Continuing with the last question, on Jan. 1 of Year 3 the equipment breaks and is deemed worthless. The bank calls in the loan. What happens in Year 3?

Now the company must writedown the value of the equipment down to $0.  At the beginning of Year 3, the equipment is on the books at $80 after one year’s depreciation.  Further, the company must pay back the entire loan.  Income statement: The $80 writedown causes net income to decline $48.  There is no further depreciation expense and no interest expense.   Cash Flow Statement: Net income down $48 but the writedown is non-cash so add $80.  Cash flow from financing decreases $100 when we pay back the loan.  Net cash is down $68.  Balance Sheet:  Cash (asset) down $68, PP&E (asset) down $80, Debt (liability) down $100 and Retained Earnings (shareholders’ equity) down $48.  Left side of the balance sheet is down $148 and right side is down $148 and we’re good!

Same question as the previous but the company finances the purchase of equipment by issuing debt rather than paying cash.

First YearIncome Statement:  No depreciation and no interest expense so no change.  Cash Flow Statement:  No change to net income so no change to cash flow from operations.  Just like the previous question, we’ve got a $100 increase in capex so there is a $100 use of cash in cash flow from investing activities.  Now, however, in our cash flows from financing section, we’ve got an increase in debt of $100 (source of cash).  Net effect is no change to cash.  Balance Sheet:  No change to cash (asset), PP&E (asset) up $100 and debt (liability) up $100 so we balance.

Second Year:  Same depreciation and tax assumptions as previously.  Let’s also assume a 10% interest rate on the debt and no debt amortization.  Income Statement:  Just like the previous question:  $20 of depreciation but now we also have $10 of interest expense.  Net result is a $18 reduction to net income ($30 x (1 – 40%)).  Cash Flow Statement:  Net income down $18 and depreciation up $20.  No change to cash flow from investing or financing activities (if we assumed some debt amortization, we would have a use of cash in financing activities).  Net effect is cash up $2.  Balance Sheet:  Cash (asset) up $2 and PP&E (asset) down $20 so left side of balance sheet down $18.  Retained earnings (shareholders’ equity) down $18 and voila, we are balanced.

A company makes a $100 cash purchase of equipment on Dec. 31. How does this impact the three statements this year and next year?

First Year:  Let’s assume that the company’s fiscal year ends Dec. 31.  The relevance of the purchase date is that we will assume no depreciation the first year.  Income Statement:  A purchase of equipment is considered a capital expenditure which does not impact earnings.  Further, since we are assuming no depreciation, there is no impact to net income, thus no impact to the income statement.  Cash Flow Statement:  No change to net income so no change to cash flow from operations.  However we’ve got a $100 increase in capex so there is a $100 use of cash in cash flow from investing activities.  No change in cash flow from financing (since this is a cash purchase) so the net effect is a use of cash of $100.  Balance Sheet:  Cash (asset) down $100 and PP&E (asset) up $100 so no net change to the left side of the balance sheet and no change to the right side.  We are balanced.

Second Year:  Here let’s assume straightline depreciation over 5 years and a 40% tax rate.  Income Statement:  Just like the previous question:  $20 of depreciation, which results in a $12 reduction to net income.  Cash Flow Statement:  Net income down $12 and depreciation up $20.  No change to cash flow from investing or financing activities.  Net effect is cash up $8.  Balance Sheet:  Cash (asset) up $8 and PP&E (asset) down $20 so left side of balance sheet doen $12.  Retained earnings (shareholders’ equity) down $12 and again, we are balanced.

How does ??? impact the three financial statements?

Varieties of this question are some of the most common technical question asked in interviews today.  This type of question attempts to test your understanding of how the three financial statements (income statement, balance sheet, cash flow statement) fit together.  The most common variation of this question is how does $10 of depreciation affect the three financial statements (answered below).  I’ve posted a few additional examples as well.

To answer this question, take the 3 statements one at a time. My advice is to start with the income statement.  Remember to tax-affect any change in revenue or costs (usually you will be told to assume a tax rate of 40%).  Work your way down to net income.  Next, tackle the cash flow statement.  The first line of the cash flow statement is net income so start with that and work your way down to net change in cash.  Last, take the balance sheet.  The first line of the balance sheet is cash so again, start with that.  The balance sheet must balance in order for your answer to be correct, which is why I recommend doing the balance sheet last.  Remember the basic balance sheet equation:  Assets = Liabilities + Shareholders’ Equity.

