Question

Through an example, developed by you, explain the meaning of the present value of the annuity of a bond.

Answer 1

The present value of an annuity is the current value of a set of cash flows in the future discounted at a specific rate.

Higher the discount rate lower the present value.

There are two types of annuity;

1. Ordinary annuity (payment at the end of the period)

2. Annuity due (payment at the beginning of the period)

Most common type of annuity is the Ordinary annuity. Hence the example will explained for this.

Present Value PV = PMT * ( ( 1 - (1 / (1 + r) ^ n ) ) / r)

PV = the present value of an annuity cash flows

PMT = annuity payment done at each period

r = discount rate

n = the number of periods in which payments are done

Example:

An investment option that pays annuity of 50000 per year for 30 years discount rate is 7%

Hence the PV of annuity = PMT * ( ( 1 - (1 / (1 + r) ^ n ) ) / r)

= 50000 * ( ( 1 - (1 / (1+0.07)^30 ) ) / 0.07

= 620,452.05

Suppose if it is annuity due

PV = PMT * ((1 - (1 / (1 + r) ^ n)) / r) * (1 + r)

= [50000 * ( ( 1 - (1 / (1+0.07)^30 ) ) / 0.07] * 1.07

= 663,883.70