Possible Alternatives to DCF
The goal of today’s lecture is to introduce a valuation method that is general and thus flexible that you can adapt to value almost any type of firm and transaction. Corporate restructuring is sufficiently diverse that strictly memorizing formulas will not be as useful as developing the economic intuition behind the valuation models we will use. Therefore, you must understand the methods and logic so you can adapt to non-standard scenarios.
As you will soon realize, the cost of valuation error is extremely high, and having a model that allows us to perform scenario analysis will help us identify the range of values that is acceptable for both acquirers and target firms. For example, do you want to win a bidding war with 16 bidders? In most cases, the winner probably made an error. We need to understand under what conditions this method are valid and hence when adaptations are needed.
The most fundamental question that everyone studying corporate finance should be asking is “what exactly is a firm”? How we define a firm will determine how we value it. This is a philosophical question that has actually been actively debated among economists for centuries. Is a firm simply a money machine that generates a stream of risky cash flows? Or can you interpret a firm as a collection of contracts? The latter interpretation could very well be what firms look like in the near future, especially given the advent of smart contracts implemented through blockchain technology and artificial intelligence.
We define a firm in this course as a sequence of income payments over time. As you learned in your introduction to corporate finance class, the present value of this sequence of income payments over time is the price of the firm today. This interpretation is very similar to a bond with its coupon payments. However, unlike a bond, we assume a firm wants to live forever and has an infinite sequence of income payments to the owners of the firm. Unlike a riskless bond, the discount rate used to discount the cash flows of a firm is not the same as the bond yield. The discount rate needs to reflect the riskiness of the cash flows. If the future income of a firm is extremely risky or volatile, then I wouldn’t be willing to pay that much for that income stream. This requires that the discount to be high. Lower risk implies lower discount rate and therefore higher price of net present value of the firm. We normally call this the discounted cash flow or DCF method.
However, let us convince ourselves that the DCF method is far superior to accounting based methods that view the firm naively from just its balance sheet. Let’s make one thing clear: accounting numbers make our valuations possible. However, using them improperly or directly to arrive at valuations is problematic. Our goal is to get the price we should pay for a firm’s stock. We focus on a firm’s stock because that is how we gain control or ownership of the firm’s cash flow.
One seemingly obvious direct solution to value a firm is to simply look at its balance sheet. We all know from our introduction to accounting that the book value of equity or “Shareholder’s Value” is equal to the difference between assets and liabilities. As I will demonstrate in the next slide, book value of equity is extremely inaccurate. Book value of equity is actually just a number to make assets equal liabilities. When it comes to the true value one should pay, summing over many accounting items with various errors will give you a wild separation between book value of equity and the market value of equity. Errors arise, for example, because accounting asset values are often very stale. That is, book value can be interpreted as the purchase price, but the sale price can change a lot over time. Assets also often include weird intangibles like goodwill whose value might initially be marked to market but can change dramatically. Also, should liabilities be accounted for at face value? This interpretation doesn’t take into account the fact that debt can be distressed. For example, should the fact that a firm is unable to make interest payments on its debt be a factor in determining its value? You are basically at the mercy of Enron style accounting if you do not look at fundamentals to get your value. Market value is a far better starting point for what you should pay. At least it tells you what you could resell it for.
Are Accounting Measures good Valuation Measure?
Just how bad are book values of equity? Or more specifically, how far does it deviate from how much one should pay for a firm? Our null hypothesis is that book value and market value of equity are the same on average. Specifically, we hypothesize that the book value of equity divided by the market value of equity should be equal to 1 on average. Rather than do any sort of fancy statistical tests, we can simply plot this ratio for all public firms in the U.S. Additionally, we could also sort U.S. firms by a firm size, which I measured using the natural logarithm of book assets. The x-axis in this graph is the natural logarithm of firm size and the left axis is the book to market ratio. The first thing you should notice is that there are many outliers that have book to market ratios far above 1 and far below 0. A negative shareholder value is hard to reconcile if the firm’s stock price is trading at a positive number. These outliers aside, we see that for most firms, the book value of equity far understates the average firm’s market value. One reason for this is that assets produce far more income than their replacement or book values.
