**Valuation.** This site is not meant to teach valuation. Please purchase the book *Valuation*from Amazon via the link on this site to really learn valuation methods. The review here is only high level and is focused on the modeling and formulas involved. First, know what it is you want to value. Most financial models are made to value equity, the enterprise, or both.

An easy example of the difference is a car purchase. A used BMW might be worth $50,000. This is akin to enterprise value. If there is a suitcase with $10,000 in the trunk that comes with the car, how much will you now pay? This is the equity value, the value of what you are getting when you purchase the title (equity) to the car. In the same fashion, if the car comes with a bank note for $20,000, you would only pay the owner $30,000. Whether you pay $60k for the car with the cash or $30k for the car with the debt, the underlying car is worth the same amount of money. In the same manner, the enterprise value of a business is determined on an un-levered basis (cash free, debt free).

A typical equation for enterprise value is Equity Value = Enterprise Value + Cash – Debt, or Ent.V = Equity – cash + debt (equity value is market cap). There is debate about using cash from the balance sheet without adjustment. Two common issues with this are inadequate working capital and investments. Companies, especially in construction, can be paid by their customers for work that has not been performed (or have other situations to a similar effect). In such a case, the company will have cash on the balance sheet, but significant negative working capital (w/o regard to cash, which is a component thereof). Subtracting the cash to get to Enterprise value would not be proper because the cash is owed to customers and is not really the company’s. With investments, companies can purchase instruments that are not cash from a GAAP standpoint (over 90 day duration), but still represent excess value. Always understand a company’s investments when looking at cash.

The most popular valuation methods are discounted cash flow (DCF), EBITDA multiple, and P/E multiple. DCF measures enterprise value when you discount un-levered (without the effect of interest or debt payments/borrowing) cash flow and equity value when you discount the levered cash flow (a so-called LBO or leveraged model). An EBITDA multiple (because it is an unlevered cash flow proxy) values enterprise value. A P/E multiple values equity value (because earnings are a proxy for leveraged cash flow). When in a “normal” situation, you ought to obtain triangulation between the three measures. If one is wildly different from the other, then either the chosen metric (multiple, discount rate, etc.) is wrong or there are strange things going on that warrant your attention. These could be: model busts, high leverage, rapidly growing capex, strange working capital movements, etc.

Please download the free Excel spreadsheet valuation example Valuation. This example uses the simple general store model as a basis for familiarity (some formulas and starting points have been changed). Please view the “Valuation” tab row 79 and below.

**EBITDA.**Multiple valuations are simple. Most definitions of EBITDA are operating income plus depreciation, which is on row 81. Ensure that you capture all of the depreciation and amortization. Often, this is only shown on the cash flow statement. To determine the value in that year, use your favorite multiple on each year’s EBITDA. To determine the current value, users of EBITDA multiples (recognizing that they only capture one year’s performance) often resort to “forward” and “trailing” multiples to determine a proxy for value. As with P/E multiples, EBITDA multiples are often more handy as an output than an input. Let your DCF valuation tell you the trailing and forward multiples, then review them to make sure they make sense. A place where EBITDA multiples (or some modification thereof) is used quite often is in contracts where valuation choices are practically limited to what has happened or dueling appraisals.**P/E.**The P/E multiple is even simpler. Just multiply by net income as on row 98. Again, convention is to often use a trailing and forward multiple.**DCF.**A DCF analysis consists of two portions, the explicit forecast period and the continuing, or terminal, value (“CV”). Of the parts, the CV is the hardest to nail down. CV often has a large impact on value. This example will walk through two common methods of determining the CV and discuss some pitfalls of both.

Between rows 101 and 106, unlevered free cash flow is determined. Rather than “shutting off” the debt and cash effects in the model, this block adjusts the cash flow for their effects. Since the cash earnings rate is low, and the company has significant debt, you should expect the unlevered cash flow to be higher than the leveraged cash flow. Note that the tax impact (shelter) of interest must be accounted for as well. As with other adjustments, this can be accomplished in a large, single formula, but is much more user friendly and clear when shown in a broad table.

