Question

Examine the following two bonds:

Bond A's market value is $1,065, it pays an annual coupon of $70, and it will mature in 5 years, paying $1,000. The yield to maturity is 6 percent.

Bond B's market value is $,1040, it pays an annual coupon of $60, and it will mature in 3 years, paying $1,000. The yield to maturity is 5 percent.

Which of the bonds trades at a greater premium to its present value? ***Please show all work***

Answer 1

Bond A:

Face Value = $1,000
Annual Coupon = $70
Time to Maturity = 5 years
YTM = 6%

Intrinsic Value = $70 * PVIFA(6%, 5) + $1,000 * PVIF(6%, 5)
Intrinsic Value = $70 * (1 - (1/1.06)^5) / 0.06 + $1,000 / 1.06^5
Intrinsic Value = $1,042.12

Market Value = $1,065

So, Bond A is trading below its present value

Bond B:

Face Value = $1,000
Annual Coupon = $60
Time to Maturity = 3 years
YTM = 5%

Intrinsic Value = $60 * PVIFA(5%, 3) + $1,000 * PVIF(5%, 3)
Intrinsic Value = $60 * (1 - (1/1.05)^3) / 0.05 + $1,000 / 1.05^3
Intrinsic Value = $1,027.23

Market Value = $1,040

So, Bond B is trading at a greater premium to its present value