John Graham Discounting This note summarizes some of the ..., Slides of Finance

Download John Graham Discounting This note summarizes some of the ... and more Slides Finance in PDF only on Docsity! 1 FINANCE 351 Corporate Finance – John Graham Discounting This note summarizes some of the discounting methodologies that we discuss in FINANCE 351. This note is not complete because there are several other methods of discounting that we ignore here (e.g., see the “flow-to-equity” approach discussed in Chapter 19 of Brealey and Myers). The intent of the note is to clarify some discounting issues that have bothered past FINANCE 351 students. NOTE: whenever we say “there is a tax advantage to debt”, we really should be saying “relative to financing completely with equity, when we finance with some debt we get to reduce our tax payment, and so there is a tax advantage to debt.” Therefore, many discounting methods discount the bulk of the cash flows with the cost of equity (rA or rE) and modify that only to account for the tax break provided by debt. We are ignoring the effects of personal taxes throughout this note. WACC: rD(1-JC) + rE D V E V C Weighted average cost of capital C the most frequently used discounting method C the D (debt), E (equity), and V (value) should be market values. It is often hard to identify market D, so book debt is used instead. However, book E should never be used. C the (1-JC) accounts for the tax advantage of interest deductibility. That is, (1-JC) reduces the discount rate, thereby increasing the NPV of a project. C Cash Flows discounted with WACC should be after-tax cash flows for an all-equity firm. In other words, do not subtract off interest expense when determining taxable income. (If you did, the cash flows would account for the tax advantage of debt, and you would be double counting the tax benefit. When using WACC, the discount rate accounts for the tax advantage to debt.) However, ignoring this interest issue, you should deduct corporate taxes from all other Cash Flows. C Use the company-wide WACC to discount cash flows with the same risk as the company at large. C If D or V changes through time, then technically, you should recalculate a new WACC each time D or V changes. Therefore, WACC is easiest to use when D/V is constant over the life of a project. In practice, small fluctuations in E or D do not result in recalculation of WACC. C technically, WACC is “correct” when debt D is fixed over the life of the project. (This assumption stems from the original Modigliani and Miller derivation of WACC.) For one thing, this means that the interest tax shields are also fixed for the life of the project and therefore they have the same risk as debt. If D is fixed over the project life, but V is not fixed, then a different WACC must be calculated each time V changes. 2 APV: C Adjusted Present Value = Base Case PV + Financing cash flows PV C according to Graham and Harvey (2001), 11% of companies use APV, although it is catching on. C the Base Case cash flows should be the after-tax cash flows for an all-equity firm (i.e., the cash flows as if the firm has no debt). In other words, do not subtract off interest expense when determining taxable income. (If you did, you would be double-counting the tax advantage of debt.) C Discount the Base Case cash flows using the return on assets, rA, which is sometimes called the unlevered cost of equity. C The return on assets can be estimated by C unlevering the equity $ C plugging the unlevered $ into the CAPM C the tax advantage of interest deductibility is captured in the cash flows used in the financing cash flows piece. C Discount the financing cash flows with the before-tax return on debt rD. C if you discounted with the after-tax cost of debt, you would be double-counting the tax advantage of debt. C discounting by rD implicitly assumes that the financing cash flows have the same risk as debt. C we often consider only the interest tax shields when valuing the financing benefits. However, other financing-related cash flows such as issuance fees, bankruptcy and other costs of debt, personal tax costs, etc., can be included. C APV requires that we can determine the debt schedule (so that we can write down the interest tax shield cash flows). APV is easiest to use when we already know the debt schedule. If we have to first determine the debt schedule, sometimes WACC is easier to use. RADR (Miles and Ezzell) C Risk Adjusted Discount Rate. C RADR is an alternative version of the Weighted Average Cost of Capital. In many sources, authors will not call it RADR but will simply refer to it as WACC (e.g., Corporate Restructuring here at Fuqua, or the Inselbag and Kaufold article discussed in lecture 9) C RADR = rA - rD(JC) D V 1 1 + +       r r A D C the general idea is that RADR discounts all cash flows by rA, as reflected in the first term in the formula, because they are all as risky as the operations of the firm. However, rA is reduced to reflect the tax advantage to debt (this occurs through the rD(JC) term). D V C Given some knowledge of the logic behind APV, it should not be surprising that RADR discounts operating/base-case cash flows by rA. However, why discount the financing cash 5 about the government backing the cash flows of a project, thereby reducing the risk of the cash flows and making them safe. This is not the same thing as the government providing the financing (see question 2b). Question 2b: How does this relate to “special loans”? Answer 2b: Imagine a scenario that the government (or an investment banker) provides a special loan (that is, a loan with an interest rate below the market interest rate). Assume that we can still obtain our usual market-rate loan for the project, and also can obtain this “extra” loan from the government. The usual way that we evaluate a project with such a loan is 1) pretend that the special loan does not exist and evaluate the project using our firm’s WACC or using APV. NOTE: any tax benefit of using debt should be captured in this part of the analysis. 