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### Valuation

How much are those cash flows worth?

Standard Techniques

- Book Value
- Earnings Multiple
- Liquidation Value
- Discounted Cash-Flow

Graham,J.andH.Campbell,2001,“TheTheoryandPracticeofCorporateFinance:EvidencefromtheField,”Graham,J.andH.Campbell,2001,“TheTheoryandPracticeofCorporateFinance:EvidencefromtheField,”JournalofFinancialEconomics,60(2-3),187-243.

Still one of the most widely used and accepted methods due to certification by accountants, while also being perhaps the most flawed.

Based on historic numbers, ignores the future.

Based on accounting numbers that are potentially flawed and subject to manipulation

Ignores intangibles like customer loyalty.

Ignores risk

The price paid for an asset may have no relation to its value in operation or if it had to be sold or replaced (especially as time passes).

Book ValueFirm (Enterprise) Value = Book Value of AssetsGeneral Motors to certification by accountants, while also being perhaps the most flawed.

Corporate Book Value =>

Common Stock (Equity) Book Value to certification by accountants, while also being perhaps the most flawed.Easy to Calculate

- Case 1: Only common stock outstanding
- Book value equals owner’s equity.

- Case 2: Common and preferred shares outstanding
- Book value equals owner’s equity minus book value of the preferred.

GM Continued to certification by accountants, while also being perhaps the most flawed.No Preferred Stock

Common's Book Value =>

Pitney Bowes Inc (PBI) to certification by accountants, while also being perhaps the most flawed.Has Preferred Stock

Subtract this =>

From this =>

Comparable Companies to certification by accountants, while also being perhaps the most flawed.Earnings Multiples

- Most common method for valuing assets: absent market values.
- Simple but with many potential pitfalls.

From V/EBIT to Market Value to certification by accountants, while also being perhaps the most flawed.

- Obtain Comp(V/EBIT) by using the value-to-earnings ratio of a “comparable” traded company (or the average from a group of comparable companies).
- Use EBIT from the firm or asset you are valuing.

Advantages of V/EBIT to certification by accountants, while also being perhaps the most flawed.

- Easy.
- Makes intuitive sense.
- If your comparables are really comparable then it should work.

Problems with V/EBIT to certification by accountants, while also being perhaps the most flawed.

- Earnings used to calculate V/EBIT are accounting figures.
- To the degree the earnings are subject to manipulation so is EBIT.

- Earnings are subject to short-term fluctuations.
- Looking for “long run” earnings.
- Might need to adjust earnings for extraordinary items.
- Be careful! Some firms have “extraordinary” items every year.

- V/EBIT assumes all companies will generate the same growth.

Other Widely Used Multiples to certification by accountants, while also being perhaps the most flawed.

- Price-to-Earnings
- Price-to-Sales
- Popular for firms with negative earnings.

- Market-to-Book value
- Also popular for firms with negative earnings.

- Asset Value-to-EBIT
- Asset Value-to-Revenues
- Also popular for firms with negative earnings.

Price-Earnings Ratios to certification by accountants, while also being perhaps the most flawed.

- Very, very popular for equity valuation!
- One major pitfall when making comparisons across companies – DEBT!
- The higher a firm’s D/E(quity) ratio the higher the P/E(earnings) ratio.
- Note:
- In D/E the “E” stands for Equity.
- In P/E the “E” stands for Earnings.
- Standard terminology, you just have to know which one is which.

P/E and Debt Example to certification by accountants, while also being perhaps the most flawed.

- A firm has an equity value of 10, earnings of $1, and no debt.
- P/E = 10.

- Assume the tax rate is TC. The firm now issues enough debt so that it pays $1/(1-TC) in interest. Earnings (which are calculated after interest and tax payments) now equal 0.
- New Earnings = 1 – 1/(1-TC) + TC/(1-TC) = 0

- So long as the price of the stock does not go to zero (which it will not if there is any expected growth in the firm) the P/E will equal ∞.
- General rule: More D → Higher P/E.

Liquidation Value to certification by accountants, while also being perhaps the most flawed.

- Useful if you are really thinking of liquidating the firm.
- Ignores any value from future operations.
- Do not use if the firm will continue as a going concern.
- Useful if you want to know if the firm is worth more dead or alive.

Discounted Cash Flow Valuation to certification by accountants, while also being perhaps the most flawed.

