Valuation - Introduction to

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1 Valuation - Introduction to Bernt Arne Ødegaard 23 November 2017 Contents 1 What is valuation? 1 2 What is valuation used for? 1 3 Myths about valuation 2 4 Discounted Cash Flow valuation When to use discounted cash flow Relative valuation 6 6 Contingent claims valuation 7 Introduction What is valuation? What is valuation used for? The main methods for doing valuation Net present value Valuation by comparables Real option methods 1 What is valuation? A cynic knows the price of everything, and the value of nothing. (Oscar Wilde) Well, let us hope that we can do both. we are not cynics. We want to set a value today on an asset that promises cashflows in the future. The future is risky. We have to make a qualified judgement. 2 What is valuation used for? Let us look at some examples: Value investing. In a 1934 book, two professors at Columbia Business School, Benjamin Graham and David Dodd called Security Analysis It advocated the search for value companies, firms that were undervalued by the stock market. The process is to sit down with as much information about the firm as possible, develop your own view about the value of the firm, and buy undervalued stocks (and sell the overvalued ones), to the degree that your estimate differs from the market price. 1

2 Private equity firms Look for firms that they view as good investment opportunities, where they can go in and force management to make changes, for example by divesting dividsions of a conglomerate. In a hostile going private deal, they buy most of the stock in the company, become the dominant investors, force the remaining owners to sell, and take the company off the exchange. Going private deals may also be more friendly, the private equity firm negotiates with firm management about terms for coming with more equity. Private equity firms will also go in with equity in nonlisted firms. In all such deals the private equity firm sits down and performs a valuation on the firm. Mergers and Aquisitions Before a merger, the two firms are valued before on set the terms of the merger. A challenge in M&A calculations is to estimate any additional value brought about by the merger (synergy). Is there synergy? How is it split? (Most of the time the selling firm gets most of the gains from the merger) Trades of shares in unlisted firms. Once a stock is not listed, suddenly illiquid, no price observed. estimating the price. A full valuation may be a way of Similarly what if one need to set the value of the values involved in inheriting a firm, or part of a firm. 3 Myths about valuation In the beginning of the book Damodaran points to some myths about valuation. These are useful starting points. 1. Valuation is objective While the methods we use in valuation are quantitative, the end result, the value estimate, is based on a set of choices that depend on judgement. The choice of which model to use The choice of inputs So different people may be asked to provide a valuation, and come up with very different answers, even from the same information. 2. A valuation is timeless No valuations may change overnight if circumstances change. 3. A good valuation is precise Unless you are valuing riskless investments you have to accept that your final estimate contains a lot of uncertainty. With most valuations you will provide sensitivity analysis that show sensitivity of your estimate to the inputs. 2

3 4. The more complicated and quantitave the model, the better Not necessarily. Any model is only as good as its match with reality the quality of inputs to the model. In particular, inputs to any model needs to be estimated, with inherent uncertainty One element of the art of valuation is to choose the right model, the simplest possible model consistent with the complexity of the asset. 5. If you make a valuation that differs from the markets valuation you believe markets are inefficient Efficient markets a market price reflects all the available information. So the markets valuation should be better than the valuation you have just carried out. Well, one need to modify what one think of as efficient markets a bit. The operational definition that most financial economists think of is that markets are aggregating the diverse opinions of various market participants, and the aggregation works through buying and selling in the financial markets. So, to change the price, one need investors that disagree with the current market price, and is willing to put one money where the mouth is. So, a valuation that differs from the market price may be part of the mechanism of moving the price, you have uncovered new information that is not yet fully reflected in the market price. On the other hand, it may be that either you have made a mistake in your calculations (always worth checking) or there may be information reflected in the market price that you don t know. Example In the early seventies, Fisher Black and Myron Scholes, developed their formula for pricing options. In addition to publishing the academic paper, they put their money where their mouth was, and started to trade warrants on equities, warrants that they priced with their newly developed formula. The warrant price on one stock in particular seemed to be very inconsistent with their valuation. It turned out that what they did not know was that the company in question were in merger talks. In option terms, the volatility of the stock was actually much larger than what they estimated, resulting in their warrant price estimate ending very far from the price at which the warrant was trading. They apparently lost quite a bit on this investment Only the number (the price) is important in the valuation, not the process. No, most of the time the process is just as important. The process of valuation results in an understanding of what drives value for an asset/firm/... Approaches to valuation Three approaches: Discounted Cash Flow valuation Relative valuation Contingent claim valuation 3

4 4 Discounted Cash Flow valuation Estimate the future cash flows of the asset Discount the cash flow with a risk-adjusted discount rate V alue = t=1 Cflow t (1 + r) t Where Cflow is the cash flow r is a discount rate reflecting the risk of the cash flows. In practice there are three ways of doing a DCF valuation of a firm. Value just the equity part, the value of the equity stake in a business. Flow to equity Value the entire firm, value to all claimaints Bond/Debtholders Equityholders Other claimants (e.g. Employee options) WACC Value the firm in pieces Value of operations add effect of debt, other nonequity claims Adjusted present value In symbols Flow-to-equity Value of equity = t=1 Cf lowequity (1 + k e ) t Where Cflowequity t is the expected cash flow to equity in period t, and k e is the cost of capital for equity. WACC Value of firm = t=1 Cflowfirm (1 + W ACC) t APV Value of firm = Value of all-equity financed firm +P V (tax benefits) P V (expected bankruptcy costs) 4

