Question

10-year corporate bond has a coupon rate of 6% with semi-annual payments. If interest rates rise to 7% on similar bonds then what is the value of the bond in the marketplace?

A 10-year corporate bond has a coupon rate of 6% with semi-annual payments. If interest rates rise to 5% on similar bonds then what is the value of the bond in the marketplace?

A 10-year corporate bond has a coupon rate of 6% with annual payments. If the current value of the bond in the marketplace is $900, then what is the Yield-to-Maturity (YTM)?

A 10-year corporate bond has a coupon rate of 6% with annual payments. If the current value of the bond in the marketplace is $1100, then what is the Yield-to-Maturity (YTM)?

Answer 1

Answer to Question 1:

Par Value = $1,000

Annual Coupon Rate = 6.00%
Semiannual Coupon Rate = 3.00%
Semiannual Coupon = 3.00% * $1,000
Semiannual Coupon = $30

Time to Maturity = 10 years
Semiannual Period = 20

Annual Interest Rate = 7.00%
Semiannual Interest Rate = 3.50%

Current Price = $30 * PVIFA(3.50%, 20) + $1,000 * PVIF(3.50%, 20)
Current Price = $30 * (1 - (1/1.035)^20) / 0.035 + $1,000 / 1.035^20
Current Price = $30 * 14.212403 + $1,000 * 0.502566
Current Price = $928.94

Answer to Question 2:

Par Value = $1,000

Annual Coupon Rate = 6.00%
Semiannual Coupon Rate = 3.00%
Semiannual Coupon = 3.00% * $1,000
Semiannual Coupon = $30

Time to Maturity = 10 years
Semiannual Period = 20

Annual Interest Rate = 5.00%
Semiannual Interest Rate = 2.50%

Current Price = $30 * PVIFA(2.50%, 20) + $1,000 * PVIF(2.50%, 20)
Current Price = $30 * (1 - (1/1.025)^20) / 0.025 + $1,000 / 1.025^20
Current Price = $30 * 15.589162 + $1,000 * 0.610271
Current Price = $1,077.95

Answer to Question 3:

Par Value = $1,000
Current Price = $900

Annual Coupon Rate = 6.00%
Annual Coupon = 6.00% * $1,000
Annual Coupon = $60

Time to Maturity = 10 years

Let Annual YTM be i%

$900 = $60 * PVIFA(i%, 10) + $1,000 * PVIF(i%, 10)

Using financial calculator:
N = 10
PV = -900
PMT = 60
FV = 1000

I = 7.45%

Annual YTM = 7.45%

Answer to Question 4:

Par Value = $1,000
Current Price = $1,100

Annual Coupon Rate = 6.00%
Annual Coupon = 6.00% * $1,000
Annual Coupon = $60

Time to Maturity = 10 years

Let Annual YTM be i%

$1,100 = $60 * PVIFA(i%, 10) + $1,000 * PVIF(i%, 10)

Using financial calculator:
N = 10
PV = -1100
PMT = 60
FV = 1000

I = 4.72%

Annual YTM = 4.72%