- Forecast free cash flows up to some terminal date.
- Estimate the cost of capital (a.k.a. discount rate).
- Estimate terminal value (a.k.a. continuing value) which equals the value after the terminal date.
- Discount to the present.
- Add value of excess cash (proxy for marketable securities) and other non-operating assets.
- Deduct debt and preferred stock to get the market value of the common shares.

Example to certification by accountants, while also being perhaps the most flawed.

- New Haven Tea company expected to produce free cash flows of 200 next year (year 1).
- Expect 10% cash flow growth per year up until year 7. Thereafter expected growth of 2% per year.
- The discount rate is 8%.

Solution to certification by accountants, while also being perhaps the most flawed.

- First seven years is a growing annuity with an initial value of 200 and a growth rate of 10%.

- Terminal value is a perpetuity starting in year 8 with an initial value of 354.3x1.1 = 389.74 and a growth rate of 2%.

Solving for the PV to certification by accountants, while also being perhaps the most flawed.

Three Main Questions to certification by accountants, while also being perhaps the most flawed.

- What are the free cash flows?
- How to estimate the terminal value?
- How do you calculate the cost of capital?

Free Cash Flow I to certification by accountants, while also being perhaps the most flawed.

Arturo likes to calculate FCF via:

Operating Profit (=EBIT)

- Taxes on EBIT
+ Increase in deferred taxes

= Net Operating Profit Less Adjusted Taxes (=NOPLAT)

+ Depreciation

+ Increase in Working Capital Requirements

+ Capital Expenditures

= Free Cash Flow

Free Cash Flow II to certification by accountants, while also being perhaps the most flawed.

- An alternative route (popular on the street) is:
- EBIT
- + Depreciation and Amortization
- = EBITDA
- EBITDA
- + Net Capital Expenditures
- + Change in Working Capital
- Cash Taxes Paid
- Cash Interest Paid
- = Free Cash Flow

From the Cash Flow Statement: Capital Expenditures + Sale of Assets = Net Capital Expenditures

A Note On NOPLAT to certification by accountants, while also being perhaps the most flawed.

- NOPLAT is supposed to represent the free cash flow to the firm before capital investment.
- My preference is to calculate “NOPLAT” as FCF + Cash Interest Paid + Net Capital Expenditures.
- Just remember if you use my version it is not really “NOPLAT.” A better term would be FCFBCINCE, but that acronym is pretty hard to pronounce!
- In the notes that follow where you see the acronym NOPLAT feel free to substitute FCFBCINCE.

Working Capital I to certification by accountants, while also being perhaps the most flawed.(Investment Needed to Operate the Company)

Arturo likes to use:

Operating Cash

+ Accounts Receivable

+ Inventories

- Accounts Payable
- Net Accruals
= Working Capital Reserves

Working Capital II to certification by accountants, while also being perhaps the most flawed.

For changes in working capital Catherine Nolan (a bond analyst and my wife) likes to use:

Changes in Accounts Receivable

+ Changes in Inventories

+ Changes in Accounts Payable

= Changes Working Capital Reserves

Why the Difference? to certification by accountants, while also being perhaps the most flawed.

- Catherine Nolan’s argument.
- Operating cash is what you want to back out, so including it is basically double counting.
- In fact it is often double counting. If a firm spends money on administrative costs and pays with a check, the SG&A account goes up and the cash account goes down.

- Net Accruals can include a number of non-cash items and can be easily manipulated. You are better of ignoring them.
- Working capital is the difference between what you owe people (accounts payable) and what you are hoping to get paid for (accounts receivable and inventories).

- Operating cash is what you want to back out, so including it is basically double counting.

Forecasting Free Cash Flows to certification by accountants, while also being perhaps the most flawed.

- Forecast Sales
- Project size of the target market.
- Project market share.

- Examine historical relationships between sales and other components of free cash flow.
- Be careful here! Are you sure the firm will continue along its current trajectory?

Forecasting Free Cash Flows to certification by accountants, while also being perhaps the most flawed.(continued)

- Check reasonableness of forecasts.
- What do the forecasts assume about the ability of the company to generate “abnormal” (economic) profits?
- Gross domestic product grows at a real rate of 3.41% in a typical year (1929-2003). That means in the long run no firm can grow faster than this.
- Are your long run estimates consistent with this?
- What do your estimates say about the firm’s long run relative market share?
- What do your estimates say about the long run size of the industry relative to the rest of the economy or related industries? For example, if you assume BookUsHotels.com will eventually produce $X in sales you must also assume that the hotel industry will as well.

