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Applied deterministic cash flow analysis—stock valuation. Kevin C.H. Chiang. Intrinsic value. A major task of fundamental analysis is about finding the present values of future expected (deterministic) cash flow streams.

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intrinsic value
Intrinsic value
  • A major task of fundamental analysis is about finding the present values of future expected (deterministic) cash flow streams.
  • Present values are also called intrinsic values, fundamental values, or economic values.
intrinsic values of stocks
Intrinsic values of stocks
  • This topic is about finding intrinsic values of stocks.
  • This task is more challenging than calculating intrinsic values of bonds.
  • The main reason for this is that (1) future, expected cash flows of stocks are highly uncertain; thus, when we use deterministic methods, we are making strong assumptions; (2) there are many ways of defining cash flows for stocks; and (3) firms (and thus their stocks) can potentially have a infinite life.
uncertain cash flows
Uncertain cash flows
  • When deterministic methods are used, the cash flow estimates are treated as if they are certain.
  • We know this is not true.
  • We usually rely on a sensitivity analysis to address this unrealistic assumption; we will talk about sensitivity analysis later.
  • That is, a “range” of fundamental values.
what cash flows
What cash flows?
  • After-tax (corporate tax) cash flows.
  • There are three (popular) different measures of cash flows used by practitioners: (1) expected dividends, (2) expected free cash flows to the firm (FCFF), and (3) expected free cash flows to equity (FCFE).
potential infinite life
Potential infinite life
  • A potential infinite life means an infinite series of cash flows.
  • It is impossible to individually discounting an infinite series of cash flows; there is no end of it.
  • We need some assumptions to make the calculation doable. The usual assumption is to assume there is a constant growth rate in cash flows.
dividends as cash flows
Dividends as cash flows
  • Dividends are the cash flows actually paid to equity investors.
  • Expected dividends should be discounted by the required rate of return on equity (cost of equity).
  • The required rate of return on equity can be estimated by the CAPM (or other asset pricing models): E(Ri) = Rf + i * (E(Rm) – Rf).
fcffs as cash flows
FCFFs as cash flows
  • FCFFs are cash flows available for distribution to debtholders and equityholders.
  • Thus, the appropriate discount rate is the required rate of return on debt and equity.
  • The discount rate is the WACC.
  • WACC = (D / (D+E))*YTM*(1-Tax rate) + (E / (D+E))*E(Ri) if bonds are used to finance 100% of (long-term) debt.
  • D is the market value of debt; E is the market value of equity.
fcfes as cash flows
FCFEs as cash flows
  • FCFEs are the cash flows available for distribution to equityholders.
  • FCFEs can be lower or higher than dividends, depending on the firm’s cash generating capacity and the firm’s dividend policy.
  • FCFEs should be discounted by the required rate of return on equity (cost of equity).
make infinite calculations possible
Make infinite calculations possible
  • The usual assumption is to assume a constant growth rate, g, in cash flows beyond certain year t, i.e., growing perpetuity.
  • PVt = CFt+1 / (r – g).
  • r is the appropriate discount rate.
an example
An example
  • Suppose that we expect IBM will pay $2 per share as dividends in 3 years, and the dividends afterwards are able to grow at 5%. The required rate of return on equity is 10%. What is the price that we expected in 2 years?
  • PV2 = CF3 / (r – g) = $2 / (10% – 5%) = $40.
calculating fcff from net income i
Calculating FCFF from net income, I
  • FCFF is the after-tax cash flow available to debtholders and equityholders after all operating expenses and operating investments have been accounted for.
  • FCFF = NI + net noncash charges + interest expense * (1 – tax rate) – net investment in fixed capital for the year – net investment in working capital for the year.
  • Noncash charges include depreciation expense, intangible-asset amortization expense, etc.
calculating fcff from net income ii
Calculating FCFF from net income, II
  • Net noncash charges must be added back because they reduce NI, but they are not cash outflows.
  • After-tax interest expense must be added back because interest expense net of the related tax shield was deducted in arriving at NI and because interest expense is a cash flow available to debtholders, i.e., part of FCFF.
  • Extra: note that if the firm issues preferred stocks, preferred stock dividends must be added back as well.
calculating fcff from net income iii
Calculating FCFF from net income, III
  • Net investment in fixed capital (long-term assets) is the cash outflow needed to sustain the firm’s current and future operations.
  • For stock valuation, working capital is defined as: accounts receivable + Inventory – accounts payable.
vtwares i
VTwares, I
  • We have VTwares’ income statement and balance sheet for Year 0 and pro forma income statements and balance sheets for Year 1, Year 2, and Year 3.
  • D: depreciation; A: Amortization.
vtwares iii
VTwares, III
  • The appropriate discount rate for FCFF is WACC.
  • WACC may change over time.
  • Analysts usually use target capital structure weights instead of current weights when calculating WACC.
  • Nowadays, there are a number of information providers posting their WACC estimates on the internet, e.g., valuepro.net.
  • Suppose that you find the WACC of VTwares to be 10%.
vtwares iv
VTwares, IV
  • Suppose that your research show that the FCFFs of VTwares will grow at a constant rate of 5% after Year 3. That is, the FCFF for Year 4 is 36*(1+5%)=37.8, etc.
  • This means we can use: PV3 = CF4 / (r – g).
  • Suppose that the market value of debt is 160. Note that the market value is different from the book value of debt, 150.
  • Suppose that the number of shares outstanding is 15.
calculating fcfe from fcff
Calculating FCFE from FCFF
  • FCFE is cash flow available to equityholders only.
  • We need to reduce FCFF by interest paid to debtholders and to add net borrowing (debt issued less debt repayments) over the year.
  • FCFE = FCFF – interest expense * (1 – tax rate) + net borrowing.
vtwares viii
VTwares, VIII
  • Using FCFF as cash flows, the valuation is $29.82 per share.
  • Using FCFE as cash flows, the valuation is $10.97 per share.
  • Differences between FCF-based estimates are usually smaller than this. This is largely due to (1) numbers are hypothetical, (2) the pro forma’s were done for only 3 years (some practitioners will do this for 5 or more years), and (3) this analysis has only 2 stages: before and after Year 3 (many practitioners use three stages, say Years 1-2, Years 3-5, and after Year 5).
dividends vs fcfs
Dividends vs. FCFs
  • About ½ of U.S. publicly traded firms do not pay dividends.
  • This make the use of dividend discount models difficult.
  • Practitioners tend to like FCF-based discount models better when (1) the firm does not pay dividends, (2) the firm pay relatively small amount of dividends relative to its capacity, and (3) outside investors may takeover the firm.
fcff vs fcfe
FCFF vs. FCFE
  • Practitioners tend to work with FCFFs for levered firms with negative FCFEs.
  • Working with FCFEs tend to be more straightforward if firms’ capital structures are relatively stable over time.
end of chapter
End-of-chapter
  • Chapter 4: Problems 5, 6, 7, 8, 9, 10, 14, and 16.