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**Valuation: Cash Flow-Based Approaches**

Dr. Nancy Mangold California State University, East Bay

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**Valuation Security Analyst and Investment Bankers**

Make buy, sell, or hold recommendations Right Price for IPO Price for a corporate acquisition

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**Valuation Economic Theory**

Value of any resource equals the present value of the returns expected from the resource, discounted at a rate that reflects the risk inherent in those expected returns

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Valuation

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**Rationale for Cash-Flow Based Valuation**

Cash is the ultimate source of value Cash serves as a measurable common denominator for comparing the future benefits of alternative investment opportunities

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Cash Flow vs Earnings Investors cannot spend earnings for future consumption Accrual earnings are subject to numerous questionable accounting methods Pooling vs purchase in acquisition valuation Expensing of R & D costs Earnings are subject to purposeful management by a firm

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Cash Flows vs Earnings Earnings are not as reliable or meaningful as a common denominator for comparing investment alternatives as cash $1 earnings (Firm 1) not equal to $1 earnings (Firm 2). $1 Cash (Firm 1) = $1 Cash (Firm 2)

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**Cash Flow-Based Valuation**

Three elements needed Expected periodic cash flows Residual (Terminal) value - Expected cash flow at the end of the forecast horizon Discount rate used to compute the present value of the future cash flows

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I. Periodic Cash Flows Cash Flow to the Investor vs Cash Flow to the Firm Cash Flow to the Investor: CF dividends expected to be paid to the investor Cash Flow to the Firm (CF dividends + CF retained by firm) If the rate of return of retained CF equals the discount rate, either CF will yield the same valuation Use Cash Flow to the Firm

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**Periodic Cash Flows: Relevant Firm Level Cash Flows**

Which cash flow amounts from the projected statement of cash flows the analyst should use to discount to present value when valuing a firm Unleveraged free cash flows leveraged free cash flows

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**Periodic Cash Flows: Relevant Firm Level Cash Flows**

Unleveraged free CF is CF before considering debt vs equity financing Unleveraged free cash flows = CFO + interest cost (net of tax) +(-) Cash flow for investing activities This pool of cash flows is available to service debt, pay dividends and provide funds to finance future earnings

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**Leveraged free cash flows**

CFO - Cash flow for investing activities +(-) net change in ST & LT borrowing +(-) Changes and dividends on on preferred stock Cash flows available to the common shareholders after making all debt service payments to the lenders and paying dividends to preferred shareholders

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**Measurement of Unleveraged and Leveraged Free Cash Flows**

Leveraged Free CF CFO before interest - Cash outflows for interest costs (net of tax savings) =leveraged CFO +(-) CF for Investing Act. +(-)CF for changes in ST< borrowing +(-)CF for changes in and Dividends on preferred stock = leveraged Free CF to Common Shareholders Unleveraged Free CF Cash Flow from Operations before subtracting Cash outflows for interest costs (net of tax savings) =Unleveraged CFO +(-) CF for Investing Act. = Unleveraged Free Cash Flow to All Providers of Capital

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**Unleveraged Free Cash Flows**

If the objective is to value the assets of a firm, then the unleveraged free cash flow is the appropriate cash flow Discount rate should be weighted average cost of capital

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**Leveraged Free Cash Flows**

If the objective is to value the common shareholders’ equity of a firm, then the leveraged free cash flow is the appropriate cash flow Discount rate should be the cost of equity capital

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**Unleveraged vs Leveraged Free Cash Flows**

The Valuation Difference = the value of total interest-bearing liabilities and preferred stock

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**Unleveraged vs Leveraged Free Cash Flows**

Value interest-bearing liabilities by discounting debt service costs (including repayments of principal) at the after tax cost of debt capital

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**Unleveraged vs Leveraged Free Cash Flows**

Valuing preferred stock by discounting preferred stock dividends at the cost of preferred equity

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**Unleveraged vs Leveraged Free Cash Flows**

Valuation for total assets (unleveraged Free CF) = Valuation for common equity (leveraged Free CF) + Value of interest-bearing liabilities + Value of preferred stock

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**Acquiring the operating assets of of another firm**

Acquiring firm will replace with its own financing structure Price to pay for the division’s assets?