To give you some statistics: the mean book to market ratio is 0.88, which is much lower than 1. The book to market ratio for Pfizer, a large U.S. pharmaceutical is 0.46. Apple’s book to market ratio is 0.23. Marriott’s book to market ratio is -0.21. Lastly, Amazon’s book to market ratio is almost 0.
Discounting Earnings to Value a Firm
So, now we know that the balance sheet does not give you good estimates if we use it directly. What about the income statement? Why don’t we just discount earnings to value a firm? For equity analysts, income statements allow us to measure and compare performance across firms. Therefore, there is going to be a lot of smoothing done by the firm to make income less spikey and volatile so that analysts can use it as a better predictor of future income. This makes the income statement good for multiples. I will talk a little more about multiples later. For now, think of multiples as simple ratios of firm value divided by some observable firm characteristic. This ratio is assumed to stay constant over time. If you believe a particular firm you are valuing has a similar ratio, you can derive its firm value by simply multiplying the observable firm characteristic by that ratio. However, as finance majors that have had some exposure to accounting, we know that earnings and accruals are not cash. As you have learned in your introduction to corporate finance courses, capital budgeting strictly requires knowing when each dollar is received. Recording when the sale is made is not enough since payment may not have been received yet. Accounting income includes many items like depreciation that are not cash at all. We care about when the new factory needs to be bought, and real cash that could be distributed to shareholders. Additionally, the value of the firm should not depend on variations in accounting inventory practices such as FIFO (first in first out) and LIFO (last in first out), which can affect income statements. This lecture is to show you how to unravel key information in accounting tables to arrive at valuation free from bias.
Black Box Model
This diagram is our starting point for valuing firms. The boundary of the firm is determined by the in and out flow of cash. The inflow of cash from different investors become the firm. Using this capital, the firm creates new cash and distributes it to outsiders holding legal claims to this new cash. Firms, therefore, from the standpoint of different stakeholders, are cash-generating machines. Different stakeholders have different cash flow claims. Debt holders have first claim to the cash and assets, but their claims are fixed. Equity holders have variable claims to the cash. Preferred stock also have variable upside claims to the cash, but they their claims are higher than common stock owners.
Real and Financial Sides of the Firm
Given this model, accounting statements reveal exactly how much cash crosses the dotted line each year. The firm is part of a financial system. The firm is the real side and outside of it is the financial market side. You can buy the outside part, but as an outsider, you cannot affect the inside part. We will call the total cash coming to the outside part “capital cash flow”. If you can forecast and do DCF analysis on this, you have the value of the firm or the inside part. For now, I will just state the capital cash flow equation, but I will go through each part of the definition slowly. The capital cash flow equation is equal to operating cash flow minus change in net working capital minus capital expenditure. Operating cash flow is just revenue minus the costs of generating those revenues. Some operating cash flow is retained in the firm through net working capital and capex. You should think of change in net working capital and capital expenditures as firm reinvestments to either grow and sustain firm operations. Whatever is left should be given back to the financial stakeholders of the firm.
Capital Cash Flow Definition
Now, let us now substitute the diagram with the mathematical model of the firm: the capital cash flow equation. We still have the dashed vertical line that separates the firm from the financial markets. Whatever operating cash flow that isn’t reinvestment in the firm belongs to the firm stakeholders. In this sense, if we can calculate the capital cash flow of the firm, then we know how much cash flow is given back to the firm stakeholders. And knowing how much stakeholders receive in aggregate, when know the value of the firm. This identity must hold in our model of the firm. In this table, I have broken down securityholders into three groups: bondholders, stockholders, and others. Cash flow are received by bondholders in the form of interest and debt repayments. However, this cash flow allocation can be undermined if new debt is issued by the firm. Similarly, stockholders can receive part of the cash flow through dividends and stock repurchases, but new stock issues can reduce the payout.
Derivation of Capital Cash Flow
Hopefully, everyone should now have a high level understanding of the financial model of the firm. The hard part now is defining what is operating cash flow, change in net working capital and capital expenditures. Fortunately for us, early valuation experts have helped us figure out how each of those three parts can be derived from accounting variables.
