Estimation of Free Cash flow to share owners (FKFA) and Free Cash flow to the firm (FKFF) -use of the indirect method – starts with the annual profit FKFA is used to value shares. FKFA is the funds that the share holders can spend without reducing the value of the firm. FKFF is used to value the firm as a whole. Does not take into account the cost of external funds

Calculation Comment Net profit (annual profit)(after tax) + DepreciationDepreciation is a cost but not an expense - Increase (+decrease) in accounts receivableCredit sales does not add liquidity - Increase (+decrease) in inventoryIncreasing the inventory is related to expenses. There is no effect on the profit as long as items are not sold. - Increase (+decrease) in other current assetsE.g. cash accounts + Increase (-decrease) in accounts payable and other short-term liabilities. + Increase in deferred taxesA cost, not an expense + Interest costs after taxThe valuation should separate the business return from its financing costs = Internally generated cash flow - Investment in non-current assetsThe firm cannot be sustained if this would go into what could be used as dividends - Investments in intangible assetsRoyalty and goodwill - Net change in other non-current assetsE.g. an increase in financial assets = FKFF + Increase (- decrease) in long-term debtChanges the cash flow available to create added value to the share holders - Interest cost after taxFinancing the firm with external funds diminishes cash flow to owners = FKFA

Example

Eb385-Bb Eb417-Bb Eb344-Bb * Eb1583-Bb1417+depr Eb793-Bb

The dividend growth model V s = D 1 /(r E -g) where: V s = stock value D 1 = Expected dividend per share next period r E = required rate of return to equity g = annual growth rate in dividends =D(t)-D(t-1)/D(t-1) Suitable for: Companies with a stable and relatively low growth in profits and dividends Companies that pay (stable) dividends in accordance with its FKFA Companies with a stable capital structure

Example: suppose that the following information is available in year 0: Profit per share = 3.50 Dividend share = 70% (assumed to be constant) Dividend per share = 2.45 Expected annual growth in profits and dividends = 4% Beta value = 0.8 Risk free rate of return 5.5% per year Risk premium = 8% per year Required rate of return = *0.08 = = 11.9% V a = (2.45*1.04)/( – 0.04) = The value of the stock is quite sensitive to the growth assumption. Suppose that the growth rate is 6% instead: V a =(2.45*1.06)/( – 0.04) = 44.02

Example (cont.): the Growth Dividend Model have an additional use Suppose that a stock is traded at 37 per share at the time of the valuation. In addition, assume that the required rate of return is 11.9 %. What is the underlying growth assumptions for the profits of this firm? 37 = (2.45*(1+g))/ (0.119 – g) g =(4.403 – 2.45)/39.45 = 4.95% This level of growth must be sustained to motivate the stock price.

A Dividend Growth Model with two growth phases (this approach can easily be extended to n phases) year n time  year 0 where: V a = share value today; U t = expected dividend time t; V a,n = ending value of the share; r = required rate of return on equity (can differ between periods); g n = annual growth in dividends after year n. extra ordinary growth g% p.a. over n years constant growth g n (perpetual)

Example: Share valuation with a two phase model Our company has today: (a) profit per share =13.10; (b) dividend per share (U) = The following projections are available for the next five years (the time over which the company is expected to experience extra ordinary growth): Beta value = 1.45 ROA = % Dividend share (U a ) = 29.5% Share of retained profits (1-U a ) = 70.5% Leverage (D/E) = 1.0 Average interest rate on debt = 6.5% Corporate tax rate = 28% The following assumptions relates to phase 2 (constant growth) g is 5% ROA = 12.5% Leverage remains unaltered The Beta value = 1.10

7 steps to solve this example: 1.Calculate the required rate of return phase 1: r = *0.08 = = 16.6% phase 2: r = *0.08 = = 13.8% 2. Calculate g (expected permanent growth) during phase 1 g = (1-U a )*r E U a = 70.5% r E = [ (0.145 – 0.065)*1.0]*(1-0.28) = 16.2% g = 11.4%

3. Projection of dividends during phase 1 YearProfit per share (increases by 11.4%) (13.10 at year 0) Dividend per share (29.5% is distributed) Calculation of value of dividends during phase 1 Apply a present value formula V = 4.31/(1.166)+……….+6.64/(1.166) 5 = 16.90

5. Calculation of expected permanent growth in phase 2 Here it is assumed that g = 5% but we miss U a U a = 1 – (g/r E ) This is the same model as we had earlier for g where r E = [ (0.125 – 0.065)*1.0]*(1-0.28) = 13.32% so U a = 1 – (0.05/0.1332) = 62.46% Indicating what? Remember that U a was 29.5% during phase 1

6. Projection of the share value during phase 2 Note: The profit per share in year 5 was estimated = and g is 5%. This means that the profit per share in year 6 is 22.50*1.05 = We have also that U a = 62.46% during phase 2. Hence, the expected dividend in year 6 is = * = The ending value of future dividends in phase 2 is = 14.75/( ) = (end of year 5). This is the expected share price. At year 0 this equals = /(1.166) 5 = Sum values over phases: = = Share value today!

A cash flow model based on FKFA Note that FKFA can differ from dividends, especially if there is a tax asymmetry between dividends and capital gains V a = FKFA 1 /(r E – g) Example: FKFA 1 = 100 r E = 15% g = 5% V a = 100/( ) = 1000 Use this approach if: The company is in a mature industry and not very different from the industry average. Investments apprx. = depreciation Beta value of stock close to 1 Leverage is stable

Example: FKFA model The following information is available for a company: The annual profit (net) is 2,059 Investments in real assets were 10,350, depreciation was 9, % of the firm is financed by debt, the remaining part with equity The financing costs (interest) was 802 Investments in operating capital amounted to The beta value of the stock is 1.05, the risk-free interest rate is 4.5%, and the risk premium is 8% There are 150 million shares in circulation The corporate tax rate is 28% FKFA is assumed to grow at a rate of 4% p.a.

Calculations: = *0.08 = ,059 9, e.g. 802*(1-0.72) = 12, ,350 = 1, e.g. (10, )* = 6,462.8 = 6,462.8*1.04/( ) = 75,519.8 millions = /150 = 503.5

Cash Flow model with two phases based on FKFA this model works best for companies that are expected to have very high levels of growth for a short time period, after which they return to a more normal growth. This model is preferred for companies that do not pay much dividends or if the dividends are much higher (or lower) than FKFA. Another application is for companies whose dividends cannot be easily estimated, like private companies, or new companies awaiting stock market entrance.

Example: Our company now have: Profit per share = 6.20 Investments per share = 2.50 Depreciation = 1.75 per share Turnover per share = 27 Dividend ratio = 20% of net profit r E = 26% Interest cost = 0.40 per share The following assumptions are made: The growth phase is expected to be 5 years r E is expected to decrease to 22% for the next 5 years The beta value is 1.15 The risk free rate of return is 4.5%, and the risk premium is 8% The dividend ratio will remain Calculate g = (1-0.2)*0.22 = 17.6% we will assume that investments, depreciation, interest costs and turnover will grow according to this rate. Assume: The operating capital is 10% of turnover, the equity-to-asset ratio is 30% (fixed).

Example cont. =(1-0.3)*( ) (1-solvency)*(Inv. Real Assets + Inv. Op. cap) =( )*0.1