The purpose of this lecture is to discuss further the flexibility of the DCF method and to provide you with additional robustness checks to make sure the number you arrived using this method is not crazy. The goal is to convince yourself that you won’t be ripped off and not overpay. So, how can we determine whether the price we arrive at using the DCF method is sound? First, there are a lot of moving parts in the DCF method. For example, we can vary our WACC assumption and our growth rate assumption and therefore get a 2 dimensional range of firm values or prices. Second, we can rely on past comparable M&A transactions and extrapolate a price or firm value. I will talk briefly about both approaches here.

Approaches to Valuing Companies

Let us review a bit. DCF valuation gets you the maximum price you would be willing to pay for the firm. Subtracting the market value of existing debt will get you the maximum price you would be willing to pay for the firm’s equity. This is what you usually want to bid for. Comparable transactions analysis yields the price you will likely have to pay to get the firm equity. This is like a benchmark test using past transactions. This is not a maximum price willing to pay. This is just a simple check to see that your valuation numbers don’t deviate too far from reality. Similarly, comparable firm analysis yields the price the firm should be trading at if publicly traded on an exchange and sold to passive investors. If the DCF value of equity exceeds the comparable transactions value, then you could have a gem on your hands. If not, consider abandoning your plans unless you can convince the target on taking a low offer. Comparable firms analysis is particularly useful to compute terminal values when the buyer is a financial buying looking to exit via IPO in the usual 3 to 5 year window. Computing the average premium for percentage by which offer price exceeds a recent stock price on a date before the deal was announced offered in past deals is an example of a comparable transactions method. Part of getting a deal done is showing the counterparty that it is in their best interest to accept the deal. One way to do this is to show some comparable transaction premia, and show that you are offering in the range that past targets have accepted.

Premium is probably the most important and commonly discussed item in a deal. Logically, premium offered should equal the offer price minus the value of the stock you are buying under the scenario of operating “as is” without any deal. Calculating this “as is” value is difficult, especially using stock prices. The deal might have been anticipated, so the stock price before the formal announcement might not be a good benchmark for “as is” price. Therefore, one should look at a firm’s historical price pattern and look for information leakage. You should choose the price from a date prior to the leakage. Other dealmakers making an offer might try to game this calculation to make the premium look larger, and sellers might game it to look smaller. Don’t take anybody’s estimate of the premium as a given. Compute it yourself.

The inability to be 100% precise strongly motivates looking at multiple measures of the quality of an offer. Accounting based transaction multiples are another valuable benchmark. For example, if past cable mergers went at 2x revenue, you can judge if a current offer is high or low on this basis just as you can judge the premium. When looking at a menu of statistics on how good an offer is, use the economic realities of the firm as guidance in eliminating outliers and converging on a decent measure.

Sensitivity and Uncertainty

In M&A when there will most likely be competitive bids, you want to avoid the scenario where your valuation or maximum willingness to pay is determined by other people’s bids rather than on information that you have about the target. You shouldn’t increase your bid just because other people’s valuations turn out to be higher than your own valuations. Overvaluations will lead to overbidding. You want to avoid the winner’s curse scenario when your overbid actually wins. Dealmakers need to know how badly errors in the assumptions in your valuation models can affect the result. So, what are some ways to be more aware of possible errors? You are more likely to win a bidding contest when you bid highest due to a bad assumption or error. To avoid this, try doing the following:

1. Make sure all assumptions are conservative and imply assets are worth less.
2. Perform sensitivity analysis on all assumptions to find out which ones impact your valuation the most. This is where DCF shines. You can create a 2 by 2 table showing valuation for different ranges of assumed parameters, such as WACC and short-term growth rates. Most sensitive parameters typically are discount rates and growth rates. Judge the reliability of your most sensitive parameters.
3. Revise sensitive parameters to be more cautious, resulting in lower valuations. Consider not paying more than these shaved or risk adjusted bids.