I will explain briefly how we arrive at capital cash flow, which is denoted as Q5 (bottom of the flow chart). However, we will start with another cash flow statement identity: net change in cash holdings. Over a given year, the net change in cash is defined as the sum of 3 parts 1) Cash from financing activities, which is Q5, 2) Net capital expenditures or cash used in investing activities, which is Q4, and 3) Cash flow from operating activities, which is the sum of Q1, Q2, and Q3. The plus and minus signs next to each accounting variable is the direction of the effect on Q5.
Arriving at our capital cash flow equation is simple Algebra. Given Q1 + Q2 + Q3 + Q4 + Q5 = Q6, we subtract Q3 from both sides, subtract Q5 from both sides, and lastly subtract Q6 - Q3 from both sides. I suspect that what should be confusing to some of you is the interpretation of Q6 - Q3. Q6 - Q3 is the change in net working capital. Q6 is our original working capital level. Working capital is the cash necessary to keep the firm operating or running. You should think of it as fuel to keep things going. Q3 is therefore any sort of efficiency changes away from the Q6 level. So, if the firm becomes leaner and more efficient, for example, the use of inventory decreases, that should increase Q3 and therefore decrease Q6 - Q3.
The Algebraic Identity
To summarize, Q1 + Q2, denoted as A, is our cash flow from operations, Q6 - Q3, denoted as B, is our net working capital, and Q4, denoted as -C, is net capital expenditures. We will go over change in net working capital and net capital expenditures in separate slides later so that it is absolutely clear everyone understands the model of the firm we are building.
Example: Circuit City (1994)
Let’s go over an example. Circuit City was a U.S. electronics retail company like Broadway Electronics in Hong Kong, but went bankrupt and subsequently liquidated. Circuit City back in the 1990s were successful because they excelled at customer service. However, during the rise of the internet, their sales tactics were out of date.
In any case, let us break down the cash flow from and to the firm using the definitions of A, B, and C. For A, we start with earnings. We add back interest payments because we want to know what earnings looked like before paying out to debt holders, who are securityholders of the firm. Second, we add back non-cash charges, that include depreciation, loss on sale property, and deferred taxes. These numbers are made up by accountants, so they should be added back to earnings. Similarly, we need to remove any revenue that isn’t cash. Adding all these components up, we get 292 million USD. For B, we want to add up changes in working capital that could affect firm efficiency. For 1994, Circuit City reduced its cash holdings and accounts payables, which are efficiency gains, but increased receivables or payments not received, inventory and current assets. So, overall, there is a net increase of 209 million USD in working capital. For C, circuit city purchased some amount of new equipment but also liquidated some others as well. Subtracting B and C from A, we arrive at our capital cash flow of -140 million USD.
However, we can arrive at this same number but summing all the cash flow received or given by all securityholders. This is real cash. No accruals, no non-cash adjustments. What was the capital cash flow actually distributed to or raised from all securityholders? It should be 140 million USD raised to fund the big net working capital and capital expenditure spending. What was the net cash distributed to or raised from the holders of interest-bearing securities? 141 million USD. So, Circuit City is mostly financed by debt. What was the net cash distributed to or raised from stockholders? 803 million USD paid. Circuit City issued 8 million USD worth of equity.
Logic of Cash Flow Identity
Therefore, the cash flow identity that is critical to our model of the firm is the one that connects capital cash flow or operating cash flow minus change in net working capital and minus capital expenditures and cash flow payouts of raised by all securityholders: debt holders, stockholders, and preferred stockholders. Given this identity, we can now better understand the corporate financing actions that are open to a firm with positive operating cash flow. Let’s do some scenario analysis with this identity to make sure everyone understands the kind of corporate financing decision I am talking about.
