MBA Finance
jaikrishna
Ch15ToolKit.xlsxChapter
| Tool Kit | Chapter 15 | 11/21/18 | |||||||||||||||||
| Capital Structure Decisions | |||||||||||||||||||
| 15-2 Business Risk and Financial Risk | |||||||||||||||||||
| Operating Leverage reflects the amount of fixed costs embedded in a firm's operations. Thus, if a high percentage of a firm's costs are fixed, hence continue even if sales decline, then the firm is said to have high operating leverage. High operating leverage produces a situation where a small change in sales can result in a large change in operating profit. The following example compares two operational plans with different degrees of operating leverage. | |||||||||||||||||||
| Figure 15-1 | |||||||||||||||||||
| Illustration of Operating and Financial Leverage (Millions of Dollars and Millions of Units, Except Per Unit Data) | |||||||||||||||||||
| 1. Input Data | Plan A | Plan U | Plan L | ||||||||||||||||
| Required operating current assets | $3 | $3 | $3 | ||||||||||||||||
| Required long-term assets | $199 | $199 | $199 | ||||||||||||||||
| Total assets | $202 | $202 | $202 | ||||||||||||||||
| Resulting operating current liabilities | $2 | $2 | $2 | ||||||||||||||||
| Required capital (TA − Op. CL) | $200 | $200 | $200 | ||||||||||||||||
| Book equity | $200 | $200 | $150 | ||||||||||||||||
| Debt | $0 | $0 | $50 | ||||||||||||||||
| Interest rate | 8% | 8% | 8% | ||||||||||||||||
| Sales price (P) | $2.00 | $2.00 | $2.00 | ||||||||||||||||
| Tax rate (T) | 25% | 25% | 25% | ||||||||||||||||
| Expected units sold (Q) | 100 | 100 | 100 | ||||||||||||||||
| Fixed costs (F) | $20 | $60 | $60 | ||||||||||||||||
| Variable costs (V) | $1.50 | $1.00 | $1.00 | ||||||||||||||||
| 2. Income Statements | Plan A | Plan U | Plan L | ||||||||||||||||
| Sales revenue (P x Q) | $200.0 | $200.0 | $200.0 | ||||||||||||||||
| Fixed costs | 20.0 | 60.0 | 60.0 | ||||||||||||||||
| Variable costs (V x Q) | 150.0 | 100.0 | 100.0 | ||||||||||||||||
| EBIT | $30.0 | $40.0 | $40.0 | ||||||||||||||||
| Interest | 0.0 | 0.0 | 4.0 | ||||||||||||||||
| Pre-tax earnings | $30.0 | $40.0 | $36.0 | ||||||||||||||||
| Tax | 7.5 | 10.0 | 9.0 | ||||||||||||||||
| Net income | $22.5 | $30.0 | $27.0 | ||||||||||||||||
| 3. Key Performance Measures | Plan A | Plan U | Plan L | ||||||||||||||||
| NOPAT = EBIT(1 − T) | $22.5 | $30.0 | $30.0 | ||||||||||||||||
| ROIC = NOPAT/Capital | 11.3% | 15.0% | 15.0% | ||||||||||||||||
| ROA = NI/Total assets | 11.1% | 14.9% | 13.4% | ||||||||||||||||
| ROE = NI/Equity | 11.3% | 15.0% | 18.0% | ||||||||||||||||
| Numbers are reported as rounded values for clarity but are calculated using Excel’s full precision. Thus, intermediate calculations using the figure’s rounded values will be inexact. | |||||||||||||||||||
| Note: ROA is not exactly equal to ROE for the Plan L or Plan U because total assets is not quite equal to equity for these plans. This is because the operating current liabilities, such as accounts payable and accruals, reduce the required equity capital investment. | |||||||||||||||||||