5 4.1 When to use discounted cash flow When one can predict the expected cash flows When one can find the cost of capital reliably To see how likely that is, take the case of firm valuation based on the current and historical accounts of a firm. The valuation in such a case proceeds in the following steps: Estimate the firm s cash flows five years in the future by taking the historical accounts as a basis for cash flow budgets the next five years. Estimate a horizon value, the value of the firm five years from now, based on an estimate of the typical growth rate for this and similar firms. Estimate a discount rate Use stock market data, either for this firm, or for similar firms, to get at the relevant risk for this firm/industry. Use that to estimate the cost to equity to the firm. Unlever the cost of equity to get an estimate of the cost of capital to the whole firm. Discount the terminal value and the budgeted cash flows for the next five years Find the value estimate Investigate the sensitivity of the estimate to changes in assumptions. (e.g. value sensitivity plots) A number of things must be in place for this to be a valid procedure. The historical accounts must have some relation to future operations of the firm if not, necessary to investigate future projects of the firm, estiamate future cash flows from the projects directly. The riskiness of the firm must not change otherwise the use of historical data for finding the right risk adjusted cost of capital result in a wrong risk adjustment alternative: estimate risk of future projects directly. What are examples of problems that can occur Negative cash flows in current accounts (firms in trouble). Can t say that the firm will have the same cash flows going forward, then it should rather be terminated. Firms being restructured (e.g. selling off divisions). Old accounts no longer relevant. Need to estimate cash flows of restructured firms. Firms involved in mergers. Accounts of the merged firm? The cash flow changes from the merger synergies? Nonlisted firms What do we do to estimate the cost of equity when we do not observe a stock price. Future contingent choices. A firm closes a production line if the market price of the product falls. Can not build such decisions into an discounted expected value sum. Need the tools of contingent claims valuation 5

6 5 Relative valuation In relative valuation, the basis for pricing and valuation is market prices of comparable assets There is any number of ways that the notion of comparable asset is implemented, leading to a plethora of different comparables and ratios. One distinguishes two main approaches: Fundamentals about firm being valued growth in earnings payout ratios risk Note similarity to discounted cash flow valuation Much of the same information is being used. Comparables Compare a firm with how similar firms are priced. Compare an asset with how similar assets are priced. Exercise 1. We want to find the stock price of a firm in the software industry. Currently, the P/E ratio for the industry is 24. We are valuing a firm that projects earnings of 10 per share next year. 1. Estimate the value of one share. Now, as this example shows, multiples are relatively simple to apply, but they are only good as long as the comparison is valid. If the firm deviates from the industry norm, what then? Is the multiple we are looking at something we expect to be common for a given peer group? Will the multiples we are looking at be stable across time? etc. However, relative valuation can be consistent with DCF valuation, they should be viewed as supplements. Here are a couple of examples from an earlier course, showing that the link between DCF valuation and valuation by relatives is closer than one think. Exercise 2. In valuation of companies one often uses the so called P/E method which says that the value can be found as an estimate of next year s net earnings multiplied by a P/E multiple, ie Value t = E t [X t+1 ] P/E multiple where X t+1 is the expected earnings of the firm. The P/E multiple is usually found by looking at industry averages. 1. How can such a procedure be reconciled with the standard stock valuation formula P t = E t[d t+1 ]? r g 6

7 2. Within this framework, is the application of industry standard P/E factors sensible? Exercise 3. A two-year Treasury bond with a face value of 1000 and an annual coupon payment of 8% sells for A one-year T bill, with a face value of 100, and no coupons, sells for 90. Compounding is discrete, annual. Given these market prices, 1. Determine the price of a two-year t-bill with a face value of 1000, paying no coupons. One may on some sense think of valuation by relatives as filling in assumptions for a DCF calculation. 6 Contingent claims valuation So, both of the above are similar, they make assumptions about the future that typically involve the ability to predict cash flows averages long time into the future. So, what is different about contingent claims valuation? Well, it involves cases where the future cash flows are contingent on something that will be revealed in the future. An obvious example: An oil company is deciding whether to invest in searching for oil in a particular block in the North Sea. They are then looking at a sequence of events First, say two years from now: Find oil No oil If they find oil: then there is the next step is developing the oil field valuable? That depends on the oil price. If it is low, not valuable, do not start developing the field, if it is high, start developing the field. This is the prototypical situation where contingent claims valuation enters: If a project/investment involves important future contingent decision, this always add value to the project. One can not value this project by assuming an expected oil price and expected probability of finding oil, one need to incorporate the future contingent decision in the valuation. This is where the concept of real option enters into the valuation calculation. So, in valuation, one will always need to play the game of spot the option If there are important future junctions where contingent decisions are made, need to evaluate if they are important enough to justify an option pricing approach. References Sheridan Titman and John D Martin. Valuation. The art and science of corporate investment decisions. Pearson, second edition,