# Valuating the levered firm

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1 Valuating the levered firm Valuation and Capital Budgeting for the Levered Firm 18-0

2 Introduction In a strict MM world, firms can analyze real investments as if they are all-equity-financed. Under MM assumptions, decisions to spend money can be separated from decisions to raise money. How to do capital budgeting when investment and financing decisions interact and cannot be wholly separated? 18-1

3 Outline Evaluating a firm with leverage and its project The Adjusted Present Value approach Flows to Equity Approach Weighted Average Cost of Capital Method Comparison of the APV, FTE, and WACC 18-2

4 1. Adjusted Present Value Approach APV = NPV + NPVF The value of a project to the firm can be thought of as the value of the project to an unlevered firm (NPV) plus the net present value of the financing side effects (NPVF). NPV= PV of unlevered cash flowinvestment Discount rate: R 0 (unlevered cost of capital) 18-3

5 NPV of financing side-effects There are four side effects of financing: The Tax Subsidy to Debt V L = V U + T C B (for perpetual debt) The Costs of Issuing New Debt and Equity Securities (e.g. payments to investment bankers) The Costs of Financial Distress arising from the use of debt Subsidies to Debt Financing: obtaining debt from a municipality at a low interest rate. 18-4

6 Example of PMM Inc. Suppose the company has a project investment costs \$10,000,000 expected EBIT: \$3,030,303 per year forever The unlevered cost of equity: R 0 = 20% The firm s marginal tax rate: T C = 34% Should the firm accept the project If the project is all financed with equity? If it is financed with \$ 5,000,000 of 10% debt and the rest with internal equity? 18-5

7 NPV to unlevered firm Annual after-tax cash flows : EBIT (1- T c ) = (\$3,030,303)(1-.34)=\$2,000,000. NPV = (\$2,000,000 /.2) \$10,000,000 = \$0 The all-equity firm should be indifferent to accepting or rejecting the project. 18-6

8 NPVF: Tax Subsidy The present value of tax subsidy: NPVF=T C B =0.34 \$ 5,000,000= 1,700,000. Remark In the MM world All cash flows are perpetual and even debt does not have a maturity date. No bankruptcy cost 18-7

9 The value of the project with leverage The Adjusted Present Value of the project is APV = NPV + NPVF = \$ 1,700,000 The firm should accept the project V U = \$1,000,000 (the value of the investment) V L = V U + T C B = \$10,000,000 + \$1,700,000. V B = \$5,000,000 V S = \$6,700,000. The entire subsidy is captured by stockholders. The D/E ratio is based on the value of the project (50/67) not on the initial investment (1:1) 18-8

10 2. Flow to Equity Approach Discount the cash flow from the project to the equity holders of the levered firm at the cost of levered equity capital, R S. There are three steps in the FTE Approach: Step One: Calculate the levered cash flows (LCFs) Step Two: Calculate R S. Step Three: Value the levered cash flows at R S. 18-9

11 Example of PMM Inc. Step1: Cash Flows to Levered Equity (EBIT B R B ) (1 T C ) = (\$3,030,303 \$500,000)(1.34) = \$1,670,000 Step 2: Calculating R S. Assuming B/S L =50/67 R s = R 0 + (B/S L ) (1 t C ) (R 0 R B ) = 20% + (50/67) (1.34) (20% 10%) = % Step 3: Valuation NPV= LCF/ R S Equity Investment = \$1,670,000 / \$5,000, 000 = \$1,700,

12 Remark The D/E ratio is 50/67 instead of 1. To determine R S, we need to know S L. However S L =PV(LCF) discounted at R S. => simultaneity problem that does not have an easy solution. In practice, we use target D/E ratio

13 3. WACC Method R WACC S S B R S B S B 1T B ( C To find the value of the project, discount the unlevered cash flows at the weighted average cost of capital. Note that the weight S/ (S+B) and B/ (S+B) are target ratios, expressed in terms of market values. R ) 18-12

14 Example of PMM Inc. B = \$5,000,000 S = \$6,700,000 R B = 10% R S = % T C = 34% R WACC = (5,000,000/11,700,000)(.10)(.64) + (6,700,000/11,700,000)(.24925) = % PV WACC = (\$3,030,303)(1.34)/ = \$11,700,000 NPV WACC = \$11,700,000 \$10,000,000 = \$1,700,000. R S, is the same as in the FTE approach (D/E=50/67). =>Simultaneity problem 18-13

15 Remarks WACC is only appropriate as a discount rate for a project when: The project has similar systematic business risk as the firm, e.g. scale - enhancing firm The project and firm have the same debt capacity. In practice, each project should be treated as if it were a mini-firm, with its own proportion of debt and equity and its own capital costs. A convenient feature of the WACC approach is that it is often easy to obtain estimates of R S, R B, B and S. (e.g., the Wall Street Journal)

