17
Valuation Chapter and Capital Budgeting for the Levered Firm
17.1 Adjusted-Present-Value Approach (APV) APV = NPV + NPVF o Value of a project to a levered firm (APV) = Project of unlevered firm + NPV of financing side effects Side effects: 1. Tax subsidy to debt - for perpetual debt, value of tax subsidy is TCB 2. Cost of issuing new securities 3. Cost of financial distress 4. Subsidies to debt financing Interest on debt issued by state/local government is not taxable to the investor (Subsidy adds value) Present value of a project is determined before initial investment at date 0 is subtracted The initial investment is subtracted for the calculation of net present value Lend a fixed percentage of market value of a project not a fixed percentage of initial investment Net present value of project under leverage APV = NPV + TC * B
17.2 Flows-to-Equity Approach (FTE) rs = Cost of equity capital for perpetuity Cash flow from project to equityholders of levered firm rs Step 1: Calculating Levered Cash Flow (LCF) Cash inflow - Cash costs - Interest . Income after interest - Corporate Tax . Levered cash flow FTE = Alternatively o Difference between cash flow that equity holders receive in an unlevered firm and cash flow that equity holders receive in a levered firm is after-tax interest payment LCF = UCF - (1-TC)*rB*B Step 2: Calculating rs B rS = r0 + * (1 - TC) * (r0 - rB) S Step 3: Valuation LCF rs PV of project is simply difference between PV of projects LCF and investment not borrowed (cash inflow debt) PV project = LCF (cash inflow debt) Present value of LCF =
1
Chapter 17
Valuation and Capital Budgeting for the Levered Firm
17.3 Weighted-Average-Cost-of-Capital Method (WACC) S B rWACC = * rs + *rB * (1-Tc) S+B S+B The target ratios are generally expressed in terms of market value. Discount unlevered cash flow of project at the weighted average cost of capital rWACC
(1 + r
t =1
UCFt
WACC
)t
- Initial investment UCF Initial investment rwacc
If project is perpetuity
17.4 A Comparison of the APV, FTE and WACC Approaches APV: values project in all-equity basis. Projects after-tax cash flow under all-equity financing is placed in numerator of equation, discount rate in denominator. Then add NPV of debt (likely to be sum of four parameters: tax effect, floating costs, bankruptcy costs, interest subsidy) FTE: discounts after-tax cash flow from a project going to equity holders of a levered firm (LCF). WACC: calculated projects after-tax cash flows assuming all-equity financing (UCF). Taxadvantage of debt is reflected in denominator of equation because cost of debt is determined net of corporate tax. All approaches perform same task: valuation in the presence of debt financing. 1. APV versus WACC: Both approaches put unlevered cash-flow in numerators Both adjust basic NPV formula for unlevered firms in order to reflect tax benefit of leverage. o APV makes this directly o WACC discounts rate is lower below ro APV discounts these flows at r0, yielding value of unlevered project. Adding PV of tax shield gives value of project under leverage. WACC discounts UCF at rwacc, which is lower than r0 2. Entity Being Valued APV and WACC, the initial investment is subtracted out in the finals step. FTE, only firms contribution to initial investment is subtracted out FTE, only future cash flows to levered equity holders are valued. Future cash flows to unlevered are valued in APV and WACC. Since LCFs are net of interest payments, whereas UCFs are not, initial investment under FTE is correspondingly reduced by debt A suggested guideline If risk of project stays constant, assume that ro stays constant FTE If debt-to-value ratio remains constant, both rs and rwacc will WACC remain constant as well. desired FTE and WACC present difficulties when debt-to-value ratio changes over time APV approach is based on level of debt in each future period 17 2
Chapter
Valuation and Capital Budgeting for the Levered Firm
Use WACC or FTE if firms target debt-to-value ratio applied to project over its life Use APV of projects level of debt is known over life of the project LBO firms begin with large amounts of debt but rapidly pays down debt over times, thus tax shields in every future year can be forecasted APV Interest subsidies and flotation costs are much easier to handle with APV approach APV handles lease-versus-buy decisions
The Three Methods of Capital Budgeting with Leverage 1. Adjusted-Present-Value (APV) method UCF (1 + r t) t + Additional effects of debt initial investment t =1 0 UCFt = Projects cash flow at date t to equityholders of an unlevered firm ro = Cost of Capital for project in unlevered firm 2. Flow-to-Equity (FTE) Method LCF (1 + r t) t ( Initial investment Amount borrowed ) t =1 s LCFt = Projects cash flow at date t to equityholders of an levered firm rs = Cost of Capital for project with leverage 3. Weighted-Average-Cost-of-Capital (WACC) Method UCF (1 + r t ) t Initial investment t =1 wacc rwacc = weighted average cost of capital Notes: 1. Middle term of APV implies that the value of a project with leverage is greater than value of project without leverage Since rwacc < ro, the WACC formula implies that value of project with leverage is greater than value of project without leverage 2. In FTE, cash flow after interest (LCF) is used. Initial investment is reduced by amount borrowed as well Guideline Use WACC or FTE if firms target debt-to-value ratio applied to project over its life Use APV of projects level of debt is known over life of project 17.5 Capital Budgeting when the Discount Rate must be estimated 1. Determine AWs Cost of Equity Capital Use security market line rs = RF + *(RM RF) 2. Determine AWS Hypothetical All-Equity Cost of Capital Standardize preceding number in some way, since companies have different target debt-to-value ratios. Easiest approach is to calculate hypothetical cost of equity for AW; assuming all-equity financing. 3
Chapter 17
Valuation and Capital Budgeting for the Levered Firm
rS = r0 +
B * (1 - TC) * (r0 - rB) S Determined first because cost of equity capital can be determined from firms beta. Assume that business risk of firm is about equal to business risk of firms already in business. If assume that business riskier select slightly higher discount rate
3. Determining rs for WWE Widget Venture: Alternatively use FTE approach, where discount rate for levered equity is determined from. B rS = r0 + * (1 - TC) * (r0 - rB) S 4. Determining rWACC for WWE Widget Venture. S B rWACC = * rs + *rB * (1-Tc) S+B S+B 17.7 Beta and Leverage Debt No-tax case: Equity = Asset * 1 + Equity Holds under assumption that Beta of debt is zero. (1 TC ) * Debt *unlevered firm The corporate-Tax case: Equity = 1 + Equity Because nominator must be more than 1 for levered firm, it follows that unlevered firm < Equity Beta of levered firms must be greater than beta of unlevered firm in either case leverage increases risk of equity Leverage increases equity beta less rapidly under corporate taxes because It creates a riskless tax shield, thereby lowering risk of entire firm
The Project is not Scale-Enhancing If project is not Scale-Enhancing, one could begin with equity betas in the industry of the project 1. calculate average unlevered Beta in the Industry 2. calculate levered beta for the Project (1 TC ) * Debt *unlevered firm Equity = 1 + Equity 3. calculate Cost of levered Equity for new project Calculate discount rate from SML. rs = RF + *(RM RF) 4. calculate the WACC for new project B S rWACC = * rB * (1 TC ) + * rS V V 5. Determine Project Value If cash flows are perpetual, NPV is. 4
Chapter 17
Valuation and Capital Budgeting for the Levered Firm
Unlevered cash flow (UCF) Initial investment rWACC
5