Valuation and Capital Budgeting for Levered firm

Determinants of Intrinsic Value: The Capital Structure Choice Net operating profit after taxes Required investments in operating capital − Free cash flow (FCF) = FCF1 FCF2 FCF∞ Value = + + ··· + (1 + WACC)1 (1 + WACC)2 (1 + WACC)∞ Firm’s debt/equity mix Weighted average cost of capital (WACC) Market interest rates Cost of debt Cost of equity Market risk aversion Firm’s business risk

Equity Valuation The value of equity is the present value of cash flows to the equity investors discounted back at the rate of return that those equity investors need to make to break even (the cost of equity). In the strictest sense of the word, the only cash flow stockholders in a publicly traded firm get from their investment is dividends, and the dividend discount model is the simplest and most direct version of an equity valuation model. The value of equity is the present value of cash flows to the equity investors discounted back at the rate of return that those equity investors need to make

Firm Valuation A firm includes not just the equity, but all claim holders. The cash flow to the firm is the collective cash flow that all claim holders make from the firm, and it is discounted at the weighted average of their different costs. A firm includes not just the equity, but all claim holders. The cash flow to the firm is the collective cash flow that all claim holders make from the firm, and it is discounted at the weighted average of their different costs.

Discounted Cash Flow Valuation What is it: In discounted cash flow valuation, the value of an asset is the present value of the expected cash flows on the asset. Philosophical Basis: Every asset has an intrinsic value that can be estimated, based upon its characteristics in terms of cash flows, growth and risk. Information Needed: To use discounted cash flow valuation, you need to estimate the life of the asset to estimate the cash flows during the life of the asset to estimate the discount rate to apply to these cash flows to get present value Discounted cash flow valuation is geared for assets that derive their value from the cashflows that they are expected to generate - most businesses and financial assets fall into this category. The inputs needed for all discounted cash flow models - cash flows, discount rates and asset life - are the same, though the ease with which they can be estimated may vary from asset to asset. When we use discounted cash flow valuation, we are assuming that we can estimate intrinsic value and that market prices can deviate from intrinsic values. We also assume that prices will revert back to intrinsic value sooner or later - this is why a long time horizon is a pre-requisit.

Basis for all valuation approaches The use of valuation models in investment decisions (i.e., in decisions on which assets are under valued and which are over valued) are based upon a perception that markets are inefficient and make mistakes in assessing value an assumption about how and when these inefficiencies will get corrected In an efficient market, the market price is the best estimate of value. The purpose of any valuation model is then the justification of this value. Market Inefficiency: Markets are assumed to make mistakes in pricing assets across time, and are assumed to correct themselves over time, as new information comes out about assets. Implicit in most valuation is the assumption that markets make mistakes and that we can find those mistakes by using the right valuation models. An often unstated assumption is that markets will correct their mistakes, resulting in excess returns for investors. If you do believe that markets are efficient, valuation still may be a useful tool in different contexts: Valuing private businesses (where there is no market to yield a price) Valuing the effect of a restructuring or a merger, where the market has not had a chance to react to the changes being considered.

Background Valuation of a firm or a project is based on two parameters: Assessment of Future cash Flow Finding out a discount rate Discount rate must reflect the risk involved in the cash flow

Discounted Cash flow Valuation: Basis for Approach where CFt is the expected cash flow in period t, r is the discount rate appropriate given the riskiness of the cash flow and n is the life of the asset. Proposition 1: For an asset to have value, the expected cash flows have to be positive some time over the life of the asset. Proposition 2: Assets that generate cash flows early in their life will be worth more than assets that generate cash flows later; the latter may however have greater growth and higher cash flows to compensate. Cash is king. A firm with negative cash flows today can be a very valuable firm but only if there is reason to believe that cash flows in the future will be large enough to compensate for the negative cash flows today. The riskier a firm and the longer you have to wait for the cash flows, the greater the cashflows eventually have to be….