In the first case, the firm invests in an existing business. This will increase CAPX on the left hand side, and so this must be funded by operating cash flow, cash on hand or net working capital, or new financing (i.e., transfer from securityholders to the firm). In the second case, sales double. This will increase A, so some other part will get the extra cash. For example, a huge dividend can be paid out to stockholders. In the third case, the firm accumulates excess cash. This will be an increase in net working capital. The cash must come from somewhere, so you might have higher A or less going to the securityholders. In the last case, the firm returns cash to stockholders. This will increase the money going out. This has to be funded by something on the left hand side, such as net working capital withdrawals or A or asset sales through CAPX.
Net Working Capital
Now, let us go over precisely what net working capital is. Net working capital is defined as current assets in place minus all accrued expenses. That means interest-bearing current liabilities should also be subtracted out. Accrued expenses are expenses that need to be paid but hasn’t. Examples of accrued expenses are salaries, wages, and taxes. There are several ways one could increase net working capital. Increasing cash holdings will mechanically increase net working capital. Increase receivables, which are payments yet to be received, and inventory, which are assets that haven’t been sold yet, will increase the current assets component. Decreases in accounts, taxes, and wages payable will reduce the accrued expenses component and thus increase net working capital. Within our model, we care about the money that is going in and out of net working capital. Therefore, the change in net working capital is money that you cannot pay to securityholders in the given year.
Intuition for Net Working Capital
But why do we use the change in net working capital? Net working capital is essentially current assets minus current liabilities. This can be viewed as being like a bank vault that can store things over long periods of time. How much is a bank vault with a million dollars in it worth if you are not able to withdraw it for 1 billion years? Same logic here: the only thing that matter is what comes out of the bank vault, and what you have to put in. Hence, we only care about change in net working capital. If a firm has a huge net working capital exceeding its stock price, consider a liquidation purchase. The only way to release the bank vault is to cease operations in most cases. Some deals aim to reduce required net working capital and earn huge NPV due to first-year release of net working capital going to the stakeholders of the firm.
Net Capital Expenditures
Net capital expenditures should be straight forward: selling a factory is thus a positive for cash flow, but buying one is negative. Investment in existing plants is also a negative.
The Three Cash Flows
Capital cash flow is very intuitive and comes straight from the cash flow statement. This is real cash, and not accrual accounting numbers. In this course, however, we will use the free cash flow method. I will give you a formula and some logic to help you understand the difference. For now, the only difference is that we will move treatment of the tax shield from cash flows to the discount rate. I will talk about the discount rate later. Tax shields are tax benefits from issuing debt. Much like mortgages and student loans, firms are allowed to deduct debt interest payments from their tax liabilities. If there are no tax shields, then capital cash flow and free cash flow are the same. I will prove it to you in a few slides.
Tax shields are only created when debt exists. The intuition is the following: taking tax shields out of the cash flow reduces the cash flow and lowers firm value. We offset this by using a lower discount rate for free cash flow. Valuing either way will give you the same answer. However, using free cash flow is more flexible. We get to assume leverage ratio and do not have to model individual debt securities and their cash flows.
Equity cash flow is mostly a trap. Many students and practitioners make errors in identifying equity cash flows as you must discount these cash flow using a different discount rate.
Capital Cash Flow Formula
This is the general formula for getting capital cash flow. It is not a bad idea to memorize this. This is simply A minus B minus C. Note how the formulation can start from EBIT or from Sales. Start where you have information. What you should pay close attention to is how we handle interest payments. Note that we do not tax the part of EBIT that will be used to pay for interest from debt. We are only taxed at EBT. After removing T_C from EBT, we add the part of the income used to service the debt back. That is our “tax shields”. After getting the correct tax bill, we add back non-cash expenses and subtract change in net working capital and capital expenditures. We will arrive at capital cash flow. In practice, it is better to just calculate free cash flow because you never have to compute interest.
Free Cash Flow Formula
Free cash flow is almost the same. The Top part is identical. The only difference is the tax bill. We ignore interest here altogether and just pay tax on EBIT. Then we adjust for non-cash expenses as usual. To reiterate, we do not add back interest because we never took it out.
Equity Cash Flow Formula
We won’t work with this model, so this is just for your reference. This is equity cash flow. The top part is identical to capital cash flow. The general idea is to get cash flow to all securityholders first, and then isolate the cash flow for equity securityholders. All the adjustments on the bottom is to isolate the part of the capital cash flow that is for equity shareholders.
