Notes(6)

An asset which is expected to produce future cash flows has a value which is equivalent to the present value of all those expected cash flows. An examination of PV = FV x PVIF_k%,n is that the value is a function of:

3. Investor's required rate of return (k) which is a function of the riskiness of the expected cash flows

The Intrinsic value is that value which an investor places on an asset given his information set (that is all the information that he has) and his expectations (beliefs). Thus one asset can have different values depending on the investor valuing it.

The basic valuation model [also known as the Discounted Cash Flow (DCF) method] therefore is given by:

Common Stocks like other assets derive their values from expected future cash flows. These cash flows are comprised of dividends which are paid from the income of the corporation and, if applicable, the selling price of the stocks at the end of some holding period. The investor expects to earn capital gains from the latter . From here onwards however, we will assume that the investor does not wish to sell the stock (hence he will only receive dividends every year), and therefore the basic stock valuation model is given by:

Since the value of a stock is dependent on the dividend then the valuation models should reflect the dividend pattern. Consider a stock which is expected to pay a constant dividend through time. It will experience no growth or decline in the future . This is a zero growth stock which is similar to a perpetuity. The price of the stock is given by:

A local company pays a dividend of $0.15 p.a. and is expected to experience no growth in the indefinite future. If the investor's required rate of return is 5% per annum and the stock is being sold for $2.50 in the market place should the investor purchase the stock?

This is the stock's intrinsic value which is the value the investor places on the stock given his information and expectations of the cash flows and the riskiness of the cash flows . The investor will purchase the stock so long as:

The market price reflects the marginal (average) investor's information or expectations which may be different from that of the individual investor and therefore the reason for the difference in value.

This is also called the Gordon model. It aims to find the expected value of a stock which is experiencing growth at about the same rate as that of the economy. The assumption is that if the company maintains its dividend payout ratio then dividends will grow at about the same rate as the economy.

The expected or intrinsic value of a stock today given the last period's dividend of D_0,a dividend growth rate to infinity of g, and the investor's required rate of return k, is equal to:

Assumption: k must be greater than g i.e. k-g (positive) which will give a positive price. (a negative price is meaningless!)

A Company last paid a dividend of $0.90 . it is expected that dividend will grow at 25% per annum for the foreseeable future and the investors are requiring 30 % per annum for stocks in this risk class. What is a fair price for the stock?

Note - the k in our normal growth equation is the required rate of return, but when we transform the equation to make k the subject (as we did above), we are finding an expected rate of return. Obviously the transformation requires that k = k^ . This equality holds if the stock market is in equilibrium, a condition that is discussed later below.

Additionally, remember that there are two components of the rate of return (Dividend yield + capital gains yield) i.e. the growth rate is also referred to as the capital gains yield. This is so because:

A Company last paid a dividend of $1.35 . It is expected to grow at 25% indefinitely and has a fair price of $11.25. What is the expected rate of return on the stock?

Some stocks will experience growth at a higher rate than that being experienced by the general economy. This may be due to several reasons

These factors would have provided the company with a competitive advantage over its rivals. The higher rate of growth as a result of the above will only last for a limited period after which the company will settle down to more stable growth.

To find the value of such a stock we need a three step approach. In step 1 we discount the individual dividends during the supernormal/non constant growth period and sum the results. In step 2 we find the price of the stock at the end of the supernormal/non constant growth period (a.k.a. Terminal/Horizon date) using only those cash flows expected in the normal growth period and then discount this price back to time zero (0). Finally, in step 3, we add the results from steps 1 & 2.

What is the price of a stock which last paid a dividend of $2 and is expected to grow at 25% over the next four years after which it will settle down at a stable rate of 10% per annum? The investor requires 40% for a stock of equivalent risk.

The above approach to find the value of a stock that experienced non-constant growth can also be adapted to find the value of a firm, particularly when the firm does not pay regular dividends, if any at all. Valuing the firm will utilize the Free Cash Flow (FCF) concept covered in chapter/topic 2. Recall that:

Free Cash Flow (FCF) = NOPAT � Net investment in operating capital

or FCF = Operating cash flow � Gross investment in operating capital

where:

NOPAT = EBIT (1-T)
Net investment in operating capital = the difference in Total Operating Capital between two years
Total Operating Capital = Net operating working capital (NOWC) + Net Fixed Assets
NOWC = Current assets � non-interest bearing current liabilities

and

Operating Cash Flow = NOPAT + Depreciation
Gross investment in operating capital = Net investment in operating capital + Depreciation

The value of firm using this FCF model is the present value of all of the firm's free cash flows discounted at what is called the weighted average cost of capital (WACC). This WACC will be covered in more detail in Chapter/Topic 9 - Cost of Capital. However for now, the WACC serves the same purpose as that of the 'interest rate' that we have been using up until this point in time i.e. it serves as the rate used to discount cash flows.

Eg. A company who has 100,000 shares of common stock outstanding was recently formed and unlikely to pay any dividends in the foreseeable future. However, its projected free cash flows (all occurring at year end) is as follows:

After the fourth year, it is projected that its FCF will grow at a rate of 10% p.a. for the indefinite future. Given that its weighted average cost of capital is 15%, compute (a) the value of the firm as a whole and (b) the value per share.

PV = 200,000(PVIF 15%, 1) + 250,000(PVIF 15%, 2) + 280,000(PVIF 15%, 3) + 310,000(PVIF 15%, 4) + [310,000(1.10)/(0.15 - 0.10)](PVIF 15%, 4)

= 200,000(0.8696) + 250,000(0.7561) + 280,000 (0.6575) + 310,000 (0.5718) + 6,820,000(0.5718)

Recall that k_x, the required rate of return on Stock X, can be found using the Security Market Line (SML) equation as was discussed in the Capital Asset Pricing Model (CAPM) in Topic # 4, Risk and Return. i.e. k_x = k_rf + (k_m - k_rf) b_x . Now, we have just earlier developed a formula to determine a stock's expected rate of return based on the variables: Price, dividends and the growth rate. i.e. k^_x = D₁ / P₀ + g. We have also seen from Chapter 5, Risk and Return, that when the expected rate of return of a stock > the required rate of return the stock, the stock is said to be under priced and when the expected rate of return is < the required rate of return of the stock, the stock is said to be over priced. In the former case, investors will want to buy more of this stock and this great demand will in turn drive the price upwards to the 'correct' price. In the latter case, investors will want to sell their stock, but not many people would want to buy these overpriced stocks. This lack of demand will in turn drive the selling price down towards the 'correct' price.

At this 'correct' price, we will see that the required rate of return = the expected rate of return. i.e.

It is at the above point that the market is said to be in equilibrium. Alternatively, the market is in equilibrium when the actual market price = the intrinsic value i.e.

Yr	0	1	2	3	4
$	0	200,000	250,000	280,000	310,000