16 APV, FTE, and WACC All three approaches attempt the same task: valuation in the presence of debt financing. APV vs WACC: both uses UCF. APV discounted at R 0 and adjusting the tax benefit directly. WACC adjusting the benefit by discounting the UCF at a lower rate. FTE: uses LCF: CF to levered equity holders The effect is reflected by a smaller CF (interest payment exempt from tax) and less investment (reduced by debt financing) 18-15

17 Example: Finite life project Consider a project of the Pearson Company. The timing and size of the incremental after-tax cash flows for an all-equity firm are: \$1,000 \$125 \$250 \$375 \$ The unlevered cost of equity is R 0 = 10% The corporate tax rate T C = 40% Should the firm accept the project If it is an all-equity firm? if the firm finances the project with \$600 of debt at R B = 8%? 18-16

18 APV The project should be rejected by an all-equity firm: \$125 \$250 \$375 \$500 NPV % \$ 1, (1.10) (1.10) (1.10) (1.10) With \$ 600 debt: Pearson s interest tax shield worth T C BR B =.40 \$ = \$19.20 each year. The net present value of the project under leverage is: 10 APV \$ t1 \$19.20 t (1.08) \$ In the real world, the interest expense on debt is tax deductible but repayment of principal is not. \$7.09 \$56.50 So, Pearson should accept the project with debt

19 FTE Step One: Levered Cash Flows Since the firm is using \$600 of debt, the equity holders only have to provide \$400 of the initial \$1,000 investment. Thus, CF 0 = \$400 Each period, the equity holders must pay interest expense. The after-tax cost of the interest is: B R B (1 T C ) = \$ (1.40) = \$

20 Step One: Levered Cash Flows CF 2 = \$ CF 1 = \$ CF 3 = \$ CF 4 = \$ \$400 \$96.20 \$ \$ \$

21 Step Two: Calculate R S B RS R0 ( 1TC )( R0 RB ) S B To calculate the debt to equity ratio,, start with S PV \$125 (1.10) \$250 (1.10) 2 \$375 (1.10) 3 \$500 (1.10) 4 4 t (1.08) B V t R S PV = \$ \$63.59 = \$1, B = \$600 when V = \$1, so S = \$ \$ (1.40)(.10.08) 11.77% \$

22 Step Three: Valuation Discount the cash flows to equity holders at R S = 11.77% \$400 \$96.20 \$ \$ \$ NPV NPV \$96.20 \$ \$ \$ \$ (1.1177) (1.1177) (1.1177) (1.1177) 4 \$

23 WACC Method Suppose Pearson s target debt to equity ratio is 1.5. S B B B S B S 1.5S 1.5 S 0.60 S 1.5S 2.5 S B R R WACC WACC (0.40) (11.77%) 7.58% (0.60) (8%) (1.40) 18-22

24 WACC Method To find the value of the project, discount the unlevered cash flows at the weighted average cost of capital NPV \$125 \$250 \$375 \$ 1, (1.0758) (1.0758) (1.0758) \$500 (1.0758) 4 NPV 7.58% = \$

25 Summary 1. The APV formula can be written as: UCF Additional Initial t APV t t (1 R ) Effect of debt investment The FTE formula can be written as: LCF Initial Amount t FTE t t1 (1 RS ) investment borrowed 3. The WACC formula can be written as NPV WACC t 1 UCFt (1 R WACC ) t Initial investment 18-24

26 Summary: APV, FTE, and WACC APV WACC FTE Initial Investment All All Equity Portion Cash Flows UCF UCF LCF Discount Rates R 0 R WACC R S PV of financing effects Yes No No 18-25

27 Which approach to choose? Use WACC or FTE if the firm s target debt-to-value ratio applies to the project over the life of the project. If D/E remains constant, so do R S and R WACC. In real world situation, WACC or FTE applies to firms with target D/E. WACC is the most widely used method. APV is based on the level of debt in each future period. Use the APV if the project s level of debt is known over the life of the project. eg. Leverage buyout: easily forecast the tax shield. Interest subsidies and flotation costs 18-26

28 Summary: APV, FTE, and WACC Which approach is best? These three methods should be viewed as complementary. Use APV when the level of debt is constant Use WACC and FTE when the debt ratio is constant WACC is by far the most common FTE is a reasonable choice for a highly levered firm 18-27

29 Remarks In order to use WACC or FTE, we should assume the company must rebalance its capital structure to maintain the same market-value D/E. If the project runs unexpectedly well (market value increases), then increase the debt proportion If the value falls, pay down debt proportionally In the real company, if the firm plans significant change in capital structure, WACC won t work. => APV 18-28

30 In real world What if the discount rate must be measured? What if the debt ratio and business risks of project differ from that of the firm? How to value the other financing-side effects? How about other sources of financing? => Measuring the discount rate Determine the risk of the project Other sources of financing Other financial side effects 18-29