Summary on CCF, FCF, and ECF
In summary, free cash flow is best. It is the same as capital cash flow but for the tax shield adjustment. For capital cash flow, we get to keep the part of the taxable cash flow that is used to service the debt. Free cash flow therefore is just the capital cash flow minus the interest times the tax rate. For a firm without any debt, free cash flow, capital cash flow, and equity cash flow are all the same.
From your introductory courses in corporate finance, you should know that this logic follows from Modigliani Miller Theorem. Leverage does not affect the value of the firm except through tax shields. Hence, all these cash flow are the same for an all equity firm. Each method just has a different way to account for the tax shield.
Discount Rate Selection: Question 1
The last part of the model is the selection of the discount rate. The discount rate intuitively should reflect how risky a firm really is. You should think of the discount rate as the opportunity cost or the required expected return a company must yield in order to make taking the risk worthwhile. The higher the risk, the higher the required expected return.
Let’s start out with a simple acquisition question: If asked to compute the price that firm A is willing to pay to buy firm T in a really “vanilla deal”, should you use A or T’s asset beta or unlevered beta to compute WACC or the weighted average cost of capital? The weighted cost of capital is the discount rate. I will talk more about the unlevered beta in later slides, but for now, you should interpret it simply as how correlated a firm’s unlevered returns are with the market, which is the only source of risk in the world. The answer is that you should use T’s unlevered beta.
Discount Rate Selection: Question 2
Consider valuing existing or new products. Suppose firm A is buying firm T in order to realize two cash flows: 1) Cash flow from firm T’s existing product lines and 2) cash flows from an entirely new product line that did not exist in either A or B’s offerings. Whose unlevered beta should be used to value which cash flow? For the first case, which is similar to the previous example, you should use T’s asset beta because those cash flows are related to firm T’s risk level. For the second case, you should use the new entity’s unlevered beta because the riskiness of the new product line is determined by the new entity’s unlevered beta.
Risk Matching Process: Theory
So what we have been doing in the previous examples is trying to match cash flows to assets that have the same risk exposures as measured through betas. Theories based on the logic in the last slide such as the capital asset pricing model imply that assets are correlated with the market should be worth less than assets that are not. If two assets have the same risk exposures or correlation with the market, they should have the same expected return. Managers of such firms should use the same discount rate. These predictions are strong. If they fail, hedge funds will aggressively trade stock until these are true. The conclusion you should draw from this slide is that to get the discount rate for a cash flow, you need to find an asset or portfolio with the same risk exposures and a known discount rate. That is the definition of risk matching. This is tricky because a security with identical risk exposures and a known discount rate rarely exists.
Risk Matching Process: Practical Uses
Suppose you are valuing the equity cash flows for Tencent. What basket of securities are you assuming has the same risk as Tencent’s equity cash flows? If we don’t know Tencent’s levered beta, we can, for example, take an average of the unlevered betas of comparable firms and relever it back to Tencent’s capital structure to get its equity cost of capital.
Free cash flows omit tax shields, but they are offset by lower discount rate. To value Free cash flows or capital cash flows, use the firm cost of capital. This is because we are considering the cash flows of all stakeholders of the firm. To value equity cash flows, use the cost of equity, which we will derive using the capital asset pricing model or CAPM.
Weighted Average Cost of Capital
The weighted average cost of capital assumes that all projects is financed with the same mix of securities as the firm. The WACC takes tax shield into consideration by getting cheaper debt due to tax shields. The debt to firm value ratio will capture how financing is considered. K_d and K_e must account for highly leveraged firm. More debt decreases bond rating and leverage also increases K_e (see Hamada’s equation).
Here is a weird twist for you to think about: How do you value free cash flows for a firm that is expected to lose a little bit of money every year? Tax shields only apply for positive income. If the income is not enough to cover interest payments, then you should pre-tax WACC.
Estimating Component Costs of Capital
When you buy a firm, you generally plan to change its business plan and its financing plan. The value you get from the firm represents your plan being enacted. That is why the cost of capital should reflect expected financing costs after the transaction takes place. To reiterate, use after-transaction numbers for everything in computing max price willing to pay.