DCF Terminology

Let’s go over some DCF terminologies that is often used in M&A transactions. Gross Present Value or GPV indicates the value of the firm before the price paid. Thus, GPV of the firm is simply the discounted value of the FCF of all periods. This is what we have been talking about since last lecture. The GPV of equity is only the equity value portion of the firm. This is the maximum offer price since the equity shares control the firm. In other words, the GPV of equity is equal to GPV of the firm minus the debt value. The NPV of equity is the GPV of equity minus the offer price. This is the value created for the acquirer’s stock value.

NPV Created for Acquirer and Target

The NPV created for both the acquirer and the target can be written in three ways, but they should all be intuitive. The total NPV value from an M&A transaction can be decomposed into the value created for the acquirer’s stockholders and the target’s stock holders. From our previous definition, the value for the acquirer’s stockholder is the GPV of equity of the target minus the price paid. The value created for all of T’s stockholders is the premium. Recall that this is the price paid minus the market value of the target’s equity before the announcement. If we cancel out the price paid, the total value created for both the acquirer and target shareholders is equal to the GPV of equity of the target firm minus the market value of the target’s equity before the merger announcement. Lastly, the GPV of equity of the target firm can be rewritten as the GPV of the merged firm minus the market value of the acquirer’s equity before the announcement. Each row are equivalent statements to build intuition for terminology. The idea is that transactions create gains for the acquirer and target shareholders alike. We can disentangle.

Total Value Created

Based on the first two lectures, it should be apparent that the impact of M&A deals are more than just acquirer and target shareholders. Of course, not all M&A is evil. Deals creating new products are often broadly good for shareholders and employees and communities. Some are quite bad. A deal with $10,000 NPV should be done by shareholders. However, sometimes, liquidations for example, can destroy perhaps billions of dollars for society in jobs, tax revenue, product choices for consumers, etc.

1. Gains/losses to management: promotions, layoffs
2. Gains/losses to employees: layoffs, wage cuts, etc.
3. Gains/losses to consumers: product quality, prices, etc.
4. Gains/losses to community: local tax revenue, traffic, etc.
5. gains/losses to national security: loss of intellectual property, military secrets, etc.

Acquisition Value Example 1

Let’s do some examples to make sure we are familiar with the terminology. Suppose GPV of target firm is $100 mil, debt assumed to be $20 mil, price paid to target shareholders is $70 mil, and pre-acquisition market value of target’s equity is $50 mil.

1. What is the GPV of the target’s equity? GPV_equity = GPV_firm - debt = 100-20 = 80
2. What is the NPV of the target’s equity? NPV_equity = GPV_equity - price = 80 - 70 = 10
3. What is the premium paid for the target? Premium = Price paid - pre-announcement price = 70 - 50 = 20
4. What is the total value created for all stockholders? NPV_equity + premium = 10 + 20 = 30

Question: Of all these, which is maximum price the acquiring firm should pay for the target firm? It should be the GPV of equity.

Acquisition Value Example 2

Let’s try another one. The Acquiring firm just announced it will pay a $200 million premium to acquire the target firm. The following are market values for the target firm before the announcement. Wages payable are $150 mil, bank loans are $250 mil, corporate bonds are $300 mil, and equity is $400 mil.

1. How much should the Wall Street Journal report that the acquiring firm made an offer for the target firm? Report the price: V_equity_pre + premium = 400 + 200 = 600
2. What is the value of the target firm before the announcement? V_firm = V_equity_pre + debt = 400 + 300 + 250 = 950
3. What is the value of the target’s asset before the announcement? Recall that the value of the firm is equal V_firm = total assets - accrued expenses. Therefore, Total assets = V_firm + accrued expenses = 950 + 150 = 1100
4. The acquiring firm’s discounted cash flow analysis of the target firm indicated that the GPV of equity from buying the target firm is $700 mil. If this analysis is correct, how much value will buying the target create for the acquiring firm’s shareholders? GPV_equity - Price = 700 - (V_equity_pre + premium) = 700 - 600 = 100.

