 # Interactions of investment and financing decisions

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Interactions of investment and financing decisions
“People asking questions lost in confusion, well I tell them there's no problem, Only solutions, Well they shake their heads and they look at me as if I've lost my mind, I tell them there's no hurry, I'm just sitting here doing time” - Lennon

Capital Budgeting Valuing a Business or Project
The value of a business or Project is usually computed as the discounted value of FCF out to a valuation horizon (H). The valuation horizon is sometimes called the terminal value.

Capital Budgeting In this case r = wacc Valuing a Business or Project
PV (free cash flows) PV (horizon value) In this case r = wacc FCF = Profit after tax + depreciation + investment in fixed assets + investment in working capital

Cost of Capital Applications
The company cost of capital is the correct discount rate for projects that have the same risk as the company’s existing business but not for those projects that are safer or riskier than the company’s average. How can you make adjustments when considering projects that have different business risk than the company? The company cost of capital can be used for cases where the financial risk of the project is similar to the financial risk of the company. How can you analyze cases where the project’s financing differs from the company’s capital structure? In other words, how can you make adjustments that consider differences in financial risk?

Including the effect on value of
financing decisions Two methods: Adjusted discount rate - Usually implemented via the weighted average cost of capital (WACC). Modify the discount rate to reflect capital structure, bankruptcy risk, and other factors. 2. Adjusted present value (APV) APV = Base-case NPV + NPV of financing decisions all-equity financed project - Assume an all equity financed firm and then make adjustments to value based on financing.

WACC without taxes r = opportunity cost of capital
Before-tax = r = rD D + rE E WACC V V constant r = opportunity cost of capital Firms usually estimate rD and rE, then calculate weighted average to find r.

WACC with taxes After-tax WACC = r* = rD (1 - Tc) D + rE E V V
Tc is the marginal corporate tax rate r* is an adjusted cost of capital - it reflects the tax advantage of debt r* is less than the opportunity cost of capital, r (i.e. the cost of capital with all-equity finance) WACC refers to the firm as a whole, i.e. it works only if a project has same risk & debt capacity as firm Discounting at WACC assumes debt is rebalanced to maintain a constant ratio of debt to market value of the firm.

WACC vs. Flow to Equity If you discount at WACC, cash flows have to be projected just as you would for a capital investment project. Do not deduct interest. The value of interest tax shields is picked up in the WACC formula. The company's cash flows will probably not be forecasted to infinity. Financial managers usually forecast to a medium-term horizon -- ten years, say -- and add a terminal value to the cash flows in the horizon year. The terminal value is the present value at the horizon of post-horizon flows. Estimating the terminal value requires careful attention, because it often accounts for the majority of the value of the company. Discounting at WACC values the assets and operations of the company. If the object is to value the company's equity, that is, its common stock, don't forget to subtract the value of the company's outstanding debt.

Geothermal Example Net 1.095 Market value b/s Profits 2.085
Project D Interest E Pretax V Tax Net rD = rE = /7.5 = Tc = .35 D/V = E/V = .6 WACC = r* = .08( ) (.6) =

Using WACC to value Geothermal
Forecast cash flow before considering interest from debt: Pretax profits 35% After-tax profits = CF from operations Assume Geothermal’s project is a perpetuity and there is no depreciation. Discount cash flow at WACC = .1084 PV = C/r* = / = 12.5 Value of equity = V - D = = OR CF to equity / rE = 1.095/.146 = 7.5

Some interim questions
How do you allow for preferred stock etc.? What’s included in debt: Long-term debt? Short-term debt? How do you estimate: cost of equity? cost of debt?

Problems with Adjusted Cost of Capital
Easy to make logical errors, e.g. assume that cost of equity is independent of leverage Does not reveal where value is coming from Cannot easily allow for - changing debt ratios - changing tax rates - other financing side effects, e.g. issue costs

Adjusted present value is equal to the NPV if all equity financed (base case NPV) plus the NPV of financing side effects (such as tax shields, issuing costs, etc.) APV = base-case NPV + NPV of financing side effects

(a) Project A has NPV of \$100,000 if financed by cash but requires \$10 m equity with issuing costs equal to \$200,000 APV = base-case NPV - issue cost = = -\$100,000 (b) Project B has NPV of -\$100,000 if financed by cash but can support an extra \$500,000 of debt. If the debt is permanent at 10%and the tax rate is 40%, APV = base-case NPV + PV (tax shield) = (.4 x 500 x .1) / .1 = +\$100,000 (c) Project C has NPV of -\$100,000 if financed by cash but can support an extra \$500,000 of debt yielding 10% for 1 year only APV = x .1 x 500/1.1 = -\$81,818 Adjusted discount rate cannot easily handle (a) or (c)

APV can handle issuing costs and other financing side effects as well as two common financing rules
Debt Fixed - Fix debt at the start and predetermine interest schedule. - tax shield amounts are predetermined. Debt Rebalanced - Adjust the debt in each future period to keep it at a constant fraction of future project value. - the amount of debt and tax shields depend on the value of the project in the future.

