Capital Structure and Valuation

8-1

8-2Example

Current Proposed

Assets $8,000 $8,000

Debt $0 $4,000

Equity $8,000 $4,000

Interest 10% 10%

Share Price $20 $20

Outstanding 400 200

8-3Capital Structure

Recession Expected ExpansionROA 5% 15% 25%Earnings $400 $1,200 $2,000ROE 5% 15% 25%EPS $1.00 $3.00 $5.00

ROA 5% 15% 25%EBI $400 $1,200 $2,500Interest 400 400 400Earnings $0 $800 $1,600ROE 0% 20% 40%EPS $0 $4.00 $8.00

Current

Proposed

8-4Miller and Modigliani: Proposition I

Recession Expected ExpansionEarnings $0 $400 $800Initial Cost: 100 x $20 = $2,000

Earnings $200 $600 $1,000Interest $200 $200 $200Net Earnings $0 $400 $800Initial Cost: 200 x $20 -$2,000 = $2,000

Strategy A: Buy 100 shares of levered equity

Strategy B: Buy 200 shares of unlevered equity using $2,000 in borrowing (Homemade Leverage)

Proposition I (no taxes): Value of the unlevered firm is equal to the value of the levered firm

8-5Miller and Modigliani: Proposition II(no taxes)

Remember: rRemember: rWACC WACC = D/A × r= D/A × rDD + E/A × r + E/A × rEE

MM(I) implies rMM(I) implies rWACC WACC is independent of leverageis independent of leverage

Define rDefine r00 is cost of capital for all-equity firm is cost of capital for all-equity firm

rr00 = unlevered earnings / unlevered equity =15% = unlevered earnings / unlevered equity =15%

Result: rResult: r00=r=rWACCWACC if there are no taxes if there are no taxes

Result: MM(II) (no taxes): rResult: MM(II) (no taxes): rEE = r = r00 + D/E × (r + D/E × (r0 0 – r– rDD))

8-6Cost of Capital and MM(2)

r0

rE

rWACC

rD

D/E

Cost of Capital (%)

8-7Taxes

Present value of the tax shieldPresent value of the tax shield

Interest = rInterest = rDD × D × D

Tax reduction = TTax reduction = Tcc × r × rDD × D × D

Under normal circumstances we can assume:Under normal circumstances we can assume:cash flow from tax reduction has same risk as debtcash flow from tax reduction has same risk as debt

cash flows are perpetualcash flows are perpetual

PV(Tax Shield) = (TPV(Tax Shield) = (Tcc × r × rDD × D) / r × D) / rDD = T = Tcc × D × D

MM(I): VMM(I): VLL = V = VUU + T + Tcc × D × D

VU = (EBIT × (1 – TVU = (EBIT × (1 – Tcc)) / r)) / r00

8-8MM(2): rE = r0 + D/E × (1-Tc) (r0 – rD)

r0

rE

rWACC

rD

D/E

Cost of Capital (%)

A declining rWACC is a direct result from MM(I), i.e, the value

of the firm rises in leverage

8-9Example

Blue Inc. has no debt and is expected to generate $4 million Blue Inc. has no debt and is expected to generate $4 million in EBIT in perpetuity. Tin EBIT in perpetuity. Tcc=30%. All after-tax earnings are paid =30%. All after-tax earnings are paid

as dividends.The firm is considering a restructuring, as dividends.The firm is considering a restructuring, allowing $10 million in debt at an interest rate of 8%. The allowing $10 million in debt at an interest rate of 8%. The unlevered cost of equity, runlevered cost of equity, r00, is 18%., is 18%.