| We can use the following formula to find the exact break-even quantity. | |||||||||||||||||||
| QBE = | F ÷ (P-V) | ||||||||||||||||||
| Plan A | |||||||||||||||||||
| QBE = | F | ÷ | ( P | − | V ) | ||||||||||||||
| QBE = | $20 | ÷ | $2.00 | − | $1.50 | ||||||||||||||
| QBE = | 40 | Units. | |||||||||||||||||
| Plan U | |||||||||||||||||||
| QBE = | F | ÷ | ( P | − | V ) | ||||||||||||||
| QBE = | $60 | ÷ | $2.00 | − | $1.00 | ||||||||||||||
| QBE = | 60 | Units. | |||||||||||||||||
| Crossover Q for A vs. U = | 80 | ||||||||||||||||||
| QBE for levered firm = | (F + Int) ÷ (P-V) | ||||||||||||||||||
| Plan L | |||||||||||||||||||
| QBE = | F − Int | ÷ | P − V | ||||||||||||||||
| QBE = | $56 | ÷ | $1.00 | ||||||||||||||||
| QBE = | 56 | Units. | |||||||||||||||||
| Crossover Q for U vs. L = | 76 | ||||||||||||||||||
| Leverage magnifies the ROE. See Panel b of Figure 15-2 below. | |||||||||||||||||||
| Figure 15-2 | |||||||||||||||||||
| Operating Leverage and Financial Leverage | |||||||||||||||||||
| Data Table for Figure | |||||||||||||||||||
| x-axis for both panels. | ROE for Panel A | ROE for Panel b | ROIC | ||||||||||||||||
| Plan A | Plan U | Plan U | Plan L | Plan U | Plan L | Line at 0 | |||||||||||||
| Q | 11.3% | 15.0% | 15.0% | 18.0% | Q | 15.0% | 15.0% | ||||||||||||
| 0 | -7.5% | -22.5% | -22.5% | -32.0% | 0 | -22.5% | -22.5% | 0 | |||||||||||
| 20 | -3.8% | -15.0% | -15.0% | -22.0% | 20 | -15.0% | -15.0% | 0 | |||||||||||
| 40 | 0.0% | -7.5% | -7.5% | -12.0% | 40 | -7.5% | -7.5% | 0 | |||||||||||
| 60 | 3.8% | 0.0% | 0.0% | -2.0% | 60 | 0.0% | 0.0% | 0 | |||||||||||
| 64 | 4.5% | 1.5% | 1.5% | 0.0% | 64 | 1.5% | 1.5% | 0 | |||||||||||
| 76 | 6.8% | 6.0% | 6.0% | 6.0% | 76 | 6.0% | 6.0% | 0 | |||||||||||
| 80 | 7.5% | 7.5% | 7.5% | 8.0% | 80 | 7.5% | 7.5% | 0 | |||||||||||
| 100 | 11.3% | 15.0% | 15.0% | 18.0% | 100 | 15.0% | 15.0% | 0 | |||||||||||
| 120 | 15.0% | 22.5% | 22.5% | 28.0% | 120 | 22.5% | 22.5% | 0 | |||||||||||
| 140 | 18.8% | 30.0% | 30.0% | 38.0% | 140 | 30.0% | 30.0% | 0 | |||||||||||
| 15-3 Capital Structure Theory: The Modigliani and Miller Models | |||||||||||||||||||
| Following are descriptions of the M&M models. | |||||||||||||||||||
| 15-3a Modigliani and Miller: No Taxes | |||||||||||||||||||
| V L = V U | |||||||||||||||||||
| 15-3b Modigliani and Miller: The Effect of Corporate Taxes | |||||||||||||||||||
| V L = V U + TD | |||||||||||||||||||
| VU = | $100 | ||||||||||||||||||
| Federal-plus-state corporate tax rate = | 25% | ||||||||||||||||||
| Pre-TCJA federal-plus-state corporate tax rate = | 40% | ||||||||||||||||||
| This figure is not shown in the textbook. | |||||||||||||||||||
| Data for Graph | |||||||||||||||||||
| Debt | VU | VL | Pre-TCJA VL | wd | |||||||||||||||
| $0 | $100 | $100 | $100 | 0% | |||||||||||||||
| $15 | $100 | $103.75 | $106 | 14% | |||||||||||||||
| $30 | $100 | $107.50 | $112 | 28% | |||||||||||||||
| $45 | $100 | $111.25 | $118 | 40% | |||||||||||||||
| $60 | $100 | $115.00 | $124 | 52% | |||||||||||||||
| Interest expense deduction limitation | |||||||||||||||||||
