Question

Suppose that the market interest rate is 5%. Calculate the present value of the following. Show how your answer is obtained.i. A coupon bond with an annual coupon payment of $135 and a face value of $1500 that matures in five years.
ii. A discount bond with a face value of $5000 that matures in one year.
iii. A fixed payment loan with annual payments of $163 that matures in three years.

Answer 1

i. A coupon bond with an annual coupon payment of $135 and a face value of $1500 that matures in five years.

Present value of annuity factor:

$PVAF = \frac{1 -(1-γ)^{-n}}{γ}$

n = period

γ = rate of interest

n = 5

γ = 0.05

Present value factor:

$PVF = \frac{1}{(1+γ)^n}$

Present value of bond $= 1500 \times PVF + 135PVAF$

$= 1500 \times \frac{1}{(1+0.05)^5} + 135 \times \frac{1 -(1.05)^{-5}}{0.05} \\ = 1175.29 + 584.47 \\ = 1759.76$

ii. A discount bond with a face value of $5000 that matures in one year.

n = 1

γ = 0.05

$= 5000 \times PVF \\ = 5000 \times \frac{1}{(1+0.05)^1} = 4761.90$

iii. A fixed payment loan with annual payments of $163 that matures in three years.

n = 3

γ = 0.05

Present value of loan $= 163 \times PVAF$

$= 163 \times \frac{1-(1.05)^{-3}}{0.05} \\ = 443.88$