Chapter 8 Valuation and Required Rates of Return

Objectives The Meaning of Worth or Value The Present Value of All Future Dividends Applying the Dividend Valuation Model to Project Valuation Estimating ΔDIV0 and ΔDIVt The Equity Approach to NPV The Debt/Equity Approach to NPV The Weighted Average Cost of Capital Approach to NPV Using the WACC Approach: An Example Estimating OCFt Estimating I0 Estimating kA Determining the Project’s NPV Using the WACC Approach: Some Considerations The Adjusted Present Value Approach to NPV Estimation

ΔDIVt = ΔR t - ΔE t - ΔINTt - ΔPRINt - ΔTAXt - N.DIVt The basic formulation of owner’s value: W0 = DIV0 + V0[DIVt] Gives us: NPV = ΔDIV0 + PV0[ΔDIVt] n NPV = ΔDIV0 + ∑ ΔDIVt t=1 (1+kE) ΔDIVt = ΔR t - ΔE t - ΔINTt - ΔPRINt - ΔTAXt - N.DIVt Where: ΔR t = the change in the firm’s cash operating revenue at time t as a result of undertaking the project ΔE t = the change in the firm’s cash operating expenses at time t ΔINTt = the change in the firm’s interest payments at time t to the suppliers of any debt capital used to finance the project ΔPRINt = the change in the firm’s principal payments at time t to the suppliers of any debt capital used to finance the project ΔTAXt = the change in the firm’s taxes at time t as a result of undertaking the project N.DIV = any dividends payable at time t to new owners who supplied additional equity capital to help finance the project

The Weighted Average Cost of Capital Approach to NPV NPV = PV0[OCFt] - I0 Where τΔINTt is accounted for in our required rate of return. The actual present value calculation would look like: n NPV = ∑ OCFt - I0 t=1 (1 + kA)t where kA is the after–tax weighted average cost of capital and is calculated as: kA = (1 - L)kE + LkD(1 - τ)

Using the WACC Approach: An Example Consider again the case of the Keystone Restaurant which we examined earlier. Assume that the managers of the Keystone use a WACC approach in their calculation of project NPV. In evaluating whether to purchase the new grill, they need to estimate the OCFt produced by the grill, the appropriate kA, and the initial investment in the grill, I0.

Estimating OCFt The managers estimate that the life of the new grill will be five years. Over that period, they expect that the operation of the grill will increase cash revenues (ΔRt) by $15,000 per year. Likewise, they expect the cash expenses associated with operating the grill (ΔEt) to be $7,000 per year. They determine that $2,000 in depreciation (assuming straight-line depreciation with a salvage value of zero at the end of five years) can be taken on the grill each year. The Keystone’s marginal tax rate, τ, is 40%.

Using the WACC Approach: An example (cont’d) Financial approach:

Using the WACC Approach: An Example (cont’d)

Using the WACC Approach: An Example (cont’d) Accounting income statement approach to OCF: Year 1 Year 2 Year 3 Year 4 Year 5 ΔRt - ΔEt - ΔDEPRt $15,000 - 7,000 - 2,000 ΔTAXABLE INCOMEt - Δ TAXt(@40%) 6,000 - 2,400 ΔNIt + ΔDEPRt 3,600 2,000 OCFt $5,600

Using the WACC Approach: An Example (cont’d)

Example: suppose that the Keystone Restaurant is considering investing in a new grill that will cost $10,000. Sixty percent of the cost will be financed from the restaurant’s earnings (ΔRE0) and the rest by borrowing at a rate (kD) of 10%. Assume that the owner’s required rate of return (kE) on a project with a risk level equal to the new grill’s risk level is 16%. What will be the kDE of this project? kDE = (1 - L)kE + LkD = (1 – (4,000/10,000))(.16) + (4,000/10,000) (.10) = (.6)(.16) + (.4) (.10) = .136 or 13.6%

Using the WACC Approach: An Example (cont’d) Estimating I0. Estimating the total initial (time 0) investment, I0, is straightforward in this case. It is just the total purchase price of the grill (including installation)—that is, $10,000. Estimating kA. Earlier, we estimated the before-tax weighted average cost of capital for the grill (kDE) to be 13.6%. When using the WACC approach, however, we need to estimate kA, the after-tax weighted average cost of capital. kA = (1 - L)kE + LkD (1 - τ) = (1 – (4,000/10,000)) (.16) + (4,000/10,000)(.10) (1 - .4) = (.6)(.16) + (.4) (.10)(.6) = .12 or 12%

Using the WACC Approach: An Example (cont’d)

Using the WACC Approach: Some Considerations The leverage ratio, L, should be based on the market values of the debt and equity used to finance the project. The kA used for a project should reflect the risk of the project, which will not necessarily be the same as the risk of the firm undertaking the project. The WACC approach to NPV implicitly assumes that the leverage ratio will be held constant over the life of the project. When the firm uses several kinds of debt in its financing:

Summary Beginning with our fundamental description of owner’s value, W0 = DIV0 + V0[DIVt], we showed how owner’s value is affected when the firm undertakes a new project or investment and have defined net present value (NPV) as the resulting change in owner’s value. Starting with the most basic expression of NPV, the retained earnings approach, we developed or presented four other approaches to calculating NPV: the equity, debt/equity, WACC, and APV approaches. The two approaches with the greatest operational application in the hospitality industry are the WACC approach, which assumes that the firm maintains a constant proportion of debt in its financing, and the APV approach, which requires that the project evaluator know exactly how much debt the project will use and exactly what the debt repayment schedule will be.