DCF Flexibility

As mentioned before, DCF is flexible because we can model each component of the capital cash flow equation separately. Note that the plus and minus signs indicate whether they increase or decrease capital cash flows, not the component.

In the case of status quo, assets is just operating income less taxes. Change in net working capital can decrease if there are new accounts payable (i.e., withholding payments to suppliers) or increase if there are new deposits or cash being held. Net CAPX can increase if you buy a factor or computer equipment or decrease if you sell a factory.

Liquidation means that you cease operations. Therefore, there will be zero assets or operating income. There won’t be any networking capital because all the cash will be withdrawn and inventories will be cleared out. Net CAPX will also decrease since factories will be sold.

If you want a target firm to become more efficient, you can model it in different ways. If you decide to incorporate it in the operating income side, you can cut administrative costs or salaries. If you want to become more efficient, you can reduce inventories and make your customers pay you faster and pay your bills slower. You could also improve efficiency through CAPX. For example, you can sell your car factories in the U.S. and buy a cheaper one in Mexico.

In the last example, you can also model product line acquisition directly into each of the components of the capital cash flow equation. For example, you could generate more sales if you absorbed marketing resources. Product acquisitions tend to expand inventories. You could model that in by increasing net working capital. Additionally, you could build more factories, and therefore increase CAPX.

Critical Assumption of Multiples

Let us talk about multiples now. Hopefully you already have some idea of what multiples are. Let us first define what multiples are and how to use them. Multiples are typically quoted in reference to either firm or equity value. So if a firm multiple is x times a characteristic such as sales, it means means we can calculate a firm’s total or enterprise value by multiplying that firm’s sales or that characteristic by x. Similarly, if an equity multiple such as price to earnings ratio is y times a characteristic or earnings, we can arrive a firm’s equity value by multiplying that firm’s earnings by y. We will differentiate between firm and equity multiples in a bit. This method makes a very strong assumption however. Mathematically, multiples valuation implies that that firm value or equity value is a linear function only 1 characteristic. This is the unit price rule. This means that no matter how large or small the observed characteristic is for a firm, firm value or equity value is proportional to that characteristic by a constant. That constant is the multiple. You can also think of the multiple as a unit price and the characteristic as a quantity. The equity or firm value is therefore just quantity times price. I use gasoline and and ketchup as examples, but price to earnings is a very popular multiple used by investors. Price to earnings ratio is the equity value of the firm per unit of earnings. This is the core assumption of using the multiples method.

Firm Multiples

Don’t confuse firm and equity multiples. Doing so is one of the larger valuation errors that students often make. The unit price has to hold at the firm or equity. Once you commit, choose numerator and denominator to be consistent. For firm multiples, you should choose a characteristic that are owned by the firm as a whole that is not net of liabilities. This is because the numerator is firm value, which include liabilities. Such characteristics typically are sales, EBIT, and EBITDA. For mobile app startups I have seen number of app downloads as a denominator for a multiple. Once you have identified the characteristic, you can calculate the firm value to firm characteristic multiple for the list of comparable firms and take an average. To derive the firm value, we multiply the observed characteristic of the firm we are trying to value by that average multiple.

Equity Multiples

We can do the same of equity multiples. Since the numerator is only equity value, the denominator or characteristic has to be net of liabilities. This can be earnings or book value of equity. The price to earnings ratio is an equity multiple.

Screening Multiples

There are of course many potential problems from using the multiple method in terms of comparability. For example, past transactions may not have the same economic conditions. The sample of firms involved in past transactions may not be similar enough to the firm you are analyzing. Similarly, using publicly traded firms may not accurate as well since the sample of firms may not be similar enough to the target firm at hand. More importantly, these sample of firms do not take into account for the merger premium.

So, once you have decided on using the multiples method, how do you know which one to use? Here, I propose a 5 step method that you can follow when you do your projects.