**Explicit Period DCF.** This is fairly straightforward. A point to consider is the timing of the cash flows. Recall that the basic excel “=NPV” formula assumes that the cash flow happens at the end of the year. This is not the case in going concerns with fairly even cash intake. Their weighted average cash receipt date is more like June 30 than December 31, because they receive cash throughout the year (if you make $10 a month, from a time standpoint, on average you received $120 on 6/30**). With high discount rates, this can make quite a difference. A work around is to “code up” your own discount factor to multiply against using half years or to use the XNPV formula (Analysis ToolPak required, see Excel Tips). The XNPV formula takes a date as an input so that you may be as precise as you desire. An important note about XNPV: it needs to know “where you sit”. If you do not put in today’s or an “as of” date, the formula assumes you started at the first date. You must include the starting date with a zero value (an empty cell will not be recognized). Rows 116-118 show all of these methods for determining the PV of the explicit forecast period.

**** **A footnote on NPVs and how they work. Please download the example: NPV Equality. July 1 is actually the middle of a year, as is shown in the examples at the top of the sheet. However, your accountant will squirm at the date on a piece of paper, people will argue with you (H1 ends 6/30), and, most importantly, your answer will further deviate from the result using a discount factor. Look at the results on row 44-49 in column B. Here you can see mathematically (and trace back) the differences between the NPV formulas. What is happening? The first two assume erroneously that all of the cash shows up at the end of the year. The next three all look at the middle of the year differently. The XNPV formula uses the exact dates. Therefore, in a leap year, you will “pay” more in interest than in a regular year (see rows 57-62). The mid-year discount factor makes no adjustment for leap or non-leap years. It also assumes that you get paid on midnight of the middle of the year, on day 182.5. This, of course, is not as realistic as being paid evenly over the year on actual days. You can reconcile the two, as is done on row 47 and columns L-N by adjusting the half year to account for the shift to July 1 and the leap year. When modeling, the difference between June 30, July 1, and mid-year is not really material. The difference between end of year and mid-year can be material. Erroneously including the investment in the plain NPV formula is quite material. Using XNPV and June 30 is a practical and rapid compromise to hard-coding the mid-year formula or using July 1, which will throw people off.

**Determining Continuing Value.** Continuing value formulas require the cash flow / earnings in the year after the last year of the explicit forecast (unless your explicit DCF period excludes the last year of the explicit forecast) and are discounted from the last year of the explicit forecast. This is often referred to as T (last year of explicit forecast) and T+1, the next year. In cell G28, a jump in A/R is hard coded to illustrate a point. The cash flow duly bounces around in 2014 and 2015. You must examine all of the activities in the final year to determine if it can be carried forward on an unadjusted basis as the perpetual cash flow value. Do not fall into the trap of applying the perpetual growth rate to the final year cash flow to determine T+1. Here, after some examination and manual calculation, T+1 was adjusted in rows 125-128. Common causes of trouble in final year projected cash flow are: tax, capital expenditures, working capital, and pensions.

Now that T+1 is determined, CV can be calculated. First, the Gordon Growth method is shown in cell B133. Next, we need to determine the PV of the CV. The same methods are used as for the explicit period. Note: If you are actually selling the business and *not* using a DCF TV/CV, you will need to use the end of the year (you get all of the cash flow for 2015 and then you sell) for your CV date (though use caution because the value of your business would most closely reflect a TV/CV, so it is almost always better to use that method). Look in cell B138 at the PV if you had failed to adjust the final year – more than double! To determine enterprise value, simply add the explicit period and the CV together. Many decision makers will want to know the portion of each, so it is helpful to determine them separately. As always, this aids in model usage as well.

NOPLAT. For a full understanding of the NOPLAT method, please purchase the Valuation text from the Amazon link. The short version is that it takes into account the economic value added by looking at the spread between return on capital and the cost of capital, whereas the Gordon Growth model assumes that growth takes place in cash flow without regard to capital deployment. In this example (rows 149-154), NOPLAT is unadjusted. Just like cash flow, you need to look at the operating income for anomalies. Also, be aware of economic distortions imbedded in operating income that might not be obvious. For example, one company was depreciating assets over 7 years that had 15 year economic life. Since NOPLAT “counts” depreciation, this had to be adjusted. Minority interests are another pitfall. If your company consolidates earnings in a non-wholly owned subsidiary (you do not own 100%, but 100% is in operating income) and the minority interest is taken out in other income “below the line”, as is typical, NOPLAT will over state economic earnings. Pensions are another headache in operating income. NOPLAT CV also has issues in very low capital companies (whereas Gordon Growth can have problems in moderate and high capital companies). A spread between ROIC and WACC is not very germane to the economic value creation of a staff leasing company or a pure engineering firm. Their return on computers or phones just does not matter in determining their value.