APV and Geothermal Base-case NPV = -10 + C/r = -10 + 1.355/.12 = +1.29
Project supports debt of \$5 million at 8% and the tax rate is 35%. Then, the annual tax shield = .35 x x 5 = .14 Financing Rule 1: Debt fixed PV(tax shield) = .14/.08 = (note: using cost of debt) APV = = 3.04

APV & Geothermal (cont.)
Financing Rule 2: Debt Rebalanced PV(tax shield 1) = .14/1.08 = .13 certain now PV (tax shield 2) = .14/(1.12 x 1.08) = .116 certain in 1 year PV (tax shield 3) = .14/( x 1.08) = .103 certain in 2 years General rule: 1. Discount at opportunity cost of capital (r) because tax shields are tied to actual cash flows: .14/.12 = 1.17 2. Multiply result by (1 + r)/(1 + rD ) because tax shields are fixed 1 year in advance: PV(tax shield) = x 1.12/1.08 = 1.21 APV = = 2.5

WACC and APV 3 valuations of Geothermal: 1. APV (debt fixed) = +3.04
APV (debt rebalanced) = +2.5 3. NPV (WACC)= /.1084 = = +2.5 NPV APV can handle different financing assumptions, how can we use WACC if use of leverage changes? How can we use WACC under the two common financing rules?

The cost of capital Opportunity cost (r): Discount rate for all-equity financed projects Adjusted cost (r*): Discount rate that reflects financing You can use WACC to calculate r*, but WACC works only if project has same business risk as firm as a whole project has same debt capacity as firm as a whole We need a formula showing how WACC changes with opportunity cost of capital and leverage. Two formulas: Debt rebalanced: Miles-Ezzell formula (see long FN on page 485) Debt fixed: MM formula (see page 485 & FN 17 on page 486)

Miles-Ezzell formula r* = WACC = r - LrD T*[1 + r]/[1 + rD ] L = Debt to value ratio T* = net tax savings per dollar of interest (in practice corporate tax rate is used). r = opportunity cost of capital (100% equity) Use when debt will be rebalanced to maintain a constant ratio of debt to value. This formula allows you to calculate r from WACC. Once you know r, you can then calculate WACC for any new debt to value ratio. Once you have WACC for new debt usage, it can be used to calculate RE for alternative levels of debt.

Miles-Ezzell formula r* = WACC = r - LrD T*[1 + r]/[1 + rD ]
Suppose you know Geothermal’s WACC is 10.84% but don’t know r. If T* = Tc r* = r (.08)(.35)(1 + r)/(1.08) = r = .12 Now you know r, you can calculate adjusted cost of capital for any debt ratio e.g.. if L = .30 r* = (.08)(.35)(1.12/1.08) = or 11.1% You can also calculate cost of equity rE at 30% debt WACC = rD (1 - T )D/V + rE E/V = r* = .08 ( )( .3) + rE (.7) = .111 rE = or 13.6% c

rE= r + (1-Tc)(r-rd)D/E – see FN page 486
M&M formula M&M’s proposition II stated that the stockholders risk and hence their required rate of return increases with the use of debt: rE= r + (1-Tc)(r-rd)D/E – see FN page 486 If debt is fixed, r* = WACC = r (1-(T*L)) – see page 485 Like Miles-Ezzell formula, it Can be used to calculate r from WACC and once have r, a new rE or WACC can be computed for alternative amounts of debt.

M&M formula: The Geothermal project example
With fixed financing if \$5 million, and firm value of \$13.04 million: L = 5/13.04 =.383 r = .12 T*=Tc=.35 then r*= r(1-T*L) = .12[1-.35(.383)] =.1039 = 10.39% NPV = 1.355/ = 3.04 (Same as APV for debt fixed )

Some questions Which formulas do managers actually use? (WACC)
What if project’s financing differs from the company’s? (Use Miles-Ezzell or MM formulas or unlevered Beta) Why not just calculate a new WACC? (Remember as leverage changes, rE changes) Can CAPM be used to estimate rE for WACC formula? (Yes) Can CAPM be used to estimate opportunity cost of capital r? (Estimate asset beta: BetaA = BetaD D/V + BetaE E/V) Now plug in to CAPM to estimate r. Should one use Tc in WACC formula? (yes)

A final example WACC = rD (1 - Tc )D/V + rE E/V
= .09( ) (.7) = What is correct discount rate if D/V = .50?

A final example (cont.) WACC = rD (1 - Tc)D/V + rE E/V
= .09( ) (.7) = What is correct discount rate if D/V = .50? Using Miles-Ezzell formula, r* = WACC = r - LrD T* (1 + r)/(1 + rD) = r (.09)(.35)(1 + r)/ (1.09) = r = Suppose rD rises to 9.5% with higher borrowing r* = (.095)(.35)(1.1325)/(1.095) =