What is the current value of Blue?What is the current value of Blue? VVUU=EBIT × (1–T=EBIT × (1–Tcc) / r) / r00 = ($4 million × 0.7) / 0.18 = $15.56 million = ($4 million × 0.7) / 0.18 = $15.56 million

What will the new value be after the restructuring?What will the new value be after the restructuring? VVLL = V = VUU + T + Tcc × D = $15.56 + 0.3 × $10 = $18.56 million × D = $15.56 + 0.3 × $10 = $18.56 million

What will the new required return on equity be?What will the new required return on equity be? rrEE = 0.18 + (10/8.56) × 0.7 × (0.18 – 0.08) = 26.18% = 0.18 + (10/8.56) × 0.7 × (0.18 – 0.08) = 26.18%

Check with: ECheck with: Eleveredlevered = ((4 – 0.8) × 0.7) / 0.2618 = $8.56 million = ((4 – 0.8) × 0.7) / 0.2618 = $8.56 million

8-10How about using rWACC?

rrWACCWACC = (10/18.56) × 0.7 × 0.08 + (8.56/18.56) × 0.2618 = 15.08% = (10/18.56) × 0.7 × 0.08 + (8.56/18.56) × 0.2618 = 15.08%

Hence, Blue has decreased its WACC from 18% to 15.08%Hence, Blue has decreased its WACC from 18% to 15.08%

VVLL = (4 × 0.7) / 0.1508 = $18.56 million = (4 × 0.7) / 0.1508 = $18.56 million

8-11Downside of DebtFinancial Distress and Agency Costs

Financial Distress costs decrease the size of the Financial Distress costs decrease the size of the firm and hence decrease the distribution to firm and hence decrease the distribution to shareholders and bondholders.shareholders and bondholders.

CostsCosts Direct costs of financial distressDirect costs of financial distress

Indirect costs of financial distressIndirect costs of financial distress

Agency costs (of debt)Agency costs (of debt)Asset substitution and risk shiftingAsset substitution and risk shifting

UnderinvestmentUnderinvestment

Milking the companyMilking the company

8-12Static trade-off theory of debt

Maximum Firm Value

Firm Value

Debt

Optimal amount of Debt

Actual Firm Value

8-13More on Agency CostsBenefits of debt

Agency cost of Equity (motive)Agency cost of Equity (motive) Shirking is less likely when issuing debtShirking is less likely when issuing debt

Perquisites are less likely with debtPerquisites are less likely with debt

Over-investment is less likely with debtOver-investment is less likely with debt

Agency cost of Free Cash Flow (opportunity)Agency cost of Free Cash Flow (opportunity) Retained earnings versus dividends?Retained earnings versus dividends?

Growth and investment opportunitiesGrowth and investment opportunities

Debt serves as a monitoring device, decreasing Debt serves as a monitoring device, decreasing managerial discretionmanagerial discretion

8-14The Pecking-Order Theory

Internal FinancingInternal Financing

External FinancingExternal Financing Debt FinancingDebt Financing

Equity Financing (last resort)Equity Financing (last resort)

Asymmetric information and SignalingAsymmetric information and Signaling

Dynamic decision, rather than staticDynamic decision, rather than static

8-15Valuation

Weighted Average Cost of CapitalWeighted Average Cost of Capital All Cash Flows discounted by discount rate that takes All Cash Flows discounted by discount rate that takes

into account leverageinto account leverage

Adjusted Present ValueAdjusted Present Value Separate cash flows from project and cash flows from Separate cash flows from project and cash flows from

financingfinancing

Flow-to-Equity ApproachFlow-to-Equity Approach Cash flows to equity holders discounted by the cost of Cash flows to equity holders discounted by the cost of

equityequity

8-16Example

You are considering a project with the following You are considering a project with the following characteristics:characteristics: Perpetual cash inflows starting in year 1 of $25,000 per yearPerpetual cash inflows starting in year 1 of $25,000 per year

Yearly operating expenses of 12% of revenuesYearly operating expenses of 12% of revenues

Initial investment outlay of $125,000Initial investment outlay of $125,000

TTcc=34% and r=34% and r00=14%, r=14%, rDD=8%=8%

Calculate the NPV for an all-equity firmCalculate the NPV for an all-equity firm

Calculate the NPV for a firm with a Calculate the NPV for a firm with a targettarget capital structure capital structure of 65% debt and 35% equityof 65% debt and 35% equity Use WACC methodUse WACC method