Its FCF again FCF= EBIT (1-Tax Rate)+Depreciation-Capital Expenditure-Δ Working Capital It is referred as unlevered Cash Flow Applicable tax benefits, if any, needed to be considered separately in the discount rate Cost of equity

Rs is the return on (levered) equity (cost of equity) The required rate of equity also depends on the financial leverage According to MM Proposition II (With Taxes) Rs is the return on (levered) equity (cost of equity) R0 is the return on unlevered equity (cost of capital) B is the value of debt S is the value of equity Simple

Lets look into different methods to calculate discount rate

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 present value of the financing side effects (NPVF). There are four side effects of financing: The Tax Subsidy to Debt The Costs of Issuing New Securities The Costs of Financial Distress Subsidies to Debt Financing

Adjusted Present Value Model In the adjusted present value approach, the value of the firm is written as the sum of the value of the firm without debt (the unlevered firm) and the effect of debt on firm value Firm Value = Unlevered Firm Value + (Tax Benefits of Debt - Expected Bankruptcy Cost from the Debt) The unlevered firm value can be estimated by discounting the free cash flows to the firm at the unlevered cost of equity The tax benefit of debt reflects the present value of the expected tax benefits. In its simplest form, Tax Benefit = Tax rate * Debt The expected bankruptcy cost is a function of the probability of bankruptcy and the cost of bankruptcy (direct as well as indirect) as a percent of firm value.

Adjusted Present Value Approach Firm Value = Unlevered Firm Value + PV of tax benefits of debt Firm Value = Unlevered Firm Value + PV of tax benefits of debt - Expected Bankruptcy Cost In this approach First the firm or project is first valued, assuming it is solely financed by equity capital

Adjusted Present Value Approach Second, benefit of tax and the cost of debt financing will be included However, even though firm can get tax benefit from debt financing , it also have other costs like issue cost, bankruptcy cost

Adjusted Present Value Approach Therefore APV = NPV all equity + NPV tax shield+ PV of other costs Example: Cash Inflow 500,000 per year Cost 72% of cash flow Initial investment= 475,000 Tc=34% R0=20% cots of capital for all equity firm Cash Flow 500,000 Costs (72% of sales) -360,000 EBT 140,000 Tax (34%) -47,600 Unlevered Cash Flow(UCF) 92,400

Example contd. Given the discount rate, the PV of the project is The NPV of the project Because the NPV is negative, the project should be rejected by ALL EQUITY FIRM Now lest assume that project is financed partly by debt amount of Rs. 126,229.50 Therefore, Equity portion is now 475,000-126,229.50=348,770.50 The NPV of the project under leverage is: APV=NPV+ tc X B The value of the project when financed with some leverage is equal to value of the project When financed with all equity plus tax shield from the debt.

WACC Most popular approach in valuation Estimates project’s value by discounting unlevered cash flows using constant WACC However, if the project is financed by both debt and equity, the interest paid to the debt is qualifies for tax exemption The tax shield is incorporated in the WACC

WACC Simple in approach Measures the cash flow available to all investors However Risk involved in project cash flows are not always amenable to being measured with a single discount rate The discount rate changes when debt to equity ratio of the firm varies on a year to year basis.

Example: Cash Inflow 500,000 per year Cost 72% of cash flow Initial investment= 475,000 Tc=34% R0=20% cots of capital for all equity firm Now lets assume that project is financed partly by debt amount of Rs. 126,229.50 and RB Therefore Equity portion is now 475,000 -126,229.50= 348,770.50

Example WACC =.183

Flow to Equity (Equity Valuation) The value of equity is obtained by discounting expected cash flows to equity, i.e., the residual cash flows after meeting all expenses, tax obligations and interest and principal payments, at the cost of equity, i.e., the rate of return required by equity investors in the firm. where, CF to Equityt = Expected Cash flow to Equity in period t (levered) rs= Cost of Equity for levered firm Forms: The dividend discount model is a specialized case of equity valuation, and the value of a stock is the present value of expected future dividends. In the more general version, you can consider: FCF to firm-Interest and debt payment In this approach, you put blinders on and consider only two questions: What cashflows can equity investors expect to make from this business? The cashflows can generally be defined as cashflows left over after a firm has met its reinvestment needs and made any debt payments… They can therefore be negative… In the strict view of equity cashflows, there are some who argue that the only cashflows to equity are dividends, which makes the dividend discount model a special case of a cashflow to equity model. What cost of equity will they attach to these cashflows? Generally should be higher for higher risk equity.