Don’t get too stressed when asked a question like this.  Just take it slowly, one statement at a time.

What are some characteristics of a company that is a good LBO candidate?

Notwithstanding the recent LBO boom where nearly all companies were considered to be possible LBO candidates, characteristics of a good LBO target include steady cash flows, limited business risk, limited need for ongoing investment (e.g. capital expenditures or working capital), strong management, opportunity for cost reductions and a high asset base (to use as debt collateral).  The most important trait is steady cash flows, as the company must have the ability to generate the cash flow required to support relatively high interest expense.

Let’s say you run an LBO analysis and the private equity firm’s return is too low. What drivers to the model will increase the return?

Some of the key ways to increase the PE firm’s return (in theory, at least) include:

  • – reduce the purchase price that the PE firm has to pay for the company
  • – increase the amount of leverage (debt) in the deal
  • – increase the price for which the company sells when the PE firm exits its investment (i.e. increase the assumed exit multiple)
  • – increase the company’s growth rate in order to raise operating income/cash flow/EBITDA in the projections
    decrease the company’s costs in order to raise operating income/cash flow/EBITDA in the projections

Why do private equity firms use leverage when buying a company?

By using significant amounts of leverage (debt) to help finance the purchase price, the private equity firm reduces the amount of money (the equity) that it must contribute to the deal.  Reducing the amount of equity contributed will result in a substantial increase to the private equity firm’s rate of return upon exiting the investment (e.g. selling the company five years later).

Walk me through an LBO analysis…

First, we need to make some transaction assumptions.  What is the purchase price and how will the deal be financed?  With this information, we can create a table of Sources and Uses (where Sources equals Uses).  Uses reflects the amount of money required to effectuate the transaction, including the equity purchase price, any existing debt being refinanced and any transaction fees.  The Sources tells us from where the money is coming, including the new debt, any existing cash that will be used, as well as the equity contributed by the private equity firm.  Typically, the amount of debt is assumed based on the state of the capital markets and other factors, and the amount of equity is the difference between the Uses (total funding required) and all of the other sources of funding.

The next step is to change the existing balance sheet of the company to reflect the transaction and the new capital structure.  This is known as constructing the “proforma” balance sheet.  In addition to the changes to debt and equity, intangible assets such as goodwill and capitalized financing fees will likely be created.

The third, and typically most substantial step is to create an integrated cash flow model for the company.  In other words, to project the company’s income statement, balance sheet and cash flow statement for a period of time (say, five years).  The balance sheet must be projected based on the newly created proforma balance sheet.  Debt and interest must be projected based on the post-transaction debt.

Once the functioning model is created, we can make assumptions about the private equity firm’s exit from its investment.  For example, a typical assumption is that the company is sold after five years at the same implied EBITDA multiple at which the company was purchased.  Projecting a sale value for the company allows us to also calculate the value of the private equity firm’s equity stake which we can then use to analyze its internal rate of return (IRR).  Absent dividends or additional equity infusions, the IRR equals the average annual compounded rate at which the PE firm’s original equity investment grows (to its value at the exit).

While the private equity firm’s IRR is usually the most important piece of information that comes out of an LBO analysis, the analysis also has other uses.  By assuming the PE firm’s required IRR (amongst other things), we can back into a purchase price for the company, thus using the analysis for valuation purposes.  In addition, we can utilize the LBO model to analyze the trend of credit statistics (such as the leverage ratio and interest coverage ratio) which is especially important from a lender’s perspective.

Explain the concept of synergies and provide some examples.

In simple terms, synergy occurs when 2 + 2 = 5.  That is, when the sum of the value of the Buyer and the Target as a combined company is greater than the two companies valued apart.  Most mergers and large acquisitions are justified by the amount of projected synergies.  There are two categories of synergies:  cost synergies and revenue synergies.  Cost synergies refer to the ability to cut costs of the combined companies due to the consolidation of operations.  For example, closing one corporate headquarters, laying off one set of management, shutting redundant stores, etc.  Revenue synergies refer to the ability to sell more products/services or raise prices due to the merger.  For example, increasing sales due to cross-marketing, co-branding, etc.  The concept of economies of scale can apply to both cost and revenue synergies.

