Estimation of Free Cash flow to share owners (FKFA) and Free Cashflow 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 shareholders can spend without reducing the value of the firm.

FKFF is used to value the firm as a whole. Does not take into account thecost of external funds

Calculation Comment

Net profit (annual profit) (after tax)

+ Depreciation Depreciation is a cost but not an expense

- Increase (+decrease) in accounts receivable Credit sales does not add liquidity

- Increase (+decrease) in inventory Increasing 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 assets E.g. cash accounts

+ Increase (-decrease) in accounts payable and other short-term liabilities.

+ Increase in deferred taxes A cost, not an expense

+ Interest costs after tax The valuation should separate the business return from its financing costs

= Internally generated cash flow

- Investment in non-current assets The firm cannot be sustained if this would go into what could be used as dividends

- Investments in intangible assets Royalty and goodwill

- Net change in other non-current assets E.g. an increase in financial assets

= FKFF

+ Increase (- decrease) in long-term debt Changes the cash flow available to create added value to the share holders

- Interest cost after tax Financing the firm with external funds diminishes cash flow to owners

= FKFA

Steelers AB

Income Statement year -3 year -2 year -1 year 0Operating revenues 1630 1997 1883 2180Operating expenses -1196 -1445 -1331 -1525Operating profit 434 552 552 655Depreciation -76 -86 -92 -99Earnings after depreciation 358 466 460 556Financial costs -76 -60 -46 -35Earnings before tax 282 406 414 521Tax -81 -104 -132 -158Annual profit 201 302 282 363

Balance Statements year -3 year -2 year -1 year 0AssetsS:a Non-current 1285 1369 1417 1583Inventories 293 343 365 417Receivables 340 346 397 385Liquid 64 70 97 88S:a Current assets 697 759 859 890S:a Assets 1982 2128 2276 2473Equity and liabilitiesShares 597 664 736 813Free reserves 81 246 349 523Total equity 678 910 1085 1336Long-term debt 1014 869 780 793Short-term debt 290 349 411 344Total debt 1304 1218 1191 1137Total equity and debt 1982 2128 2276 2473

Example

Calculation of Free Cash Flow year -2 year -1 year 0Annual profit 302 282+ Depreciation 86 92- Increase accounts receivable -6 -51- Increase inventories -50 -22+ Increase accounts payable 59 62+ Net of tax financing costs 43 33Internally generated cash flow 434 396- Inv.in non-current assets -170 -140Free cash flow to the firm 264 256+ Increase in long-term debt -145 -89-Net of tax financing cost (1-s) -43 -33Free cash flow to the share owners 76 134

363

99

12 Eb385-Bb 397

-52 Eb417-Bb365

-67 Eb344-Bb411

25.2 35*0.72

380.2

-265 Eb1583-Bb1417+depr99

115

13 Eb793-Bb780

25.2

103

The dividend growth model

Vs = D1/(rE-g)

where:

Vs = stock valueD1 = Expected dividend per share next periodrE = required rate of return to equityg = 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 = 0.055 + 0.8*0.08 = 0.119 = 11.9%

Va = (2.45*1.04)/( 0.119 – 0.04) = 32.25

The value of the stock is quite sensitive to the growth assumption. Suppose that the growth rate is 6% instead:

Va =(2.45*1.06)/( 0.119 – 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 thevaluation. In addition, assume that the required rate of return is11.9 %.

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 ntime

year 0

where: Va = share value today; Ut = expected dividend time t; Va,n = ending valueof the share; r = required rate of return on equity (can differ betweenperiods); gn = annual growth in dividends after year n.

extra ordinary growth g% p.a. over n years constant growth gn (perpetual)

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Example: Share valuation with a two phase model

Our company has today: (a) profit per share =13.10; (b) dividendper share (U) = 3.85.

