Corporate Finance

Time Value of Money 
 51

In general,

Effective rate = [1 + (r/m)]m – 1 (5)

where r = nominal annual rate and
m= number of times compounding is done in a year.

Try calculating the effective rate in the above example when compounding is done daily, quarterly, and
semi-annually.
Let us extend the idea a little bit. Following data is available for a fixed deposit scheme:

Investment = Rs 5000

Rate of interest = 13 percent

Compounding = Semi-annual

Term = 5 years

The future value would be:

FV = A[1 + (r/m)]m × n (6)

where n = number of years

FV = 5000 [1 + (0.13/2)]2 × 5 = Rs 9385

Had the compounding been annual,

FV = 5000 (1 + 0.13)^5 = Rs 9212

The difference of Rs (9385 – 9212) = Rs 173 is due to semi-annual compounding.

Perpetuities

Some investments make a regular income for ever. Suppose Company-X declares a dividend of Rs 2 per
share. It is expected to remain at this level for ever (the firm is a going concern). If the appropriate discount
rate is 13 percent, the present value of this perpetual stream = (Rs 2/0.13) = Rs 15.40.
In general,

PV of a perpetuity = Per period amount /Discount rate (7)

PV = A/K

If an amount is to grow at a constant rate for ever it is called a growing perpetuity. The present value of a
growing perpetuity can be estimated using the following formula.

PV =

gk

A

–

where k is the discount rate and g is the growth rate.