| The TCJA limits deductibility of interest expenses for purpose of tax deductibility to 30% of EBITDA for the years 2018-2021 and 30% of EBIT for subsequent years. Interest expenses exceeding this level may be carried forward to offset future taxes. When applying this rule to EBIT and using reasonable values for rsu and rd, the maximum wd that can utilize the tax shield immediately is: | |||||||||||||||||||
| Reasonable values of: | |||||||||||||||||||
| T = | 25% | ||||||||||||||||||
| rsu = | 12% | ||||||||||||||||||
| rd = | 8% | ||||||||||||||||||
| Interest expense deduction limit (IntLim)= | 30% | ||||||||||||||||||
| Max wd = | [(IntLim)(rsu)] / [ { (1-T)rd } + {IntLim)(rsu)T} ] | ||||||||||||||||||
| Max wd = | 52.2% | ||||||||||||||||||
| Check: | |||||||||||||||||||
| wd = | 52.2% | ||||||||||||||||||
| VU = | $100 | ||||||||||||||||||
| Debt given wd = | [w d (V U )]/[1 − (w d T)] | ||||||||||||||||||
| = | $60.00 | ||||||||||||||||||
| Interest based on D = | $4.80 | ||||||||||||||||||
| EBIT implied by VU = | (VU rsU)/(1 - T) | ||||||||||||||||||
| = | $16 | ||||||||||||||||||
| Interest / EBIT = | 30.0% | ||||||||||||||||||
| 15-3c Miller: The Effect of Corporate and Personal Taxes | |||||||||||||||||||
| TCJA rates | Pre-TCJA rates | ||||||||||||||||||
| This figure is not shown in the textbook. | VU = | $100 | $100 | ||||||||||||||||
| Combined federal plus state corporate tax rate = TC = | 25.0% | 40.0% | |||||||||||||||||
| Personal tax rate on debt = Td = | 32.0% | 33.0% | |||||||||||||||||
| Effective personal tax rate on stock = Ts = | 12.0% | 12.0% | |||||||||||||||||
| Value in bracket = | 2.9% | 21.2% | |||||||||||||||||
| Data for Graph | Pre-TCJA wd | ||||||||||||||||||
| Debt | VU | VL | Pre-TCJA VL | wd | |||||||||||||||
| $0 | $100 | $100 | $100 | 0% | 0% | ||||||||||||||
| $10 | $100 | $100.29 | $102.12 | 10% | 10% | ||||||||||||||
| $20 | $100 | $100.59 | $104.24 | 20% | 19% | ||||||||||||||
| $30 | $100 | $100.88 | $106.36 | 30% | 28% | ||||||||||||||
| $40 | $100 | $101.18 | $108.48 | 40% | 37% | ||||||||||||||
| $50 | $100 | $101.47 | $110.60 | 49% | 45% | ||||||||||||||
| 15-4A Trade-Off Theory | |||||||||||||||||||
| V L = V U + TD + Financial distress costs | |||||||||||||||||||
| VU = | $100 | ||||||||||||||||||
| Federal plus state corporate tax rate = | 25% | ||||||||||||||||||
| Figure 15-3 | |||||||||||||||||||
| Effect of Financial Leverage on Value | |||||||||||||||||||
| Data for Graph | This formula gives a reasonable result for financial distress costs: Fin dis = a -(1-ae^ZD) | ||||||||||||||||||
| Note: Cell heigth and width are locked for cells colored | Parameter for reasonable financial distress function = Z = | 0.09 | |||||||||||||||||
| Data to create graph and other data | |||||||||||||||||||
| Leverage (D) | VU | M&M II
Michael Ehrhardt: M&M Result Incorporating the Effects of Corporate Taxation: Value if There Were No Bankruptcy-Related Costs | Actual Value | Horzontal axis | wd | TD | Fin dis costs | ||||||||||||
| $0 | $100 | $100 | $100.00 | 60 | 0% | $0.00 | $0.00 | ||||||||||||
