Stock Valuation

Investors buy common stock with the hope that they would be able to recoup the cost of their investment in the form of returns on the investment. Since common stock is equity that is perpetual in nature, the return on investment would be in the form of capital gains when it is sold (if it is sold higher than it is bought) or cash dividends.Cash dividend paid is a cash inflow to the investor, so the value of a share of stock to the investor should be equal to the present value of all future cashflows expected to be received from that stock. The price of a share of common stock would then be:

As said earlier common stock is perpetual and does not mature. So the value should be the present value of an infinite stream of cash flows. This is easier said than done because of the complexity of accurately determining dividends to be paid in perpetuity. Dividends vary and are not fixed and this makes it difficult to determine the value of the stock; this is where the dividend valuation model comes in. We would seek to determine the required rate of return and then deal with different assumptions regarding dividend growth.

Dividend Valuation Model

The current price of a share of common stock is =

Where po represents the price of a share of stock today, and re the required rate of return on common stock. The required rate of return shareholders demand compensates them for investing in the company rather than elsewhere and also for the time vale of money where a dollar today is worth more than a dollar to be received tomorrow.

DIVIDEND GROWTH

If the current dividend is $5 per share and the required rate of return is 10%, then the value of the stock would be:

Po= $5 / 0.10

Po= $50

So if you pay $50 per share and dividends remain constant, you would earn 10% on your investment and be able to recoup the cost of the investment through dividends in 10 years.

If dividends grow at a constant rate g in perpetuity, the present value of the common stock is the present value of all future dividends. The formula is

We then represent the next period’s dividend D₁in terms of this period ‘s dividend D₀compounded one period at the rate g.

D₀ (1+g) = D₁ we now fix in the figures into the previous equation and this gives:

This is known as the discount valuation model where

P₀= Price or value of the share of stock

D_{1 =}Dividend for the next period

D0 = Current Dividend

g = Growth rate

Taking the previous example, we take a few changes that current dividend is $5, and the dividend is capitalized at 10%; instead of remaining the same till perpetuity, the dividends are expected to grow at a rate of 8% per year forever. The value of the share would then be:

= $270

Because dividend for each year continues to grow, then the stock would be worth more than when the dividends are expected to remain the same yearly. Above, we only considered when the growth is positive and increasing. What of if it were on a decline?

Let us now take an example of if dividends where on a decline:

A stock has a current dividend of $3 per share and the required rate of return is 10%. If dividends are expected to decline 5% each year, what is the value of the share of stock today.

From the above, we can deduce that D_{0 =}$3, re = 10%, and G = -5%. Fixing this figures into the dividend valualtion model, we have:

=$19

Two periods from now and we have:

= $18.05

Required rate of return

Required rate of return is the time value of money + compensation. The required rate of return seeks to compensate investors for the time value of money and risk.

Formula for deriving the required rate of return

Re = (D1 / P0) + g

Where re = required rate of return

G = growth rate

Return On Common stock

When we hold common stock, we get returns by either capital gains (an increase in the value of the stock) or through dividends. So therefore, return on stock is comprised of two components which are

The appreciation or depreciation in the market price of the stock
Return in the form of dividends
This can be broken down into capital yields and dividend yield.

Return on stock = Capital Yield + Dividend Yield

Capital yield =

Dividend yield =

Example, supposing 100 shares of a company was bought by you in 2014 for $27 and during 2014, the company paid $0.37 per share as dividends thereby making a total of $37 in dividends. If the whole 100 shares are sold at the end of 2014 for $37, what was your return on your investment?

Possible Solution

Capital Yield: