Question

A bond that pays a higher coupon rate of interest commands a higher price, and the price of existing bonds falls when market interest rates rise. Explain, using the present value formula, why both of these facts are true.

Answer 1

Bond price = Prsent value of future coupon payments (C) + Present value of redemption price (face value, V)

= C x P/A(r%, N) + V x P/F(r%, N)

= [C / (1 + r)] + [C / (1 + r)2] + [C / (1 + r)3] + [C / (1 + r)4] + ..............[C / (1 + r)N] + [V / (1 + r)N]

Therefore,

(I) Values of V, r and N being constant, the higher the value of C (due to higher coupon rate), the higher the bond price.

(II) Values of V, C and N being constant, the higher the value of r, the lower the bond price.