For cost of debt, use the yield to maturity on the firm’s publicly traded corporate debt. Make sure you are looking at its yield and not coupon rate. Additionally, make sure you are looking at the market value price or yield and not the book value.
For cost of equity, we will restrict ourselves to the capital asset pricing model for simplicity, but just know that there are other asset pricing models out there.
Using CAPM to Determine the Cost of Equity
This is the CAPM model that can be used to calculate the cost of equity. You should have seen this model in your introduction to investments course, so I won’t go through its derivation. I will provide you with some intuition, however. Assuming that the world has only 1 source of risk, if people are risk averse and only cared about minimizing portfolio variance, you get this equilibrium result in which asset returns are simply a linear function of the overall market return. You can think of the risk free rate as the benchmark that assets have to beat. The equity risk premium is therefore any returns in excess of the risk free rate (R_M - R_f). Beta is therefore the scale of the asset returns relative to the overall market.
So, which risk free rate do you choose? 30 days bill or 10-year Treasury? There is a lot of disagreement overall which tenor to chose. Most practitioners use the longer-term. The most correct way is to match a rate to each year of the DCF, but this produces more work than necessary.
How do we get the betas? Estimating the betas is beyond the scope of this course, but I want to emphasis that we need expected future equity premium, not historical. So choosing the most relevant or recent stock returns history is smarter than using the entire history. If stock returns aren’t available, we need to find comparables.
Using Betas to Match Business and Financial Risk
The key to deriving a suitable beta for the firm is to separate how business and financial risk impact the discount rate. We do this in two steps. In the first step, we identify the firms that are the most comparable in business risk to the firm we are thinking about acquiring. For example, suppose we are valuing a private fast food restaurant chain. Which set of publicly traded firms are comparable in business risk? Perhaps McDonalds, Burger King, Wendy’s, Fairwood, or Cafe de Coral. Suppose we are valuing a private clothing retailer. Which set of publicly traded firms are comparable in business risk? Perhaps Gap, Uniqlo, or H&M. You can get betas for these publicly traded firms from Factiva or bloomberg, for example. Once you have decided on the set of firms, you need to calculate their unlevered betas and take an average. We want to remove any tax benefit distortions resulting from its capital structure. In the second step, we calculate the estimated levered beta by adjusting it with your future planned leverage ratio.
Adjusting Beta for Changes in Leverage
This is called Hamada’s equation and I will prove it to you here.
The Discounted Cash Flow Framework
We are almost done with the model.You will get one free cash flow in each year. Discount it to present using exponents. It is typical to forecast cash flows only for 5 to 10 years. High growth firms should get 10, slow growth firms 5. Tech firms maybe 15. Forecast as far out as necessary such that you see the firm has growth that has declined to low long-term levels. Thus, very long forecasts for tech firms are appropriate.
The value of the firm beyond forecast is estimated using some terminal value. There are more than one way to do this.
Terminal Values
Always start by asking yourself: “under the plan of my transaction, what will I be doing with the asset during those late years?” Constant growth annuity assumes the acquirer wants to keep the firm for a long time and eventually integrate it into its core business. I will talk about market multiples later, but it is another approach similar to a constant growth annuity. Liquidation value is used if the acquirer plans to sell the firm. The terminal value could also be zero if the acquirer plans to harvest the acquisition and then ceases to produce anything.
Which Terminal Value Methods Work Best?
Logically, which terminal value method works best for these cases?
Annuity, Scrap, or Sale
Be careful to note that time N refers to the last forecast year. For a 5 year forecast, you would have the terminal value as of year 5 if you put your free cash flow from year 5 into the formula. Hence, you still have to discount this terminal value using your five year discount factor.
The WACC is the same WACC in your DCF. g is a long-term growth rate. A reasonable assumption is “conservative estimate of long term economic growth plus inflation”. Standard numbers like 2 to 3 percent are common, with higher figures used in the past when inflation was much higher.