In practice, synergies are “easier said than done.”  While cost synergies are difficult to achieve, revenue synergies are even harder.  The implication is that many mergers fail to live up to expectations and wind up destroying shareholder value rather than create it.  Of course, this last fact never finds its way into a banker’s M&A pitch.

Why might one company want to acquire another company?

There are a variety of reasons why companies do acquisitions.  Some common reasons include:

  • – The Buyer views the Target as undervalued.
  • – The Buyer’s own organic growth has slowed or stalled and needs to grow in other ways (via acquiring other companies) in order to satisfy the growth expectations of Wall Street.
  • – The Buyer expects the deal to result in significant synergies (see the next post for a discussion of synergies).
  • – The CEO of the Buyer wants to be CEO of a larger company, either because of ego, legacy or because he/she will get paid more.

What is goodwill and how is it calculated?

Goodwill, a type of intangible asset, is created in an acquisition and reflects the value (from an accounting standpoint) of a company that is not attributed to its other assets and liabilities.  Goodwill is calculated by subtracting the target’s book value (written up to fair market value) from the equity purchase price paid for the company.  This equation is sometimes referred to as the “excess purchase price.”  Accounting rules state that goodwill no longer should be amortized each period, but must be tested once per year for impairment.  Absent impairment, goodwill can remain on a company’s balance sheet indefinitely.

If a company with a low P/E acquires a company with a high P/E in an all stock deal, will the deal likely be accretive or dilutive?

Other things being equal, if the Price to Earnings ratio (P/E) of the acquiring company is lower than the P/E of the target, then the deal will be dilutive to the acquiror’s Earnings Per Share (EPS).  This is because the acquiror has to pay more for each dollar of earnings than the market values its own earnings.  Hence, the acquiror will have to issue proportionally more shares in the transaction.  Mechanically, proforma earnings, which equals the acquiror’s earnings plus the target’s earnings (the numerator in EPS) will increase less than the proforma share count (the denominator), causing EPS to decline.

What factors can lead to the dilution of EPS in an acquisition?

A number of factors can cause an acquisition to be dilutive to the acquiror’s earnings per share (EPS), including: (1) the target has negative net income, (2) the target’s Price/Earnings ratio is greater than the acquiror’s, (3) the transaction creates a significant amount of intangible assets that must be amortized going forward, (4) increased interest expense due to new debt used to finance the transaction, (5) decreased interest income due to less cash on the balance sheet if cash is used to finance the transaction and (6) low or negative synergies.

Walk me through an accretion/dilution analysis…

The purpose of an accretion/dilution analysis (sometimes also referred to as a quick-and-dirty merger analysis) is to project the impact of an acquisition to the acquiror’s Earnings Per Share (EPS) and compare how the new EPS (“proforma EPS”) compares to what the company’s EPS would have been had it not executed the transaction.

In order to do the accretion/dilution analysis, we need to project the combined company’s net income (“proforma net income”) and the combined company’s new share count.  The proforma net income will be the sum of the buyer’s and target’s projected net income plus/minus certain transaction adjustments.  Such adjustments to proforma net income (on a post-tax basis) include synergies (positive or negative), increased interest expense (if debt is used to finance the purchase), decreased interest income (if cash is used to finance the purchase) and any new intangible asset amortization resulting from the transaction.

The proforma share count reflects the acquiror’s share count plus the number of shares to be created and used to finance the purchase (in a stock deal).  Dividing proforma net income by proforma shares gives us proforma EPS which we can then compare to the acquiror’s original EPS to see if the transaction results in an increase to EPS (accretion) or a decline in EPS (dilution).  Note also that we typically will perform this analysis using 1-year and 2-year projected net income and also sometimes last twelve months (LTM) proforma net income.

How do we use the Treasury Stock Method to calculate diluted shares?

To use the Treasury Stock Method, we first need a tally of the company’s issued stock options and weighted average exercise prices.  We get this information from the company’s most recent 10K.  If our calculation will be used for a control based valuation methodology (i.e. precedent transactions) or M&A analysis, we will use all of the options outstanding.  If our calculation is for a minority interest based valuation methodology (i.e. comparable companies) we will use only options exercisable.  Note that options exercisable are options that have vested while options outstanding takes into account both options that have vested and that have not yet vested.