1. The first step is to define the sample of relevant firms. You can filter based on many things such as industry, product type, size or leverage.
2. The second step is to compute the range of multiples for all firms in your relevant sample of firms. For each multiple type, we take the average across firms to come up with our predictor. The question is whether this predictor or average multiple does well in predicting the the price or value of the firms in our sample.
3. The third step is to measure how well our predictor does in predicting the true value or price of the firms in our sample. I decide to measure how well our predictors do by taking the difference between the actual price and the predicted price using our average multiple and dividing that difference by the actual price or firm value. After some simple Algebra, I show that this measure if pricing error is the same as calculating the error in multiples.
4. Lastly we compute the standard deviation of the sample errors for each multiples type. We choose the multiple type that has the smallest standard deviation.

Component Analysis

What if the transaction you are thinking about is complicated? For example, what if you are only thinking about purchasing specific cash flows from a conglomerate? Additionally, what if you plan on creating new riskier sources of cash flow from a new product? The beauty of the DCF method is that in order to arrive at overall value, all we need to do is add up the present value of each of these cash flows and make sure we discount these cash flows with the correct discount rate. This way, DCF allows us to value firms component by component. Assuming efficient markets, we can divide up a firm into various cash flow streams and discount each of them according to how risky those streams of cash flows are. That is, we assume there are no costs to creating contracts to sell rights to various cash flows. If you believe that there are market inefficiencies, you can make adjustments to the value of the cash flow component by component.

Debt Externalities

To reiterate, in our valuation method so far, we started off our baseline model in which capital structure doesn’t matter. It doesn’t matter how much equity or debt the firm uses to finance its operations, the value of the firm will be the same. This is the result from the Modigliani Miller Theorem. FCF, CCF, and APV method make one adjustment: the government will reduce tax liability if the firm makes interest payments on debt. These tax shields will increase the value of the firm. However, in this model, we are still assuming markets are efficient. In a world where markets are inefficient, it is possible that capital structure does matter. Specifically, taking on too much debt can increase bankruptcy risk, which can affect the overall risk or value of the firm. Using the FCF/CCF method is a bit clunky, but the APV method, which allows to study the firm’s equity and liabilities separately. In the case in which a merger between firms will produce a credit rating downgrade, the firm is at greater risk of going bankrupt or unable to pay off all of its creditors. You as dealmakers can make this risk adjustment directly through the cost of debt variable by finding comparable firms with similar credit ratings and firm characteristics and using the average yield to maturity as a substitute.

For example, suppose the equity value of the acquiring firm is 1 billion USD that has a cost of equity 10%, which is relatively low risk firm and debt value is 100 million USD with a cost of debt of 8%. The target firm also has an equity value of 1 billion USD with the cost of equity of 20% but has a debt value of 100 million USD with the cost of debt of 12%. Assume that the acquiring firm buys the target firm for 900 million usd plus a premium.

In a world of efficient markets, we can just value each of these components separately, add them up, and arrive at a price. The acquiring firm would own the 1 billion usd low risk equity firm with 10% cost of capital, the 100 million usd debt with yield to maturity at 8%, the 1 billion dollar high risk equity firm at 20% cost of capital, the 100 million usd debt with yield to maturity at 12%, 200 million usd of synergies, and lastly minus the 900 million cash premium. The target firm gets the 900 million usd cash premium.

If the firm became riskier due to debt externalities, then the value of the total debt can decline (say 180 million total) with a higher discount rate. We can easily make this adjustment component-wise and simply sum the parts again and arrive at the firm’s present value.

Deciding how much to actually Offer

So, how much should you offer? Let us review what we have learned so far in this class. The DCF method gives you the warranted value of the firm under your assumptions. This is your maximum willingness to pay for the firm. You should not offer any price above this warranted value. The hard part is convincing your counterparty that there are gains from the sale on both sides. If you know the assumptions that they are making, you can derive a range of possible prices you can offer. You also have historical transactions in your toolbox to convince your counterparty that what you are offering is not different from the past.