Example Cash Flow 500,000 Costs (72% of sales) 360,000 Interest (10% of 126,229.50) -12,622.50 EBT 127,377.05 Tax (34%) 43,308.20 Levered Cash Flow (LCF) 84,068.45 Second Step: Calculate Step 3: Valuation

Example contd. NPV of the project is

Summary: APV, FTE, and WACC APV WACC FTE Initial Investment All All Equity Portion Cash Flows UCF UCF LCF Discount Rates R0 RWACC RS PV of financing effects Yes No No

A Comparison of the APV, FTE, and WACC Approaches All three approaches attempt the same task: valuation in the presence of debt financing. Assumed that a constant cash flow in perpetuity Even cash flow differs, if valuation models are applied correctly, the choice of valuation model should not affect the NPV estimate WACC is most popular: Include both equity and debt. Tax shield of interest is treated as a decrease in the cost of capital. But cost of capital is affected by change in capital structure

A Comparison of the APV, FTE, and WACC Approaches Flow to Equity Useful when debt levels changes on year to year basis Cost of equity does not changes with change in debt level if D/E ratio is maintained. only views the project from the prospective of equity holders’ If D/E changes, it makes calculation more complex. APV APV is very useful when capital and tax structure is uncertain. No fixed debt ratio is necessary. The firm is valued as a whole without consideration for its debt and equity and debt is considered as an independent variable Adds the tax shield benefit arising of interest payments separately.

A Comparison of the APV, FTE, and WACC Approaches All three approaches attempt the same task: valuation in the presence of debt financing. Guidelines: Use WACC or FTE if the firm’s target debt-to-value ratio applies to the project over the life of the project. Use the APV if the project’s level of debt is known over the life of the project. In the real world, the WACC is, by far, the most widely used.

Comparison Whenever a target debt ratio is set up for the long term, WACC and its associated methods might be an acceptable approximation. This is often the case of many larger corporations in advanced and stable countries. However, the situation is often different for smaller firms everywhere, and in many countries where: a) high economic uncertainty press firms to build in considerable financial flexibility and be prepared to quickly adjust the amount and profile of their debts in reaction to political and macroeconomic developments

Estimating Inputs: Discount Rates Critical ingredient in discounted cashflow valuation. Errors in estimating the discount rate or mismatching cashflows and discount rates can lead to serious errors in valuation. At an intuitive level, the discount rate used should be consistent with both the riskiness and the type of cashflow being discounted. Equity versus Firm: If the cash flows being discounted are cash flows to equity, the appropriate discount rate is a cost of equity. If the cash flows are cash flows to the firm, the appropriate discount rate is the cost of capital. Currency: The currency in which the cash flows are estimated should also be the currency in which the discount rate is estimated. Nominal versus Real: If the cash flows being discounted are nominal cash flows (i.e., reflect expected inflation), the discount rate should be nominal While discount rates are a critical ingredient in discounted cashflow valuation, I think we spend far too much time on discount rates and far too little on cashflows. The most significant errors in valuation are often the result of failures to estimate cash flows correctly…. As companies increasingly become global, and multiple listings abound (Royal Dutch has six equity listings in different markets) the consistently principle becomes very important. The currency used in estimating cash flows should also be the currency in which you estimate discount rates - Euro discount rates for Euro cashflows and peso discount rates for peso cash flows. Recently, I came across a valuation of a Mexican company, where the cashflows were in nominal pesos but the discount rate used was the dollar cost of capital of a U.S. acquirer…. As a result, the value was inflated by more than 300%….

APV APV = NPV equity + NPV Financial side effects + NPV Flotation cost NPV all equity NPV = -Purchase price + PVIFA *EBDT (1-tc) +PVIFA *Dep * tc NPV Financial Side effects NPV= Debt – PVIFA* Interest (1- tc) – PVIF * Debt NPV Flotation cost NPV = - Flotation cost + PVIFA * tc * (flotation cost/n) Note: Discount Dep tax shield at risk free rate (if given) Relation of Levered Beta and Unlevered Beta Beta levered = [1+ (1- tc) (B/S) ] Beta unlevered Confidential – Not to be cited, or reproduced without permission - Premchander

Beta levered and unlevered Confidential – Not to be cited, or reproduced without permission - Premchander