The following projections are available for the next five years (the time overwhich the company is expected to experience extra ordinary growth):• Beta value = 1.45• ROA = 14.50 %• Dividend share (Ua) = 29.5%• Share of retained profits (1-Ua) = 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

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7 steps to solve this example:

1. Calculate the required rate of returnphase 1: r = 0.05 + 1.45*0.08 = 0.166 = 16.6%phase 2: r = 0.05 + 1.1*0.08 = 0.138 = 13.8%

2. Calculate g (expected permanent growth) during phase 1g = (1-Ua)*rE

Ua = 70.5%

rE = [0.145 + (0.145 – 0.065)*1.0]*(1-0.28) = 16.2%

g = 11.4%

3. Projection of dividends during phase 1

Year Profit per share

(increases by 11.4%)

(13.10 at year 0)

Dividend per share

(29.5% is distributed)

1 14.60 4.31

2 16.26 4.80

3 18.12 5.35

4 20.19 5.96

5 22.50 6.64

4. Calculation of value of dividends during phase 1Apply a present value formula

V = 4.31/(1.166)+……….+6.64/(1.166)5 = 16.90

5. Calculation of expected permanent growth in phase 2Here it is assumed that g = 5% but we miss Ua

Ua = 1 – (g/rE) This is the same model as we had earlier for g

where rE = [0.125 + (0.125 – 0.065)*1.0]*(1-0.28) = 13.32%

so Ua = 1 – (0.05/0.1332) = 62.46%

Indicating what? Remember that Ua 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 = 22.50 and g is 5%.

This means that the profit per share in year 6 is 22.50*1.05 = 23.62

We have also that Ua = 62.46% during phase 2. Hence, the expecteddividend in year 6 is = 0.6246 * 23.62 = 14.75

The ending value of future dividends in phase 2 is

= 14.75/(0.138-0.05) = 167.66 (end of year 5). This is the expected

share price .

At year 0 this equals = 167.66/(1.166)5 = 77.79

7. Sum values over phases: 16.90 + 77.79 = 94.69 = 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

Va = FKFA1/(rE – g)

Example:FKFA1 = 100rE = 15%g = 5%

Va = 100/(0.15-0.05) = 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 9,700• 50 % of the firm is financed by debt, the remaining part with equity• The financing costs (interest) was 802• Investments in operating capital amounted to 242.5• 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.

Required rate of return (CAPM):

Calculation of Free Cash Flow Annual profits+ depreciation- Increase operating capital+ interest net of tax '= Cash Flow from operations - Investment in real assets FKFF+ Increase in long-term debt- interest net of tax FKFA

Calculation of Company valueTotal value (millions)Value (p.s)

Calculations:

= 0.045 + 1.05*0.08 = 0.129

2,059

9,700

-242.5

577.4 e.g. 802*(1-0.72)

= 12,093.9

-10,350= 1,743.9

5296.3 e.g. (10,350+242.5)*0.5

-577.4= 6,462.8

= 6,462.8*1.04/(0.129-0.04) = 75,519.8 millions

= 75519.9/150 = 503.5

Cash Flow model with two phases based on FKFA

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this model works best for companies that are expected to have veryhigh levels of growth for a short time period, after which they return toa more normal growth.

This model is preferred for companies that do not pay much dividendsor if the dividends are much higher (or lower) than FKFA.

Another application is for companies whose dividends cannot be easilyestimated, like private companies, or new companies awaiting stockmarket 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• rE = 26%• Interest cost = 0.40 per share

The following assumptions are made:• The growth phase is expected to be 5 years• rE 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-assetratio is 30% (fixed).

year 0 1 2 3 4 5Turnover 27 31.752 37.340352 43.912254 51.640811 60.729593Net profit 6.20 7.2912 8.5744512 10.083555 11.85826 13.945314+depreciation 1.75 kr 2.058 2.420208 2.8461646 3.3470896 3.9361773- Increase operating capital -0.4752 -0.558835 -0.65719 -0.772856 -0.908878+ Interest after tax 0.4 0.4704 0.5531904 0.6505519 0.765049 0.8996977Operating Cash Flow 8.35 9.3444 10.989014 12.923081 15.197543 17.872311- Investment real assets -2.5 -2.94 -3.45744 -4.065949 -4.781557 -5.62311FKFF 6.4044 7.5315744 8.8571315 10.415987 12.2492Increase long-term debt 2.3906 2.8113926 3.3061977 3.8880885 4.5723921Increase interest costs -0.4 -0.4704 -0.55319 -0.650552 -0.765049 -0.899698FKFA 8.3246 9.7897766 11.512777 13.539026 15.921895

Valuation 0 1 2 3 4 5FKFA 8.3246 9.7897766 11.512777 13.539026 15.921895Endvalue 192.1608Present value 7.3216 7.5727192 7.8324695 8.1011294 109.50492Share value 140.3328

Example cont.

=(1-0.3)*(2.94+0.48)

(1-solvency)*(Inv. Real Assets + Inv. Op. cap)

=(31.75-27)*0.1