Unformatted text preview: 1 CAPITAL BUDGETING FOR THE LEVERED FIRM Ross, Westerfield & Jaffe “Corporate Finance” 7th ed. Chapter 17 After‐tax WACC 2 By discounting project cash flows at the firm’s WACC, we assume: The project risk is the same as the overall firm’s risk The project supports the same amount of debt to value as the firm’s overall capital structure Miles and Ezzell (1980): the formula works for any cashflow if the firm adjusts its borrowing to maintain a constant debt ratio over time Using WACC: Tricks of the trade 3 How do extend the WACC to account for different sources of financing? Find the expected rate of return for each source of financing Weigh each cost separately to find a weighted average The weight for each element is proportional to its market value Using WACC 4 What about short term debt? Practitioners often ignore short‐term debt Maturity should match the life of the project Error is small iff: Short term debt is incidental or one‐off The firm is not a short term net borrower Rules of thumb 10% of total liabilities Net working capital is negative Using WACC 5 What about current liabilities? Netted out against current assets Net cash flows of the project accounts for changes in net working capital Short term debt excluded if it is to be included in the WACC After‐tax WACC 6 To value the firm: Use WACC to discount firm cash flows as long as debt to equity ratio is expected to remain constant If using WACC, we do not deduct interest Value of the tax shield is picked up in the after‐tax WACC Forecast to medium term and add in a terminal value After‐tax WACC : Example 7 The next table shows the valuation of Project Morrison that requires an investment of $1000 and whose future cash flows depend on the state of the world. The year is good with probability 0.85 and bad with probability 0.15. Assume that the tax = 40%, RE= 12% and RD=10%. Further assume that the firm maintains a leverage ratio (D/V) of 50%. This information give us: After tax WACC = R* = 0.5(0.1)(1‐0.4) + (0.5)(0.12) = 9% After‐tax WACC : Example 8 Year EBIT G B 0 ‐1000 ‐1000 1 800 20 2 600 20 3 600 10 4 500 5 5 500 5 After‐tax WACC : Example 9 Year EBIT Tax (40%) G B G B 0 ‐1000 ‐1000 1 800 20 320 8 2 600 20 240 8 3 600 10 240 4 4 500 5 200 2 5 500 5 200 2 Expected Cash Flow Present Value After‐tax WACC : Example 10 Year EBIT Tax (40%) B Present Value ‐1000 G Expected Cash Flow ‐1000 G B 0 ‐1000 ‐1000 1 800 20 320 8 409.8 375.96 2 600 20 240 8 307.8 259.07 3 600 10 240 4 306.9 236.98 4 500 5 200 2 255.45 180.97 5 500 5 200 2 255.45 166.02 NPV: 219.01 WACC vs. Flow‐to‐Equity 11 To value equity: Use WACC, the value of equity is the value of the firm less the value of the debt Use the flow‐to‐equity method: Discount the cash flows to equity by the required rate to equity BUT only if leverage is constant WACC: Common mistakes 12 Manager Q is campaigning for a pet project. He knows his firm has a good credit rating and could borrow up to 90% of the project costs. This means wd = 0.9 and we = 0.1. The firm’s borrowing rate is 8% and the required rate of return on equity is 15%. Corporate tax rate = 0.35. Therefore: WACC = 0.08 (0.9) (1‐0.35) + 0.15 (0.1) = 0.062 or 6.2 % WACC: Common mistakes 13 1. 2. 3. It is the project, not the firm that can be 90% debt financed Any advantage due to more than normal debt should be attributed to the existing assets and investments, not the new one The cost of capital does not decline to 6.2%. We can expect both costs of debt and of equity to increase as more debt is taken on Adjusting WACC for business risk 14 If business risks change or differ for a project than for a firm: The project cost of capital is different Can use the Pure Play approach to find industry benchmark Employ a more subjective adjustment 15 Capital Budgeting When the Discount Rate Must Be Estimated A scale‐enhancing project is one where the project is similar to those of the existing firm. In the real world, executives would make the assumption that the business risk of the non‐scale‐
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. 16 Adjusting WACC: Change in debt ratios How do we adjust the discount rate when project debt is different from the firm debt level? Suppose a firm has 40% debt to equity and is going to finance 20% of a new projects cost with debt. At the firm level RE = 14.6%, RD = 8% Given firm’s costs of capital, RA, RE and RD; what is the project WACC? Recalculate WACC at the new debt level 17 Adjusting WACC: Change in debt ratios There are three steps: 1. Unlevering the WACC: calculate WACC at 40%. According to MM I (w/o taxes), RA is independent of leverage so this is also the WACC at zero debt (unlevered firm) RA = 0.08(0.4) + 0.146(0.6) = 12% 2. Estimate the RD and RE at the new debt levels (MM II) Assume RD is constant, then RE = 0.12 + (0.12‐0.08)(0.25) Relever the firm: calculate WACC at the new debt levels WACC = 0.08(1‐0.35)0.2 + 0.13(0.8) = 11.44% 3. 18 Adjusting WACC: Change in debt ratios Alternatively, we can unlever and then relever equity beta to find cost of equity through CAPM: Unlever beta: using old debt ratios 1. βA = (D/V) βD + (E/V) βE Relever equity beta: using new debt ratios 2. 