Once we have this option information, we subtract the exercise price of the options from the current share price (or per share purchase price for an M&A analysis), divide by the share price (or purchase price) and multiply by the number of options outstanding.  We repeat this calculation for each subset of options reported in the 10K (usually companies will report several line items of options categorized by exercise price).  Aggregating the calculations gives us the amount of diluted shares.  If the exercise price of an option is greater than the share price (or purchase price) then the options are out-of-the-money and have no dilutive effect.

The concept of the treasury stock method is that when employees exercise options, the company has to issue the appropriate number of new shares but also receives the exercise price of the options in cash.  Implicitly, the company can “use” this cash to offset the cost of issuing new shares.  This is why the diluted effect of exercising one option is not one full share of dilution, but a fraction of a share equal to what the company does NOT receive in cash divided by the share price.

Which is less expensive capital, debt or equity?

Debt is less expensive for two main reasons.  First, interest on debt is tax deductible (i.e. the tax shield).  Second, debt is senior to equity in a firm’s capital structure.  That is, in a liquidation or bankruptcy, the debt holders get paid first before the equity holders receive anything.  Note, debt being less expensive capital is the equivalent to saying the cost of debt is lower than the cost of equity.

When using the CAPM for purposes of calculating WACC, why do you have to unlever and then relever Beta?

In order to use the CAPM to calculate our cost of equity, we need to estimate the appropriate Beta.  We typically get the appropriate Beta from our comparable companies (often the mean or median Beta).  However before we can use this “industry” Beta we must first unlever the Beta of each of our comps.  The Beta that we will get (say from Bloomberg or Barra) will be a levered Beta.

Recall what Beta is:  in simple terms, how risky a stock is relative to the market.  Other things being equal, stocks of companies that have debt are somewhat more risky that stocks of companies without debt (or that have less debt).  This is because even a small amount of debt increases the risk of bankruptcy and also because any obligation to pay interest represents funds that cannot be used for running and growing the business.  In other words, debt reduces the flexibility of management which makes owning equity in the company more risky.

Now, in order to use the Betas of the comps to conclude an appropriate Beta for the company we are valuing, we must first strip out the impact of debt from the comps’ Betas.  This is known as unlevering Beta.  After unlevering the Betas, we can now use the appropriate “industry” Beta (e.g. the mean of the comps’ unlevered Betas) and relever it for the appropriate capital structure of the company being valued.  After relevering, we can use the levered Beta in the CAPM formula to calculate cost of equity.

What is Beta?

Beta is a measure of the riskiness of a stock relative to the broader market (for broader market, think S&P500, Wilshire 5000, etc).  By definition the “market” has a Beta of one (1.0).  So a stock with a Beta above 1 is perceived to be more risky than the market and a stock with a Beta of less than 1 is perceived to be less risky.  For example, if the market is expected to outperform the risk-free rate by 10%, a stock with a Beta of 1.1 will be expected to outperform by 11% while a stock with a Beta of 0.9 will be expected to outperform by 9%.  A stock with a Beta of -1.0 would be expected to underperform the risk-free rate by 10%.  Beta is used in the capital asset pricing model (CAPM) for the purpose of calculating a company’s cost of equity.  For those few of you that remember your statistics and like precision, Beta is calculated as the covariance between a stock’s return and the market return divided by the variance of the market return.

How do you calculate the cost of equity?

To calculate a company’s cost of equity, we typically use the Capital Asset Pricing Model (CAPM).  The CAPM formula states the cost of equity equals the risk free rate plus the multiplication of Beta times the equity risk premium.  The risk free rate (for a U.S. company) is generally considered to be the yield on a 10 or 20 year U.S. Treasury Bond.  Beta (See the following question on Beta) should be levered and represents the riskiness (equivalently, expected return) of the company’s equity relative to the overall equity markets.  The equity risk premium is the amount that stocks are expected to outperform the risk free rate over the long-term.  Prior to the credit crises, most banks tend to use an equity risk premium of between 4% and 5%.  However, today is assumed that the equity risk premium is higher.

What is WACC and how do you calculate it?

The WACC (Weighted Average Cost of Capital) is the discount rate used in a Discounted Cash Flow (DCF) analysis to present value projected free cash flows and terminal value.  Conceptually, the WACC represents the blended opportunity cost to lenders and investors of a company or set of assets with a similar risk profile.  The WACC reflects the cost of each type of capital (debt (“D”), equity (“E”) and preferred stock (“P”)) weighted by the respective percentage of each type of capital assumed for the company’s optimal capital structure.  Specifically the formula for WACC is:  Cost of Equity (Ke) times % of Equity (E/E+D+P) + Cost of Debt (Kd) times % of Debt (D/E+D+P) times (1-tax rate) + Cost of Preferred (Kp) times % of Preferred (P/E+D+P).