**Comparing the results.** The inverse of an EBITDA multiple of 5 is 20%. An EBITDA multiple of 5 is like a cap rate of 20% applied to a single year of cash flow. A P/E of 10 is like a cap rate of 10% applied to after-tax, after-depreciation cash flow. See rows 168-172. All of the results here are similar. This is not unusual, and these are common inputs for these formulas. When there are large differences, they are driven by the differences between the formulas. Examples include: low capital expenditure with high depreciation, high leverage creating large tax shelters on debt, high (or low) tax rates, etc.

A DCF, when properly constructed, is the best value method. Why? (1) “…TDA” is real. Just ask a ship owner how maintenance bills compare to depreciation. Assets wear out and need to be replaced. If you have figured value without regard to the wasting of assets (in the hope that capital expenditures are similar to long run asset replacement), you can have big trouble. Also, try not to pay the government their taxes. Tax treatment and tax rates matter to ultimate investment performance. (2) Net income (P/E) is distorted by capital structure and accounting decisions. The value of the firm should not change based on capital structure / what they are paying in interest expense or if they are depreciating assets faster than they wear out. (3) Working capital matters. There is a large gulf between a construction firm that is ahead of its customers (actually generates cash as it grows) and the poor middle market manufacturers waiting for GM to pay their bills 90 days later. Ignoring this in valuation can kill you. Only a properly constructed DCF takes these issues into account.

**Pitfalls in CV. **Please see the continuing value discussion above for a discussion of common adjustments necessary in using perpetual earnings / cash numbers. There is an illustration of a common pitfall in CV on the ship tab of the valuation example. In the ship example, you can see how a “standard” model is ignoring the business reality of periodic dry docks and waste of the long lived asset. A common misperception is that long time periods (i.e., small discount multipliers) will cover this up – “that’s so far out, who cares?” The NOPLAT formula does a better job because it is “listening” to the accountants, who we know are closet economists. The full time period DCF is closest to reality. The normal model would have cost you $7 million vs. the full DCF value, while the NOPLAT model might have cost you the deal by being $14mm low. The normal model also hides the fact that this company might have long term problems with this price level in the market place at a 15% cost of capital because the company is worth very close to what the ship is worth. This problem is not unique to ships. Any long-lived asset (like a factory or refinery) can present similar issues.

**The valuation inputs.** Discount Rate. The discount rate should be not your WACC, but your WACC adjusted for business risk. If you are looking to buy an Afghan mining company or a U.S. public utility your WACC is interesting, but has nothing to do with the risk adjusted returns. While it may make sense to use a lower discount rate than your WACC (say an Afghani company looking to buy a U.S. Utility), in practice this is difficult unless the acquisition is a significant part of your business *and* the markets will recognize this and adjust your capital costs accordingly. After all, it is a cost of capital. “Borrowing” at 15% to buy at 8% is not the best strategy. Nor is using 15% to value a business where the intrinsic risk is 30% a good idea. It is possible to model risk with a Monte Carlo model simulation, but in practice this is very hard, and sticking with an appropriate value cut-off (percentile of result) is difficult as well.

Terminal Growth Rate. Please recognize the implication of forever. Make yourself a spreadsheet with lots of rows and show some far-out examples. For the particular country (inflation growth, GDP growth) does your assumption make sense? If you grow at the terminal rate will you really be 10% of GDP in 50 years? Also, processing power and space are basically free. Why not run the model out far before applying a CV?

ROIC. This is really tough to determine. There are some good rules of thumb that can be had from looking at public comps. Recall that this is not ROA. ROA has lots of depreciation built in. This is the return on new assets. If possible, look at the growth capital spending (not maintenance) of the company and the cash profit growth associated with that capital (for example, not pricing) to find out what returns on capital have been. In mature industries it will not be high. In industries with large asset bases to earnings or revenue it will not be high. If refineries could get 25% ROIC everyone would build one, and then it would not be true. Don’t be fooled about the future from old assets or written down assets.