3. βE = βA + (βA – βD) (D/E) Use CAPM to find RE and RA 19 Adjusting WACC: Change in debt ratios An important underling assumption is that the firm rebalances its capital structure Capital structure is maintained through borrowing/repayment/ new issues E.g. firm maintains a 40% debt level For practical purposes its sufficient to assume a gradual adjustment toward long run target ratio For significant changes in the capital structure, WACC adjustments wont work. We should use the APV method. Adjusted Present Value (APV) 20 Explicitly adjust the cash flows and present values for the costs and benefits of financing APV = Base Case NPV + PV Impact Base Case = All equity finance firm NPV PV Impact = all costs/benefits directly resulting from project. APV: Example I 21 A project requires $10m investment and offers an after‐tax cash flows of $1.8m per year for 10 years. The business cost of capital is 12% (also the cost of equity for an all equity firm) 10
1.8 NPV 10 $0.17 million
t
t 1 (1.12) APV: Example I 22 Suppose the firm decides to issue stock to raise funds for the investment. The issue costs 5% of the gross proceeds. To raise $10 million, firm will need to issue stock worth 10,000,000 (1 .05) $10,526,000 APV = Base Case NPV – Issue Costs = 170,000 – 526,000 = ‐$536,000 APV: Example I 23 Suppose, instead, the firm takes on debt equal to $5m, repaid in equal installments, at 8% interest rate Base case value: $170,000 as before What is the value of the tax shields due to debt? APV Example I 24 Year PVt Interest/(1+rD t = rDDTC = rDD) Tax = rDDTC Debt outstanding Interest Tax shield PV of tax shield 1 2 5,000,000 400,000 140,000 129,600 4,500,000 360,000 126,000 108,000 3 4,000,000 320,000 112,000 88,900 4 3,500,000 280,000 98,000 72,000 5 3,000,000 240,000 84,000 57,200 6 2,500,000 200,000 70,000 44,100 2,000,000 160,000 56,000 32,600 1,500,000 120,000 42,000 22,700 9 1,000,000 80,000 28,000 14,000 10 500,000 40,000 14,000 6,500 Total 576,000 7 8 APV = Base value + PV tax shields = 170,000 + 576,000 = $746,000 APV: Example II Project Morrison 25 The following table exhibits the cash flows in two states of the world. As before, RD=10%, tax rate= 40% and assume RA=12% Base Case: Year EBIT Tax (40%) B Present Value ‐1000 G Expected Cash Flow ‐1000 G B 0 ‐1000 ‐1000 1 800 20 320 8 409.8 365.89 2 600 20 240 8 307.8 245.38 3 600 10 240 4 306.9 218.45 4 500 5 200 2 255.45 162.34 5 500 5 200 2 255.45 144.95 NPV: 137.01 26 APV: Example II Project Morrison Revisited Present value of tax shield: project is financed 50% by debt Year EBIT Interest G B 0 ‐1000 ‐1000 1 800 20 2 600 20 3 600 10 4 500 5 5 500 5 G Taxable profit B G B Tax G B 27 APV: Example II Project Morrison Revisited Present value of tax shield: project is financed 50% by debt Year EBIT Interest G B 0 ‐1000 800 2 Tax ‐1000 1 Taxable profit G B G B G B 20 50 20 750 0 300 0 600 20 50 20 550 0 220 0 3 600 10 50 20 550 0 180 0 4 500 5 50 5 450 0 180 0 5 500 5 50 5 450 0 180 0 28 APV: Example II Project Morrison Revisited Present value of tax shield: project is financed 50% by debt Year Tax Saving PV G B rDDTC 0 1 20 8 16.55 2 20 8 15.04 3 20 4 13.22 4 20 2 11.82 5 20 2 10.74 PV Total NPV = Base case + PV of tax shield = 137.01 +67.37=204.38 67.37 APV Example III 29 Consider a project of the Pearson Company, the timing and size of the
incremental aftertax cash flows for an allequity firm are:
–$1,000
0 $125
1 $250
2 $375
3 The unlevered cost of equity is rA = 10%: The project would be rejected by an allequity firm: NPV < 0. $500
4 APV Example III 30 Now, imagine that the firm finances the project with $600 of debt at rD = 8%. Pearson’s tax rate is 40%, so they have an interest tax shield worth TCDrD = .40×$600×.08 = $19.20 each year. The net present value of the project under leverage
is: APV = Base case NPV + PV of tax shield APV Example III 31 Note that there are two ways to calculate the NPV of the loan. Previously, we calculated the PV of the interest tax shields. Now, let’s calculate the actual NPV of the loan: APV Base case NPV PV of the loan
APV $56.50 63.59 $7.09 APV 32 When we know precisely how much debt a firm will have APV is the easiest way to value the tax shield Use APV when debt level is exogenous ~ E{C} TC RD D
V RA
RD Consistent with MM ~ E{C} TC D
RA APV and Financing Rules 33 Assume a project costs $12.5m to set up, the yearly cash flows are $1.35m indefinitely. Further, the firm cost of capital = 12% and TC = 35% Base‐case NPV = ‐12.5 + 1.355/0.12 = ‐$1.21m The project supports debt of $5m at 8% rate. Annual tax shield = 0.35 x 0.08 x 5 = $140,000 What is the value of the tax shields? Depends on the financing rule APV and Financing Rules 34 Financing rule 1: debt fixed as a fraction of project cost, to be repaid on a predetermined schedule Tax shield to be discounted at cost of debt: APV = base case NPV + PV(tax shield) = ‐1.21 + (140,000/0.08) = $0.54 m APV and Financing Rules 35 Financing rule 2: debt rebalanced to keep it at a constant fraction, here 40%, of future project value Tax shield to be discounted at project’s cost of capital APV = base case NPV + PV(tax shield) = ‐1.21 + (140,000/0.12) = ‐$ 0.04 m APV and Financing Rules 36 The firm has a cost of equity of 14.6% wD = 5/12.5 = 0.4; wE = 7.5/12.5 = 0.6 WACC = 0.08(1‐0.35)(0.4) + 0.146(0.6) = 10.84% NPV = ‐12.5 + (1.355/0.1084) = 0 We now have valued the project three different ways: 1.