To estimate the cost of equity, we will typically use the Capital Asset Pricing Model (“CAPM”) (see the following topic).  To estimate the cost of debt, we can analyze the interest rates/yields on debt issued by similar companies.  Similar to the cost of debt, estimating the cost of preferred requires us to analyze the dividend yields on preferred stock issued by similar companies.

If a company incurs $10 (pretax) of depreciation expense, how does that affect the three financial statements?

The most common version of this type of question.  Note that the amount of depreciation may be a number other than $10.  To answer this question, take the three statements one at a time.

First, the income statement:  depreciation is an expense so operating income (EBIT) declines by $10.  Assuming a tax rate of 40%, net income declines by $6.  Second, the cash flow statement:  net income decreased $6 and depreciation increased $10 so cash flow from operations increased $4.  Finally, the balance sheet:  cumulative depreciation increases $10 so Net PP&E decreases $10.  We know from the cash flow statement that cash increased $4.  The $6 reduction of net income caused retained earnings to decrease by $6.  Note that the balance sheet is now balanced.  Assets decreased $6 (PP&E -10 and Cash +4) and shareholder’s equity decreased $6.

You may get the follow-up question:  If depreciation is non-cash, explain how this transaction caused cash to increase $4.  The answer is that because of the depreciation expense, the company had to pay the government $4 less in taxes so it increased its cash position by $4 from what it would have been without the depreciation expense.

How do you calculate fully diluted shares?

To calculate fully diluted shares, we need to add the basic number of shares (found on the cover of a company’s most recent 10Q or 10K) and the dilutive effect of employee stock options.  To calculate the dilutive effect of options we typically use the Treasury Stock Method.  The options information can be found in the company’s latest 10K.  Note that if the company has other potentially dilutive securities (e.g. convertible preferred stock or convertible debt) we may need to account for those as well in our fully diluted share count.

What is the difference between basic shares and fully diluted shares?

Basic shares represent the number of common shares that are outstanding today (or as of the reporting date).  Fully diluted shares equals basic shares plus the potentially dilutive effect from any outstanding stock options, warrants, convertible preferred stock or convertible debt.  In calculating a company’s market value of equity (MVE) we always want to use diluted shares.  Implicitly the market also uses diluted shares to value a company’s stock.

Why do you subtract cash in the enterprise value formula?

Cash gets subtracted when calculating Enterprise Value because (1) cash is considered a non-operating asset AND (2) cash is already implicitly accounted for within equity value.  Note that when we subtract cash, to be precise, we should say excess cash.  However, we will typically make the assumption that a company’s cash balance (including cash equivalents such as marketable securities or short-term investments) equals excess cash.

What is Minority Interest and why do we add it in the Enterprise Value formula?

When a company owns more than 50% of another company, U.S. accounting rules state that the parent company has to consolidate its books.  In other words, the parent company reflects 100% of the assets and liabilities and 100% of financial performance (revenue, costs, profits, etc.) of the majority-owned subsidiary (the “sub”) on its own financial statements.  But since the parent company does not 100% of the sub, the parent company will have a line item called minority interest on its income statement reflecting the portion of the sub’s net income that the parent is not entitled to (the percentage that it does not own).  The parent company’s balance sheet will also contain a line item called minority interest which reflects the percentage of the sub’s book value of equity that the parent does NOT own.  It is the balance sheet minority interest figure that we add in the Enterprise Value formula.

Now, keep in mind that the main use for Enterprise Value is to create valuation ratios/metrics (e.g. EV/Sales, EV/EBITDA, etc.)  When we take, say, sales or EBITDA from the parent company’s financial statements, these figures due to the accounting consolidation, will contain 100% of the sub’s sales or EBITDA, even though the parent does not own 100%.  In order to counteract this, we must add to Enterprise Value, the value of the sub that the parent company does not own (the minority interest).  By doing this, both the numerator and denominator of our valuation metric account for 100% of the sub, and we have a consistent (apples to apples) metric.

