Question

Please complete the following problems. Please explain and show your work for all calculations: You intend to purchase a 10-year, $1,000 face value bond that pays interest of $60 every six months. If the yield to maturity is 10% with semiannual compounding, how much should you be willing to pay for this bond? A ten year bond with a coupon rate of 12% (payable annually) and a face value of $1,000 is selling for $1,192.50 today. What is the bond’s yield to maturity? A ten year bond with an annual coupon rate of 12% payable semi-annually is selling for $1,059.75 today. Its face value is $1,000. What is the bond’s yield to maturity?

Answer 1

Answer to Question 1:

Face Value = $1,000
Semiannual Coupon = $60

Time to Maturity = 10 years
Semiannual Period = 20

Annual YTM = 10%
Semiannual YTM = 5%

Price of Bond = $60 * PVIFA(5%, 20) + $1,000 * PVIF(5%, 20)
Price of Bond = $60 * (1 - (1/1.05)^20) / 0.05 + $1,000 / 1.05^20
Price of Bond = $1,124.62

Answer to Question 2:

Face Value = $1,000
Current Price = $1,192.50

Annual Coupon Rate = 12%
Annual Coupon = 12% * $1,000
Annual Coupon = $120

Time to Maturity = 10 years

Let Annual YTM be i%

$1,192.50 = $120 * PVIFA(i%, 10) + $1,000 * PVIF(i%, 10)

Using financial calculator:
N = 10
PV = -1192.50
PMT = 120
FV = 1000

I = 9%

Annual YTM = 9.00%

Answer to Question 3:

Face Value = $1,000
Current Price = $1,059.75

Annual Coupon Rate = 12%
Semiannual Coupon Rate = 6%
Semiannual Coupon = 6% * $1,000
Semiannual Coupon = $60

Time to Maturity = 10 years
Semiannual Period = 20

Let Semiannual YTM be i%

$1,059.75 = $60 * PVIFA(i%, 20) + $1,000 * PVIF(i%, 20)

Using financial calculator:
N = 20
PV = -1059.75
PMT = 60
FV = 1000

I = 5.50%

Semiannual YTM = 5.50%
Annual YTM = 2 * 5.50%
Annual YTM = 11.00%