2) value the loan itself. If the loan rate is below the market rate, the loan will have positive NPV, which can be added to 1) to increase the value of the overall project. What discount rate should we use in 2)? We assume that we take the special loan and stick it straight into the bank. Now, we pay interest on this special loan, we have interest expense and therefore experience the tax benefit of debt. However, we stuck the proceeds of the loan into the bank, so we earn interest on the loan proceeds, AND have to pay tax on this interest. If the “special loan” has exactly the same interest rate as the market rate, the tax we pay on the interest we earn exactly offsets the tax savings from the interest expense, and therefore the “special loan” is a complete wash, a zero-NPV transaction. We know from class that if we discount all of any loan’s cash flows (principal receipt, principal payback, interest payback, and interest tax shield) by the after-tax cost of debt, the loan has zero NPV. Therefore, the correct discount rate to use in part 2) is the after-tax cost of debt: (1-JC)rD. NOTE: if the special loan has an interest rate that is less that our market-determined rD, then the special loan will have NPV>0, and this will add value to the project. Question 2c: When we discount by the after-tax cost of debt as described in Answer 2b to determine the value of loan in step 2) above, should the cash flows from the special loan contain the tax benefits of interest deductions? Answer 2c: Yes, as implied in Answer 2b, the special loan cash flows should contain the tax shielding benefit, even though we are discounting by the after-tax cost of debt. This seems like a violation of the logic of WACC (capture the tax advantage in the discount rate but not in the cash flows) vs. APV (capture the tax advantage in the cash flows but not the discount rate). However, we are already capturing the tax advantage of doing the project in step 1) above. There is not really a tax advantage to the special loan per se (because we stick the proceeds in the bank and have to pay tax on interest earned, which offsets the interest deduction associated with the special loan). Therefore, we really should not think of the special loan providing a tax advantage in addition to that captured in step 1) above. 6 Question 2d: What if, contrary to Question 2b, our only source of financing comes from the special loan? That is, what if we can not obtain our usual market-rate financing in addition to the government financing? Answer 2d: In this case we should write down all loan cash flows for the special loan (principal receipt, principal payback, interest payback, and interest tax shield) and discount them by the before- tax market-based cost of debt (just like in the APV). In this case, the first three types of loan cash flows do not equal zero in present value, and so add value to receiving a special loan beyond those reflected in the interest tax shields. Question 3: Don’t special loans also affect our choice of the appropriate discount rate to use when evaluating lease vs. buy? Answer 3: Most often, $1 of increased leasing reduces debt capacity by $1, so the after-tax cost of debt is the correct discount rate to use. (And when we write down the cash flows for the “buy option” we do not include the effect of interest expense because the tax advantage of debt is captured in the discount rate.) If there is a “special loan” that effectively increases debt capacity for the firm, however, then we should use WACC to discount the lease vs. buy cash flows. NOTE: a lessor’s “special loan” does not have to offer a reduced borrowing rate, as long as it increases debt capacity. For example, consider a firm with $500 of total debt capacity, including that associated with a new project it is considering. The firm has a $200 project that it can finance with $120 in debt and uses the other $380 in debt capacity to finance other projects. If a lessor approaches this firm and offers to provide lease financing for the entire $200 of the project, what will the firm’s bankers say? If they say, “because you used $200 of leasing, your remaining debt capacity is only $300" then leasing does not add to the firm’s debt capacity (even if the lessor had claimed that it was offering a “special financing deal”). If the bankers say, “You still have $380 in debt capacity in addition to the $200 in leasing” then the firm actually has increased it’s debt capacity through leasing. In this case, referring to Lecture 5, the λ for this loan is 120/200=0.6, and the firm discounts with WACC. The bottom line here is that what really matters is what the outside bankers (or bond market) have to say about your debt capacity, not what the lessor claims about “special loans”. Question 4: I have heard people say “discount after-tax cash flows with an after-tax rate.” What does it mean when they say this? Answer 4: I am not sure why this statement is so popular. It is true that WACC and RADR both define cash flows as being after-tax (but without having subtracted