Corporate Finance

60
Corporate Finance

Measuring Return

Suppose an investor purchased 100 shares of XYZ Industries at the rate of Rs 120 each, received dividends
amounting to Rs 600 during the year, and then sold the shares at Rs 140 at the end of the year. The rate of
return an investor receives from buying shares and holding them for a given period of time is equal to the
cash dividends received plus the capital gain (or minus the capital loss) during the holding period divided
by the purchase price of the security.
Expressed as a formula, realized return would be:

R= [D 1 + (P 1 – P 0 )]/P 0 (1)
where
D 1 = Dividend received,
P 1 = Selling price, and
P 0 = Purchase price.

The rate of return on XYZ investment = Rs 2600/12000 = 21.6 percent.

Now consider a multi-period situation. The investor has a 3-year investment horizon.

Purchase price = Rs 200

Dividend receipts = Rs 5, Rs 6, and Rs 10 respectively.

Selling price = Rs 225

One measure of return is the arithmetic average of returns in these three years.

R = [R 1 + R 2 + R 3 ]/3

where
R is the investment return and
R 1 , R 2 , R 3 are periodic returns.

Another measure is the geometric mean of returns.

Rg = [(1 + R 1 )(1 + R 2 )(1 + R 3 )]1/3 – 1

In general, the geometric mean of returns

Rg= [(1 + R 1 )(1 + R 2 )(1 + R 3 ) ··· (1 + RN ]1/N – 1 (2)

where N is the number of periods.