31 Measuring the discount rate Ex Discount rate(wacc) of World-Wide Widgets AW WWE D/E 4/6 1/3 R B 12% 10% β 1.5 R F 8% R M R F 8.5% Tc 40% What is the discount rate for WWE to use for its venture? 18-30

32 Measuring the discount rate 1. Using the equity β of the existing company with the same risk to determine its R S. CAPM: R S = R F + β (R M R F ). R F is the risk free (riskless) rate R M : Expected return on the market portfolio 2. Using R S of the existing company to determine a hypothetical R 0 Under MM II: R S = R 0 + B/S (1 T C ) (R 0 R B ). B/S: ratio for the company with the same risk 3. Using R 0 and the firm s target D/E to determine R S of the project 4. Computing R WACC 18-31

33 Measuring discount Rate of a scaleenhancing project A scale-enhancing project is one where the project is similar to those of the existing firms. In the real world, executives would make the assumption that the business risk of the nonscale-enhancing project would be about equal to the business risk of firms already in the business. No exact formula exists for this. Some executives might select a discount rate slightly higher on the assumption that the new project is somewhat riskier since it is a new entrant

34 How to determine the risk (β)? Recall that the risk of a security can be measured by Cov( Ri, RM) βi 2 σ Market The risk of a project can be measured by β of firm with similar business if the project is scaleenhancing Taking into account the financing side effect

35 Measuring the risk for scaleenhancing projects E.g. β for scale-enhancing project of CFL. Inc. Capital structure of CFL.Inc. B= \$100 Riskless debt T C =0.34 S= \$200 β equity =2.0 (regression analysis) What is the risk of the scale-enhancing project if it is all equity financed? (Hint: β Project = β Unlevered firm ) What is the discount rate of the project, providing that R F =10% and R M R F =8.5%? 18-34

36 Remark on the levered β β Equity β Unleveredfirm (1 T The leverage increases the risk of equity. However, leverage increases the equity beta less rapidly under corporate taxes. C )(β Unleveredfirm β Debt ) Leverage creates a riskless tax shield, thereby lowering the risk of entire firm. B S L 18-35

37 What if the project is not scale enhancing? If project is not scale enhancing : the risk is not comparable to the existing firms of the industry. We would begin with an industry average beta to compute the R 0, instead of referring to the beta of a specific firm

38 Exercise 17.Projects that are not scale enhancing Blue Angle Inc. is considering a new project: Company target B/S ratio B/S C =0.40 Industry target B/S ratio B/S I =0.35 Industry beta β=1.20 Market risk premium (R M R F ) =7% Risk-free rate R F =5% = R B Tax rate T C =40% Project cost I= \$475,000 (financed at target B/S ratio) Project Year 1 (after-tax) cash flow \$80,000 Growth rate in cash flow for years 1-5 g= 5% 18-37

39 Other sources of financing Market value balance sheet may has more entries Current assets Current liabilities cash, Inventory accounts payable accounts receivable short-term debt Property, plants, equipmt Long-term debt (D) Preferred stock(p) Growth opportunities Equity (E) Total assets Liabilities + equity 18-38

40 How to discount when there are more than two sources of financing There is one cost for each element. The weight for each element is proportional to its market value. Eg. In the presence of preferred stocks R WACC = R B (1-T C ) B/V + R P P/V + R E E/V R is the rate of return on the preferred stock. P is the value of preferred stock outstanding V= D+P+E

41 Other financing side effects Subsidized financing Flotation cost Cost of financial distress In these cases, the firm s D/E is not necessarily to be constant. => APV is a preferred approach

42 Example of PPM The company has a project investment costs \$10,000,000 expected EBIT: \$3,030,303 per year forever The unlevered cost of equity: R 0 = 20% The firm s marginal tax rate: T C = 34% Annual after-tax cash flows : EBIT (1- T c ) = (\$3,030,303)(1-.34)=\$2,000,000. NPV = (\$2,000,000 /.2) \$10,000,000 = \$

43 Subsidized financing Suppose a municipal government decides that the investment is socially (or politically) desirable and agrees to raise the \$5,000,000 debt financing as a municipal bond, at the municipality's borrowing rate, R B = 7%. Interest income on a muni is exempt from Federal tax, so the muni rate is typically below the rate on corporate debt (10%)

44 Flotation costs When a company raises funds through external debt or equity, it must incur flotation costs. Assume that the municipal government no longer sponsored the project and PPM, Inc. must obtain \$5,000,000 with new debt at the market interest rate of 10%. Flotation costs are 12.5% of gross proceeds

45 Cost of financial distress Firms should continue to exploit tax shields on interest until the benefits are offset by the marginal costs of financial distress. This means that financial distress costs are likely to be non-trivial for an optimally-financed firm. Unfortunately, financial economists are no help here

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