| $6 | $100 | $101.50 | $101.30 | 60 | 6% | $1.50 | $0.20 | ||||||||||||
| $12 | $100 | $103.00 | $102.40 | 60 | 12% | $3.00 | $0.60 | ||||||||||||
| $18 | $100 | $104.50 | $103.50 | 60 | 17% | $4.50 | $1.00 | ||||||||||||
| $24 | $100 | $106.00 | $104.28 | 60 | 23% | $6.00 | $1.72 | ||||||||||||
| $30 | $100 | $107.50 | $104.56 | 60 | 28% | $7.50 | $2.94 | ||||||||||||
| $36 | $100 | $109.00 | $103.95 | 60 | 33% | $9.00 | $5.05 | ||||||||||||
| $42 | $100 | $110.50 | $101.83 | 60 | 38% | $10.50 | $8.67 | ||||||||||||
| $48 | $100 | $112.00 | $97.12 | 60 | 43% | $12.00 | $14.88 | ||||||||||||
| $54 | $100 | $113.50 | $87.97 | 60 | 48% | $13.50 | $25.53 | ||||||||||||
| 15-6 Estimating the Optimal Capital Structure | |||||||||||||||||||
| Adding debt decreases taxes (because interest expenses are deductible) but also increases the cost of debt (because the additional debt is riskier). Additional debt also increases shareholder risk as measured by beta and the cost of equity. Managers should identify percentage of debt (wd) that maximizes shareholder wealth and implement that capital structure unless there are other compelling reasons (e.g, information asymmetry, current market conditions, etc.). | |||||||||||||||||||
| 15-6a Current Value and Capital Structure | |||||||||||||||||||
| Figure 15-4 shows Strasburg's current situation. | |||||||||||||||||||
| Figure 15-4 | |||||||||||||||||||
| Strasburg’s Current Value and Capital Structure (Millions of Dollars Except Per Share Data) | |||||||||||||||||||
| Input Data | Capital Structure and Cost of Capital | ||||||||||||||||||
| Stock price (P) | $22.50 | Market value of equity (S = P x n) | $2,250 | ||||||||||||||||
| # of shares (n) | 100 | Total value (V = D + S) | $2,500 | ||||||||||||||||
| Market value of debt (D) | $250.00 | % financed with debt (wd = D/V) | 10.00% | ||||||||||||||||
| Tax rate | 25% | % financed with stock (ws = S/V) | 90.00% | ||||||||||||||||
| EBIT | $400 | Cost of equity: rs = rRF + b(RPM ) | 12.67% | ||||||||||||||||
| Net operating capital | $2,000 | ||||||||||||||||||
| Growth rate (gL) | 0% | Weighted average cost of capital: | |||||||||||||||||
| Cost of debt (rd) | 8.00% | WACC = rd (1 − T)(wd) + rs (ws) | 12.00% | Note: WACC is rounded to 4 decimal places. | |||||||||||||||
| Beta (b) | 1.01 | ||||||||||||||||||
| Risk-free rate (rRF) | 6.67% | ||||||||||||||||||
| Mkt. risk prem. (RPM) | 5.94% | ||||||||||||||||||
| ROIC and Free Cash Flow | Estimated Intrinsic Value | ||||||||||||||||||
| NOPAT = EBIT(1 − T) | $300 | Vop = [FCF(1 + gL)]/(WACC − gL): | $2,500.00 | ||||||||||||||||
| ROIC = NOPAT/Op. Cap. | 15% | + Value of ST investments | $0.00 | ||||||||||||||||
| Inv. in Op. Cap. = Δ Cap. | $0 | Estimated total intrinsic value | $2,500.00 | ||||||||||||||||
| − Debt | $250.00 | ||||||||||||||||||
| Free cash flow: | Estimated intrinsic value of equity | $2,250.00 | |||||||||||||||||
| FCF = NOPAT − Δ Cap. | $300 | ÷ Number of shares | $100.00 | ||||||||||||||||
| Estimated intrinsic price per share | $22.50 | ||||||||||||||||||