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**Acquiring the operating assets of of another firm**

CF these assets will generate Use unleveraged free cash flows (Operating cash flows - cash outflow for investing) Discount these projected cash flows at the weighted average cost of capital of the new division

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**Engage in a leveraged buy out (LBO) of a firm**

Managers offer to purchase the outstanding common shares of the target firm at a particular price if current shareholders will tender them The managers invest their own funds for a portion of the purchase price (usualy 20% - 25%) and borrow the remainder from various lenders

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**Engage in a leveraged buy out (LBO) of a firm**

The managers use the equity and debt capital raised to purchase the tendered shares After gaining voting control of the firm, the managers direct the firm to engage in sufficient new borrowing to repay the bridge loan obtained to execute LBO

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**Engage in a leveraged buy out (LBO) of a firm**

The lenders have a direct claim on the assets of the firm Managers shift any personal guarantees they made on the bridge loans to the firm

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**Price of LBO Use Valuation of common equity**

Leveraged free cash flows discounted at the cost of common equity capital

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Price of LBO Or Use Valuation of total assets and subtract the market value of the debt raised to execute the LBO. PV of unleveraged free cash flows using the weighted average cost of debt and equity capital

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Price of LBO The projected debt service costs after the LBO will differ significantly Valuation of the equity must reflect the new capital structure and the related debt service cost The cost of equity capital will increase as a result of the higher level of debt in the capital structure

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**Nominal Vs Real Cash Flows**

Nominal cash flows include inflationary or deflationary components Real cash flows filter out the effect of changes in general purchasing power Valuation should be the same whether one uses nominal cash flow amounts or real cash flow amounts, as long as discount rate used is consistent with CF

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**Nominal Vs Real Cash Flows**

If projected cash flows ignore changes in the general purchasing power of the monetary unit Then the discount rate should incorporate an inflation component Nominal CF million (land price) Discount rate s/b 1/1.02 /1.1 Interest rate 2% and inflation rate 10% Value

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**Nominal Vs Real Cash Flows**

If projected cash flows filter out the effects of general price changes Then the discount rate should exclude the inflation component Real CF million (land price)/1.1 (inflation rate) Discount rate s/b 1/1.02 Land Value

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**Nominal Vs Real Cash Flows**

A firm owns a tract of land that it expects to sell one year from today for 115 million The selling price reflects a 15% increase in the selling price of the land General price level is expected to increase 10% The real interest rate is 2%

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**The Value of Land Discount rate including expected inflation**

115m x 1/(1.02)(1.1)= million Discount rate excluding expected inflation (115 million/1.10) x 1/1.02 = million

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**PreTax vs After-Tax Cash Flows**

Discount pretax cash flows at a pretax cost of capital Discount after-tax cash flows at an after-tax cost of capital Valuation will be the same

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**Selecting a Forecast Horizon**

For how many future years should the analyst project periodic cash flows? Theoretically: the expected life of the resource to be valued (machine, building ) To value the equity claim on the portfolio of net assets of a firm, the resource has indefinite life Analyst must project the years of CF and residual value at the end of forecast horiz.

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**Selecting a Forecast Horizon**

Prediction of CF requires assumptions for each item in the IS and BS and then deriving the related CF

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**Selecting a Forecast Horizon**

Using a relatively short forecast horizon (3-5 years) enhances the likely accuracy of the projected periodic cash flows near term cash flows is often an extrapolation of the recent past near term cash flows have the heaviest weight in the PV computation But a large portion of the total PV will be related to the residual value

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**Selecting a Forecast Horizon**

The valuation is difficult when near-term cash flows are projected to be negative in rapidly growing firm that finances its growth by issuing common stock All of the firm’s value relates to the less detailed estimation of the residual value

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**Selecting a Forecast Horizon**

Selecting a longer period in the forecast of periodic cash flows (10-15 years) Reduces the influence of the estimated residual value on the total PV Predictive accuracy of detailed cash flow forecasts this far into the future is likely to be questionable

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**Selecting a Forecast Horizon**

It is best to select as a forecast horizon the point at which a firm’s cash flow pattern has settled into an equilibrium This equilibrium position could be either no growth in future cash flows or growth at a stable rate Security analysts typically select a forecast horizon in the range of 4-7 years

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**II. Residual Value Residual Value at end of Forecast Horizon**

