/1.06^2

jeff jeffy answered 1 year ago

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