Terminal Value via Multiples
Rather than model the terminal value of a target firm explicitly through steady growth rates to perpetuity, one can also assume that the target firm will mature and become a particular type of firm after a period of supernormal growth. For instance, pretend we are a fast food conglomerate and we are thinking about buying a private fried chicken company. If we believe this fried chicken company will become and operate very similar to KFC or Jollibee, we can derive its implied firm terminal value through observable firm characteristics, such as sales, total assets, etc. In practice, we typically assume firm value is proportional to this firm characteristic. That is why we call this the multiples method. We will revisit this strong assumption in the next set of slides. But let me give you an example. Suppose the firm value market multiple for fried chicken fast food is 2.5x of sales. If the target firm has 100 mil USD of sales, then its implied firm value is 250 mil USD.
Since we are computing just firm or enterprise value, we have to make sure that the characteristic captures the value to all stakeholders of the firm. If the characteristic is exclusive to just one type of stakeholder, such as equity stakeholders, then the multiple could be misleading. Imagine buying a $200,000 Ferarri from Donald Trump. You feel like you could out negotiate Donald Trump after buying it for just $175,000. But after you signed the deal, a week alter, a creditor says you owe them $85,000 because of an unpaid secured loan on the car. This is a problem because the creditors also have a stake in the car, but we forgot to take their stake into account. Taking their stake into account, you actually are paying $260,000. Being careless with what multiple you put in as a terminal value is identical to making the above mistake, which essentially is forgetting about liabilities.
Alternative DCF Approaches
From my understanding most deals use the firm DCF method, which is basically done in three steps, which we have gone over already. The first step is to obtain the overall value of the firm or the enterprise value. We start with the discounted FCFs with terminal value to all the acquirer’s securityholders from the purchase of the target. Next, to get the value of equity of the target, we simply subtract the target’s existing debt. Remember that in order to get control of the firm, we only need to pay for the equity part of the firm. Lastly, to calculate the total value gained or NPV of the equity part of the firm, we subtract the offer price to be paid to the target’s equity holders. This last part is import because from the perspective of the acquirer, you should never offer a price above the value of the equity, otherwise you are losing money. In other words, the value of equity that you have calculated should be the maximum price that you are willing to pay. Offering any price above this maximum price would mean you are overpaying.
The incremental DCF approach is also sometimes used as well, which is a way to calculate the value of the synergies directly resulting from a merger or acquisition. We will do a case study related to the incremental DCF approach in a few weeks. What you should notice is that the premium paid or the difference between the offer price and the pre-deal value of the target shares should be less than or equal to the discounted value of the synergies. Therefore overall value gained or the NPV of the equity is equal to the discounted synergies minus the premium paid. Another way of stating this is to notice that the value of the target firm or the acquirer’s maximum willingness to pay for the target firm should be its stand-alone or pre-deal value plus its synergies. Stand alone value means the firm “as is” without any assumption on supernormal growth due to synergies. Discounting the synergies is a bit tricky. Rather than try to come up with a proper WACC for the combined firm, people typically just use both the target’s and acquirer’s WACC to come up with a range for the value of the synergies and therefore the maximum price range that should be paid.
Balance Sheet View
Let us now put our cash flow definition of the firm in terms of the balance sheet view of the firm. To review, the left side is the asset side of the balance sheet and the right side is the liabilities. You should think of liabilities as money that leaves the firm. The highlighted area is the definition of the firm because they are the stakeholders of the firm. Accrued expenses, as mentioned before, are expenses that haven’t been paid out. They can include unpaid taxes and employee salaries. However, they are not stakeholders of the firm. If asked to value the firm, this is what we are after. IF we are asked to value the common equity of the firm, we simply subtract the value of debt and preferred stock.
Rearrange Balance Sheet to get Firm Value
Thus, this balance sheet view of our definition of the firm gives us another perspective on calculating capital cash flow. The value of the assets less the accrued expenses is the value of the firm. Recall from the capital cash flow definition that capital cash flow is cash flow to everything to the right of the value of the firm. Hence, valuing capital cash flow gets you the value of the firm. Hence, A minus B minus C can be represented by the total value of assets less accrued expenses.