Use APV methodUse APV method

Use FTE methodUse FTE method

8-17Answers

Unlevered firm valuation Unlevered firm valuation

Cash Inflows $25,000Operating Expenses $ 3,000Operating Income $22,000Tax $ 7,480Unlevered Cash Flow (UCF)$14,520

NPV = –$125,000 + ($14,520 / 0.14) = –$21,286

To theshareholders

8-18Answer

WACCWACC

rWACC = (D/V) × (1–Tc) × rD + (E/V) × rE

rWACC = (0.65) × (1– 0.34) × 0.08 + (0.35) × rE

rE = r0 + (D/E) × (1 – Tc) × (r0 – rD)rE = 0.14 + (65/35) × (1 – 0.34) × (0.06) = 0.2135 = 21.35%

rWACC = (0.65) × (1– 0.34) × 0.08 + (0.35) × 0.2135 = 10.906%

NPV = –$125,000 + ($14,520 / 0.10906) = $8,138

8-19Answer

APVAPV

APV = NPV + NPVFNPVF = Tc × DAPV = –$21,286 + (0.34 × 0.65 × (APV + $125,000))0.779 × APV = $6,339APV = $8,138

Verify the target capital structure:Firm borrows 0.65 × ($125,000 + $8,138)Firm borrows 0.65 × $133,137 = $86,539.52Firm uses $125,000 – $86,539.52 = $38,460.48 in equity

NPV of Financing Side Effects

8-20

VL = VU + Tc × DVL = 125,000 – 21,286 + 0.34 × 0.65 × VL

VL = 133,138 D = 0.65 × 133,138

Answer

FTE methodFTE method

Cash Inflows $25,000Operating Expenses $ 3,000Operating Income $22,000Interest (8% of $86,539.52) $ 6,923Income after interest $15,077Tax $ 5,126Levered Cash Flow (LCF) $ 9,951

From before, rE = 21.35% and PV = $9,951 / 0.2135 = $46,609NPV = – $38,460 + $46,598 = $8,138

To theshareholders

8-21Evaluation

Valuation for all-equity firm is easyValuation for all-equity firm is easy

Valuation for levered firm is complexValuation for levered firm is complex tax shieldstax shields

bankruptcy, agency, and other costsbankruptcy, agency, and other costs

WACC, APV, and FTE methodWACC, APV, and FTE method constant risk over life of project (constant rconstant risk over life of project (constant r00))

constant debt/value constant debt/value ratioratio over life of project (constant r over life of project (constant rEE and r and rWACCWACC))

FTE and WACC work well under this scenarioFTE and WACC work well under this scenario

if debt/value ratio is changing use APV (based on the if debt/value ratio is changing use APV (based on the levellevel of debt) of debt)

APV works well for LBO’s and cases with interest subsidies and flotation costs (see APV works well for LBO’s and cases with interest subsidies and flotation costs (see example in Appendix 17A).example in Appendix 17A).

8-22Beta revisited

Remember the following:Remember the following:

LeveredLevered EquityEquity = = L L = = Unlevered AssetsUnlevered Assets × (1 + (D/E)) × (1 + (D/E))

Assumes Assumes DebtDebt = 0 = 0 and no corporate taxesand no corporate taxes

With corporate taxes (assume With corporate taxes (assume DebtDebt = 0) = 0)::

LL = = UU × [1 + (1–T × [1 + (1–Tcc) × (D/E)]) × (D/E)]

Unlevered Firm Unlevered Firm < < LeveredLevered EquityEquityRemember: RE > R0 > RD

8-23What if Beta of debt 0?

LL = = U U + [(1–T+ [(1–Tcc) × () × (U U – – DD) × (D/E)]) × (D/E)]

L = levered equityU = unlevered equity (100% equity firm)D = debtE = equity