Forecasting Free Cash Flows to certification by accountants, while also being perhaps the most flawed.(continued)

- Discount Rates
- Be consistent in dealing with free cash flows and discount rates.
- Discount rates should reflect market and not firm specific risk.
- Common mistake is to increase the discount rate in response to firm specific risk.
- Example: A pharmaceutical firm has a 25% chance of making a breakthrough. This does not influence the discount rate. It does influence the expected future cash flows. In this case PV = .25(PV w/ breakthrough) + .75(0).

Reasonable Forecasts Some Guidelines to certification by accountants, while also being perhaps the most flawed.

- What are the assumptions about the company’s ability to create economic profits?
- Key drivers for economic growth are the Return on Investment Capital (ROIC) and the growth rate (g).

Calculating ROIC and g to certification by accountants, while also being perhaps the most flawed.

Invested Capital = Long Term Assets + Working Capital Requirements

where:

The accuracy of your valuation will depend upon the degree to which you accurately forecast ROIC and g.

Valuation and Growth a Few Examples to certification by accountants, while also being perhaps the most flawed.

- All of the following firms are perpetual growth firms.
- They use a constant investment rate (a.k.a. “plowback”) rule.
- They have a constant ROIC (a.k.a. “return on equity”).

Example 1 – Base Line No Growth Firm to certification by accountants, while also being perhaps the most flawed.

Example 2 – Value Creating Firm to certification by accountants, while also being perhaps the most flawed.

Example 3 –Growing But No Value Added Firm to certification by accountants, while also being perhaps the most flawed.

ROIC vs. Discount Rate to certification by accountants, while also being perhaps the most flawed.What it Implies

- ROIC > Discount Rate
- Normal. Firm earns an above average return on some investments. Should stop investing when the marginal investment has a return equal to the discount rate.

- ROIC = Discount Rate
- Likely the firm is over investing! Its investments with returns below the interest rate are offsetting those above. Other possibility, all investments by the firm earn exactly the rate of interest. Yea, sure.

- ROIC < Discount Rate
- Value destruction. Buy out management and stop the firm before it invests again!

Example 4 – No Growth, Value Destroying Firm to certification by accountants, while also being perhaps the most flawed.

Example 5 – Growing, Value Destroying Firm to certification by accountants, while also being perhaps the most flawed.

Ways of Estimating Earnings Growth to certification by accountants, while also being perhaps the most flawed.

- Look at the past.
- The historical growth in earnings per share is a typical starting point.

- Look at what others are projecting.
- Other analysts may be using information you do not have. It is often useful to know what their estimates are.

- Look at fundamentals.
- How much are they investing?
- What is the return on their investment?

Estimating the Firm’s Terminal (Continuing) Value to certification by accountants, while also being perhaps the most flawed.

- Free cash flows (FCF) grow at a constant rate after the forecast horizon.
- Used far more often than any other method.
- Just remember, in the long run NO firm can grow faster than GDP!

r = discount rate, g = growth rate, T = end of the forecast horizon

Terminal Value Estimation to certification by accountants, while also being perhaps the most flawed.Constant Growth – Continued

- Be careful when you use this formula, as your CAPEX in the FCF calculation should match the growth rate you choose.
- This is once again related to the ratio Sales/Fixed Assets.
- One can show that the previous formula can be written in the following way:

ROIC = long-term return on newly invested capital.

This formula may be easier to use than the previous formula since you do not have to estimate CAPEX. Instead it is estimated for you from g and ROIC.

Estimating TV’s to certification by accountants, while also being perhaps the most flawed.Convergence Approach

- Assumes that competitive forces will ensure that after the forecast horizon, returns on the firm’s new investments will equal the discount rate (r).
- ROIC = r and so,

Estimating TV to certification by accountants, while also being perhaps the most flawed.Accounting Values

- Terminal value = Book Value of Invested Capital
- Backward looking.
- Easy to use.

Calculating Terminal Asset Value from Projected Book Value to certification by accountants, while also being perhaps the most flawed.

- PBI grew at about 5% in 2002 and 2% in 2003.
- Average growth rate of 3.5% is not unreasonable.
- In 2003 total assets (book value) equaled 8,891,388.
- Suppose want TV as of 2010 (seven years later) = 8,891,388x1.0357 = 11,312,329.

Economic Value Added to certification by accountants, while also being perhaps the most flawed.(EVA)

EVA = Invested Capital x (ROIC – r)

- What is this?
- A popular buzz word!
- The value the firm created via its investments. Remember, firms should invest so long as the marginal return on equity (ROIC) exceeds the interest rate. This means a typical firm should have a positive EVA.

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