The Value of the Firm
As shown through my proof, the DCF valuation of capital cash flow and free cash flow should yield the same firm value. It doesn't matter if you account for tax shield in the cash flow or the discount rate, both account for it and thus you get the value of the firm. The goal is usually to get max price you should pay for equity. To do this, just remember to subtract the value of existing debt and preferred stock to get the value of common equity you wish to purchase. Do not subtract new debt that you will have to issue to complete the acquisition since that is already incorporated in the price.
Internal Rate of Return Calculations
Sometimes, you want to know the the implied internal rate of return on a target’s cash flow given the price you are about to pay. Recall that the IRR is simply the required return that makes you break even. So once you have the price of the entire firm and its modeled cash flow, you can solve for the interest rate in which the price or present value minus the discounted cash flow is equal to 0. You can use the IRR function or Goal Seek in Excel to do this. We will do a case study that asks you to do this. In general, if the IRR is greater than WACC, you should accept the project of acquisition.
The Adjusted Present Value Model
The last valuation that I want to talk about is the adjusted present value model, which is often used by private equity firms in leveraged buyouts. We will also do a case study on this. The benefit of using the APV method is that we can model the debt structure more precisely if it changes over time. The APV method consists of two parts. The first part is the same as the FCF method. However, instead of using the after-tax WACC, we simply discount using the k_e or the cost of equity implied by CAPM. Recall that FCF doesn’t subtract out interest payments before paying taxes on EBIT. So, the second step is adding back the tax savings on paying interest on debt. Tax shields is therefore the future dollar interest payments from the debt schedule times the tax rate. This tax savings should be discounted at k_d. The total value of the firm should be equal to the sum of the FCF discounted at the unlevered cost of equity plus tax shield cash flow discounted at the pre-tax cost of debt.
How FCF/Constant WACC and APV are Linked?
To remind you again, we are still working in the Modigliani-Miller world in which capital structure shouldn’t change the value of the firm. We have only added one additional assumption that taking on debt can yield tax savings. Therefore, any additional value added to the hypothetical equity value of the firm should come from the discounted value of the tax shields. This is exactly the APV method. All equity firm plus the present value of the tax shield is equal to the FCF discounted using the after tax WACC. However, note that the FCF method only holds in the case of constant capital structure. If the capital structure changes, APV should be a more accurate measure of firm value.
When to use FCF/Constant WACC
To summarize, use the FCF if you believe the target firm you are thinking about buying will have a capital structure that will stay constant over time. That means that will have a constant level of debt over time. In general, this is easiest method to implement and used most widely by investment bankers and practitioners.
When to use APV
The APV method allows you to model the debt payment structure specifically. This is when the APV method might give you a more accurate valuation. If you are given a list of actual bonds that will be sold to finance the deal, then APV method is easy to implement since you only need to compute the payments to maturity times the tax rate and discount those payments by the average yield. Alternatively, one could use a variable WACC model, but this tends to be inaccurate since it is hard to predict and commit to a leverage ratio in the future. APV is also more useful in the case of buying firms that have been incurring big losses. Those losses can be carried forward to a future tax break. I will go over a simple example of a tax loss carryforward.
Tax Loss Carryforward Example
Tax loss carryforward is another type of tax shields that can be used in the APV method. In this example, the tax rate is 35% and the cost of debt implied by the CAPM is 8%. This imaginary firm has been losing money for three years. In the U.S., firms that are making money pay taxes. However, firms that are losing money get some tax benefits. If the firm is losing money, it can accumulate essentially negative taxes or taxes on their losses. Assume that the firm only started losing money at Year 0. That is why the beginning tax loss is 0. The Tax loss carryforwards is simply 35 percent times the income before taxes, assuming the income before taxes is negative. Otherwise, it is 0. The change in tax loss carryforwards is accumulates after each period it losses money. The Ending Balance row is the accumulated tax loss carryforwards at the end of each year. In the year in which the firm starts making money, the firm can cash out the accumulated tax loss carryforwards. This is money from the government. We discount and sum the tax-loss carryforwards just like FCF.