off interest expense when determining tax liability). (APV defines cash flows in the same way for the base case value of the firm.) And both WACC and RADR incorporate the tax benefits of debt into the discount rate and 7 so effectively use an after-tax discount rate. So, the statement that you hear people make is true for WACC and RADR. However, APV does not use after-tax discount rates so the statement is not universally true. Question 5: Should something really “risky” like drilling for oil be discounted with a large discount rate? For example, should I double $ to account for this extra “risk”? Answer 5: It is important to separate out “uncertainty” from “risk”. In this example, the probability of finding oil is really about uncertainty: there is a positive probability that revenues will be zero because the well will not produce oil. In general, uncertainty should be captured in the cash flows by using expected cash flows (i.e., a weighted average of positive cash flows in the case where we strike oil and zero cash flow when we do not strike oil). When discounting, we think of “risk” as being market risk, as measured by the CAPM. This type of risk is captured in the discount rate. (Some people argue that there are more “risk factors” than just market risk, like book-to-market risk, that might show up in the discount rate but we ignore them here.) As long as the “risk” of striking oil is uncorrelated with the market return and so $=0, then we should discount this project with the risk-free rate. Or, the after-tax risk-free rate if we finance with debt and realize a tax benefit. This answer should make it clear that, no, you should not double $ to account for the “risk” of getting a dry well. Question 6: Should rD be the debt coupon rate, or expected cost of debt, in the WACC formula? Answer 6: Where it says rD in the WACC formula (and in the other formulae), we should really use the expected cost of debt, E(rD), with the expectation being taken over all possible scenarios, including those in which the firm is bankrupt and therefore does not make interest payments. Taking the expectation eliminates the amount that default risk adds to the cost of debt. This implies that using junk or subordinated debt, for example, will not increase WACC, if the expected payment on junk or subordinated debt is equal to the rD that applied before the junk or subordinated debt wsa issued. Question 7: If rConvertible < rE, should I think of convertible debt as a cheap form of equity? Answer 7: Convertible debt is effectively a combination of debt and equity. It should not be thought of as being “cheaper” or more expensive financing than debt or equity. If rConvertible is equal to the appropriate weighted average of (1-JC)rD and rE, then the cost of convertible debt is the appropriate market price and should not be thought of as a cheap form of equity. For convertible debt to be thought as being “cheaper” than just a combination of debt and equity, it must “solve” an agency 10 WACC vs. APV Question 9: I have heard it said that correctly applying the APV and WACC should give me the exact same numeric answer. But when I try this, it does not always work out. What am I doing wrong? Answer 9: There are two ways of understanding the differences between APV and WACC. The first is that when you apply WACC, the debt weight is debt-to-VALUE. The value should include the value added by the very project that you are evaluating. When the value does not include the NPV added by the project under consideration, the WACC method only provides an approximation to the correct answer. The second source of discrepancy can arise because of what WACC is implicitly assuming about the dolar amount of debt when a project is “X% debt financed.” This point is illustrated in Lecture 5 and Lecture 9, and I will not discuss it further here. To further explore the first point, note that the positive NPV added by a project is effectively “internal equity” provided by the project itself. This internal equity should factored into the weighted average cost of capital when determining WACC. To clarify these points numerically, consider the following example: Assume that cash flows are certain and rE = rA = rD = 10%. You want to do a project that costs $50 in t=0 and pays off $110 after-tax in t=1. You use $40 of debt to finance the project. The corporate tax rate is JC=50%. A) What is the APV of the project? -$50 + + = $51.82 because $4 of interest is used, which produces tax shielding cash 110 11. 2 11. flows of $2. B) Set up the same problem in a WACC framework. What numerical value does WACC need to be to produce the same NPV as you got in part A)? Be precise. What numerical value does D/V need to be (within the WACC formula)? We know that -$50 + =$51.82. Therefore, WACC needs to be 8.035%. Therefore, 110 1+WACC rD (1-Jc) + (1- )rE = 8.035%. Noting that rE = rD = 10% and Jc=50%, solving for the debt-to- D V D V value ratio implies that =0.393 and =0.607. D V E V 11 C) How does your answer to B) square with what we know about the value of Equity and Debt when we announce NPV>0 projects? Or, said differently, does your answer to part B) make sense? As soon as we announce the project and our financing intentions to the market, but before we even spend the $50 in t=0, the value of the firm is $101.82. (Given that the value of debt is 40, this implies equity is worth $61.82 upon announcement.) Therefore, = = 0.393, just as we found in D V 40 10182. part B). Yes, the answer in B) makes sense. APV and WACC give the same answer.