= Periodic Cash Flow n-1 x 1+g r-g Where n= forecast horizon g= annual growth rate in periodic cash flows after the forecast horizon r= discount rate

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Residual Value Leveraged free cash flow of a firm in year 5 is 30 millions 0 growth expected Cost of equity capital = 15% Residual value = 30 x (1+0.0)/( ) = 200 million PV of RV (in Year 5)= 200 x 1/(1.15)5 = 99.4 million

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**Residual Value Add growth rate = 6% Residual value =**

30 x (1+0.06)/( ) = million PV = x 1/(1.15)5 = million

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**Residual Value Add growth rate = -6% Residual value =**

30 x (1-0.06)/(.15 - (-0.06) = million PV = x 1/(1.15)5 = 66.8 million Analysts frequently estimate a residual value using multiples of 6-8 times leveraged free cash flows in the last year

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**Difficulty in Using Residual Value**

When the discount rate and growth rate are approximately equal The denominator approaches zero and The multiple becomes exceedingly large. When the growth rate exceeds discount rate The denominator becomes negative, the resulting multiple becomes meaningless

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**Alternative Approach to Estimate Residual Value**

Use free cash flow multiples for comparable firms that currently trade in the market this model provides a market validation for the theoretical model The analyst identifies comparable companies by studying growth rates in free cash flows, profitability levels, risk characteristics and similar factors.

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III. Cost of Capital The analyst uses the discount rate to compute the present value of the projected cash flows The discount rate equals the rate of return that lenders and investors require the firm to generate to induce them to commit capital given the level of risk involved

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Cost of Capital Cost of debt capital equals the after-tax cost of each type of capital provided to a firm

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Cost of Debt Capital Common practice excludes operating liability accounts from weighted average cost of capital The present value of unleveraged free cash flows is the value of total assets net of operating liabilities which equals debt plus shareholders’ equity

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**Cost of Debt Capital The cost of debt capital equals**

(1- marginal tax rate) x yield to maturity of debt The yield to maturity is the rate that discounts the contractual cash flows on the debt to the debt’s current market value The yield=coupon rate if the debt sells at par(face) value

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Cost of Debt Capital Capitalized lease obligation have a cost equal to the current interest rate on collateralized borrowing with equivalent risk

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Cost of Debt Capital The analyst should include the present value of significant operating lease commitment in the calculation of the weighted average cost of capital

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Cost of Debt Capital If the analyst treats operating leases as part of debt financing, then the cash outflow for rent should be reclassified as interest and repayment of debt in leveraged and unleveraged free cash flow

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**Cost of Preferred Equity Capital**

Dividend rate on the preferred stock

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**Cost of Common Equity Capital**

Capital Asset Pricing Model (CAPM) In equilibrium, the cost of common equity capital equals the market rate of return earned by common equity capital

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**Cost of Common Equity Capital**

R(i) = R(f) + b (R(m) - R(i)) Cost of common equity = Interest rate on risk free securities + Market beta (Average return on the market portfolio - Interest rate on risk free securities)

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Cost of Equity Capital

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**Risk Free Interest Rate**

Yield on LT US government securities Not a good choice, the longer the term to maturity, more sensitive to changes in inflation and interest rates, greater systematic risk Common practice to use the yield on either short or intermediate-term US government securities as risk free rate Historically averaged around 6%

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**Market Return Depends on period studied**

Historically the market rate of return has varied between 9 and 13% The excess return over the risk free rate has varied between 3 and 7 percentage points

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Market Returns Financial reference sources publish market equity beta for publicly traded firms Standard & Poor’s Stock Reports Value Line, Moody’s Considerable variation in the published amounts for market beta among different sources due to period used to calculate the betas

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**Adjusting Market Equity Beta**

to Reflect a New Capital Structure The market equity beta computed using past market price data reflects the capital structure in place at a particular time Analyst can adjust this equity beta to approximate what it is likely to be after a change in the capital structure

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**Adjusting Market Equity Beta**

Unleverage the current beta then releverage it to reflect the new capital structure Current leveraged equity beta = Unleveraged Equity beta [1+(1-income tax rate) ( Current market value of debt)/ current market value of equity)]

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**Adjusting Market Equity Beta**