One might ask, instead of adding minority interest to Enterprise Value, why don’t we just subtract the portion of sales or EBITDA that the parent does NOT own.  In theory, this would indeed work and may in fact be more accurate.  However, typically we do not have enough information about the sub to do such an adjustment (minority owned subs are rarely, if ever, public companies).  Moreover, even if we had the financial information of the sub, this method is clearly more time consuming.

Why can’t you use EV/Earnings or Price/EBITDA as valuation metrics?

Enterprise Value (EV) equals the value of the operations of the company attributable to all providers of capital.  That is to say, because EV incorporates all of both debt and equity, it is NOT dependant on the choice of capital structure (i.e. the percentage of debt and equity).  If we use EV in the numerator of our valuation metric, to be consistent (apples to apples) we must use an operating or capital structure neutral (unlevered) metric in the denominator, such as Sales, EBIT or EBITDA.  These such metrics are also not dependant on capital structure because they do not include interest expense.  Operating metrics such as earnings do include interest and so are considered leveraged or capital structure dependant metrics.  Therefore EV/Earnings is an apples to oranges comparison and is considered inconsistent.  Similarly Price/EBITDA is inconsistent because Price (or equity value) is dependant on capital structure (levered) while EBITDA is unlevered.  Again, apples to oranges.  Price/Earnings is fine (apples to apples) because they are both levered.

Walk me through a Discounted Cash Flow (“DCF”) analysis…

In order to do a DCF analysis, first we need to project free cash flow for a period of time (say, five years).  Free cash flow equals EBIT less taxes plus D&A less capital expenditures less the change in working capital.  Note that this measure of free cash flow is unlevered or debt-free.  This is because it does not include interest and so is independent of debt and capital structure.

Next we need a way to predict the value of the company/assets for the years beyond the projection period (5 years).  This is known as the Terminal Value.  We can use one of two methods for calculating terminal value, either the Gordon Growth (also called Perpetuity Growth) method or the Terminal Multiple method.  To use the Gordon Growth method, we must choose an appropriate rate by which the company can grow forever.  This growth rate should be modest, for example, average long-term expected GDP growth or inflation.  To calculate terminal value we multiply the last year’s free cash flow (year 5) by 1 plus the chosen growth rate, and then divide by the discount rate less growth rate.

The second method, the Terminal Multiple method, is the one that is more often used in banking.  Here we take an operating metric for the last projected period (year 5) and multiply it by an appropriate valuation multiple.  This most common metric to use is EBITDA.  We typically select the appropriate EBITDA multiple by taking what we concluded for our comparable company analysis on a last twelve months (LTM) basis.

Now that we have our projections of free cash flows and terminal value, we need to “present value” these at the appropriate discount rate, also known as weighted average cost of capital (WACC).  For discussion of calculating the WACC, please read the next topic.   Finally, summing up the present value of the projected cash flows and the present value of the terminal value gives us the DCF value.  Note that because we used unlevered cash flows and WACC as our discount rate, the DCF value is a representation of Enterprise Value, not Equity Value.

How do you use the three main valuation methodologies to conclude value?

The best way to answer this question is to say that you calculate a valuation range for each of the three methodologies and then “triangulate” the three ranges to conclude a valuation range for the company or asset being valued.  You may also put more weight on one or two of the methodologies if you think that they give you a more accurate valuation.  For example, if you have good comps and good precedent transactions but have little faith in your projections, then you will likely rely more on the Comparable Company and Precedent Transaction analyses than on your DCF.

Of the three main valuation methodologies, which ones are likely to result in higher/lower value?

Firstly, the Precedent Transactions methodology is likely to give a higher valuation than the Comparable Company methodology.  This is because when companies are purchased, the target’s shareholders are typically paid a price that is higher than the target’s current stock price.  Technically speaking, the purchase price includes a “control premium.” Valuing companies based on M&A transactions (a control based valuation methodology) will include this control premium and therefore likely result in a higher valuation than a public market valuation (minority interest based valuation methodology).

The Discounted Cash Flow (DCF) analysis will also likely result in a higher valuation than the Comparable Company analysis because DCF is also a control based methodology and because most projections tend to be pretty optimistic.  Whether DCF will be higher than Precedent Transactions is debatable but is fair to say that DCF valuations tend to be more variable because the DCF is so sensitive to a multitude of inputs or assumptions.