| Numbers are reported as rounded values for clarity but are calculated using Excel’s full precision. Thus, intermediate calculations using the figure’s rounded values will be inexact. | |||||||||||||||||||
| Notes: | |||||||||||||||||||
| 1. The weighted average cost of capital is rounded to 4 decimal places. | |||||||||||||||||||
| 2. Strasburg's sales, earnings, and assets are not growing, so it does not need investments in operating capital. Therefore, FCF = NOPAT − Investment in operating capital = EBIT(1 − T) − $0 = EBIT(1 − T) . The growth in FCF also is 0. | |||||||||||||||||||
| 15-6b Preliminary Steps to Identify the Optimal Capital Structure | |||||||||||||||||||
| Begin the process by choosing the percentage of debt (wd, based on market values) that corresponds with each capital structure to be considered. Also, use the current capital structure to estimate the unlevered beta (bU) because it will be needed to identify the cost of equity for each capital structure under consideration. | |||||||||||||||||||
| Capital Structures to be Considered | |||||||||||||||||||
| Capital Structures Under Consideration (wd) | |||||||||||||||||||
| 0% | 10% | 20% | 30% | 40% | 50% | ||||||||||||||
| Estimating the Unlevered Beta with the Hamada Equation | |||||||||||||||||||
| Hamada developed his equation by merging the CAPM with the Modigliani-Miller model. We use the model to determine beta at different amount of financial leverage, and then use the betas associated with different debt ratios to find the cost of equity associated with those debt ratios. Here is a version of the Hamada equation: | |||||||||||||||||||
| bU = b / [1 + (1-T) x (D/S)] | |||||||||||||||||||
| Here b is the levered beta, bU is the beta that the firm would have if it used no debt, T is the marginal tax rate, D is the market value of the debt, and S is the market value of the equity. | |||||||||||||||||||
| Most analysts use the following version based on market weights of debt and equity: | |||||||||||||||||||
| bU = b / [1 + (1-T) x (wd/ws)] | |||||||||||||||||||
| Following is information about the current capital structure, which will be used to estimate the unlevered beta. | |||||||||||||||||||
| Levered beta (b) = | 1.01000 | ||||||||||||||||||
| Current percentage financing provided by debt (wd) = | 10% | ||||||||||||||||||
| Current financing provided by equity (ws) = | 90% | ||||||||||||||||||
| Federal-plus-state tax rate (T) = | 25% | ||||||||||||||||||
| bU = | 0.93231 | ||||||||||||||||||
| 15-6c Steps to Identify the Optimal Capital Structure | |||||||||||||||||||
| To identify the optimal capital structure, apply the following steps to each capital structure under consideration: (1) Estimate the levered beta and cost of equity. (2) Estimate the interest rate and cost of debt. (3) Calculate the weighted average cost of capital. (4) Calculate the value of operations, which is the present value of free cash flows discounted by the new WACC. The objective is to find the amount of debt financing that maximizes the value of operations. | |||||||||||||||||||