Income tax rate = .35 Debt/equity ratio = .60 Change D/E ratio to 140% Unleveraged equity beta x 0.9 = X [1+ ( ) (0.60/1.0)] X = 0.65

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**Adjusting Market Equity Beta**

Releveraged market beta Y = 0.65 [ 1 + ( )(1.4/1.0)] Y= 1.24

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**Evaluating the Cost of Equity Capital Using CAPM: Criticisms**

Market betas do not appear to be stable over time and are sensitive to the time period used in their computation The excess market rate of return is not stable over time and is likewise sensitive to the time period Fama and French suggests that during the 1980s size was a better proxy for risk than market beta

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**Weights Used for Weighted Average Cost of Capital**

Should use the market values of each type of capital Market value of debt securities is disclosed in notes to financial statements Market price quotations for equity securities provide the amounts for determining the market value of equity

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**A Firm’s Capital Structure on Balance Sheet**

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**Cost of Capital LT Debt 8% x (1-.35) = 5.2% Preferred Equity 4%**

Common Equity 6% + .9 (13% - 6%) = 12.3%

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**Weighted Average Cost of Capital**

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**Valuation of a Single Project**

Investment = 10 million Unleveraged CF 2 million/year forever Financing 6 million debt Financing 4 million Common Equity Debt interest rate 10% Tax rate 40% Cost of Capital %

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**Value of Common Equity Unleveraged Free Cash Flow 2,000,000**

Interest paid on Debt .10*6,000,000 (600,000) Income Tax Savings on Interest .4*600,000 240,000 Leveraged Free CF 1,640,000

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**Value of Common Equity The value of the project to the common equity**

/.25625=6,400,000 Excess over investment 6,400,000-4,000,000=2,400,000 The factor of PV of an annuity that last forever is 1/r

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**Value of Debt + Equity Value of Debt After tax cost for debt is 6%**

6% = (10% * (1-40%)) The common equity cost %

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Value of Debt + Equity

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**Value of Debt + Equity Type of Capital Amt Weight Cost Weighted**

Average Debt 6M .48387 .06 .02903 Common Equity 6.4M .51613 .25625 .13226 Total 12.4 M 1.00 .16129

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**Value of Debt + Equity PV (Debt + Equity) is**

2,000,000/ = 12,400,000 Subtracting 6 million of debt Common Equity is 6.4 million

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**Valuation of Coke Yr 8 Yr 9 Yr 10 Yr 11 Yr 12 CF from Operations 3,610**

3,788 3,974 4,166 4,366 CF from Investing -1,198 -1,390 -1,534 -1,691 -1,866 CF from Debt Financing 1,017 1,355 1,619 1,835 1,988 Leveraged Free CF 3,429 3,753 4,059 4,310 4,488

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Year 12 Residual Value The analyst make assumption about net cash flows after year 12 The average compound growth rate of leveraged free CF between year 8-12 is 7%, assume it will remain at 7%

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**Year 12 Residual Value Yr 7 market beta is .97 Risk free rate = 6%**

Excess Mkt Return over Risk Free Rate = 7% Cost of Equity Capital = 6% + .97(7%) = 12.8% 4,488 x = $82,796

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**Present Value Year CF 12.8 Factor PV 8 3,429 .88652 3,040 9 3,753**

.79719 2,992 10 4,059 .69674 2,828 11 4,310 .61768 2,662 12 4,488 .54759 2,458 Aft 12 82,796 (4488x(1.07/ )) 45,338 Total 59,318

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**Price per Share price per share**

59,318 million/2,481 million shares = 23.91 Coke’s market price in yr 7 = 52.63

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**Price Difference Inaccurate projections of future cash flow**

Errors in measuring the cost of equity capital Market inefficiencies in the pricing of Coke

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**Advantages- Present Value of Cash Flow Valuation**

Focus on cash flows Projected amounts of CF result from projecting likely amounts of revenues, expenses, assets, liabilities and shareholders’ equity which require the analyst to think through many future operating, investing and financing decisions of a firm

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**Disadvantages of the PV of Future Cash Flow Valuation**

The residual or terminal value tends to dominate the total value in many cases This residual value is sensitive to assumptions made about growth rates after the forecast horizon The projection of cash flows can be time consuming and costly when analyst follow many companies and identify under and overvalued firms regularly.

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