2.
3. APV (debt fixed) = $5.4 m APV (debt rebalanced) = ‐ $ 0.4 m NPV (after‐tax WACC) = $ 0 m APV and Financing Rules 37 Case 2 is only an approximation of case 3. When rebalancing, interest in current year is fixed (discount at cost of debt) but future interest depends on project value (value subsequent shields at cost of capital) Discount at cost of capital: PV(approx.) = 0.14/0.12 = 1.17m Multiply the PV by a factor (1+RA)/(1+RD): PV(exact)= 1.21m APV = base case NPV + PV(tax shield) = ‐1.21+1.21 = 0 m This adjustment is in line with the modification by Miles and Ezzell : 1 RA
D )
WACC RA RDT (
1 RD
V APV vs. After‐tax WACC 38 Decision rules: When a corporation maintains a constant leverage ratio, it can value projects by discounting the cash flows of an all equity firm at the tax‐adjusted WACC (or use FTE method) If the firm has fixed absolute debt levels, then you need to compute firm or project value using APV APV vs. After‐tax WACC 39 Often a constant discount rate (constant capital structure weights) are inconsistent with projected changes to capital structure. E.g.: LBO’s Planned M&A activity Future stock buy back plans APV vs. WACC 40 When RE and RD is known, practitioners tend to use after‐tax WACC Use industry WACC if firms are closely comparable When project financing differs from that of the firm or if the overall debt policy changes Unlever the firm beta or cost of capital Relever using project or the new debt ratios APV vs. WACC 41 Possible to use APV when debt ratios are fixed, but such calculation can be needlessly cumbersome APV works best when firm fixes an absolute debt level This strategy might cause successful firms to underuse their tax shields Transfer of wealth from equity holders to debt holders Rebalancing may be a more reasonable strategy and assumption to make Beta and Leverage 42 Recall that an asset beta would be of the form: Cov(UCF , Market) β Asset σ2
Market In a world without corporate taxes, and with riskless corporate debt, the relationship between the beta of the unlevered firm and the beta of levered equity is: In a world without corporate taxes, and with risky corporate debt, it can be shown that the relationship between the beta of the unlevered firm and the beta of levered equity is: Beta and Leverage: with Corp. Taxes 43 In a world with corporate taxes, and riskless debt, it can be shown that the relationship between the beta of the unlevered firm and the beta of levered equity is: Debt β Equity 1 (1 TC ) β Unleveredfirm Equity Debt
Since 1 Equity (1 TC ) must be more than 1 for a levered firm, it follows that Equity > Unlevered firm. Beta and Leverage: with Corp. Taxes 44 If the beta of the debt is non‐zero, then: β Equity β Unlevered firm (1 TC )(β Unlevered firm D β Debt ) EL Beta and Leverage: Example 45 The J.Lowes Corporation is considering a $1m investment with estimated unlevered cash flows of $300,000 per year into perpetuity. The firm will finance the project with a riskless debt amounting to an debt to equity ratio of 1:1. The three competitors in this industry are currently unlevered with betas of 1.2,1.3 and 1.4. Assuming a risk free rate of 5%, a market risk premium of 9% and a corporate tax rate of 34%, what is the NPV of the project? Beta and Leverage: Example 46 Unlever: Calculate the average unlevered beta βU,A= (1.2 + 1.3 + 1.4)/3 = 1.3 2.
Relever: (1 TC ) D E (1 ) U E E (1 (1 .34)1 / 1)1.3 2.16
3.
Calculate rE and WACC: rE = 0.05 +2.16(.09) = 0.244 WACC = rA = 0.5(0.66)0.05 + 0.5(.244) = 0.139 Then NPV = ‐ $1m + (300,000/0.139) = $1.16m 1. ...
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 Spring '12
 FarahSaid
 Debt, Net Present Value, Trigraph, APV

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