Question

Show that if the coupon rate on a bond is larger than the yield-to-maturity, than the price

must be higher than the par value.

Answer 1

This can be proved by using a numerical example.

Let face value = $100

Annual coupon rate = 10%

Annual coupon = $100 x 10% = $10

Years to maturity = 5

Yield-to-maturity = 7% (which is less than 10%)

Therefore,

Bond price ($) = Present value of future coupon payments + Present value of face value

= 10 x P/A(7%, 5) + 100 x P/F(7%, 5)

= 10 x 4.1002** + 100 x 0.7130**

= 41.002 + 71.30

= 112.302 > 100

Therefore, if coupon rate is higher than yield-to-maturity, then bond price is higher than the par value.

**From P/A and P/F Factor tables