| Estimating the Levered Beta and Cost of Equity (rs) | |||||||||||||||||||
| Use the previously calculated unlevered beta (1.0526) and Equation 15-11a to determine the levered beta for each of the capital structures being considered. For example, the levered beta for a capital structure with 20% debt is: | |||||||||||||||||||
| bU = | 0.9323 | ||||||||||||||||||
| T = | 25% | ||||||||||||||||||
| wd = | 20% | ||||||||||||||||||
| ws = | 80% | ||||||||||||||||||
| b = | bU x [1 + (1-T) x (wd/ws)] | ||||||||||||||||||
| b = | 1.107 | ||||||||||||||||||
| Repeating this process for each capital structure provides an estimate of the levered beta for each capital structure: | |||||||||||||||||||
| wd = | 0% | 10% | 20% | 30% | 40% | 50% | |||||||||||||
| b = | 0.932 | 1.010 | 1.107 | 1.232 | 1.398 | 1.632 | |||||||||||||
| The cost of equity is: | |||||||||||||||||||
| rs = rRF + b(RPM) | |||||||||||||||||||
| Risk-free rate (rRF) = | 6.670% | ||||||||||||||||||
| Mkt. risk prem. (RPM) = | 5.940% | ||||||||||||||||||
| The cost of equity for each capital structure is: | |||||||||||||||||||
| wd = | 0% | 10% | 20% | 30% | 40% | 50% | |||||||||||||
| rs = | 12.21% | 12.6694% | 13.25% | 13.99% | 14.98% | 16.36% | |||||||||||||
| Figure 15-5 charts the relationship between the cost of equity and the amount of debt financing. | |||||||||||||||||||
| Data for Figure 15-5 | |||||||||||||||||||
| wd | 0% | 10% | 20% | 30% | 40% | 50% | |||||||||||||
| rRF | 6.67% | 6.67% | 6.67% | 6.67% | 6.67% | 6.67% | |||||||||||||
| bU ´ RPM | 5.54% | 5.54% | 5.54% | 5.54% | 5.54% | 5.54% | |||||||||||||
| (b − bU)´ RPM | 0.00% | 0.46% | 1.04% | 1.78% | 2.77% | 4.15% | |||||||||||||
| Figure 15-5 | |||||||||||||||||||
| Strasburg’s Required Rate of Return on Equity at Different Debt Levels | |||||||||||||||||||
| Estimating the Cost of Debt (rd) | |||||||||||||||||||
| Investment bankers and commercial bankers can provide estimates of the expected interest rate for each capital structure under consideration. Discussions with its bankers indicate that Strasburg's cost of debt goes up as the percentage of debt goes up. The investment bankers' estimates are shown in Line 4 of Figure 15-6. Note: the percentages are based on market values. | |||||||||||||||||||
| Figure 15-6 also shows the previously calculated betas and costs of equity. The following sections explain the remaining information in the figure. | |||||||||||||||||||
| Figure 15-6 | |||||||||||||||||||
| Estimating Strasburg's Optimal Capital Structure (Millions of Dollars) | |||||||||||||||||||
| Percent of Firm Financed with Debt (wd) | |||||||||||||||||||
| 0% | 10% | 20% | 30% | 40% | 50% | ||||||||||||||
| 1. ws | 100.00% | 90.00% | 80.00% | 70.00% | 60.00% | 50.00% | |||||||||||||
| 2. b | 0.932 | 1.010 | 1.107 | 1.232 | 1.398 | 1.632 | |||||||||||||
| 3. rs | 12.21% | 12.67% | 13.25% | 13.99% | 14.98% | 16.36% | |||||||||||||
| 4. rd | 7.80% | 8.00% | 8.20% | 8.70% | 10.10% | 12.20% | |||||||||||||
| 5. rd (1−T) | 5.85% | 6.00% | 6.15% | 6.53% | 7.58% | 9.15% | |||||||||||||
| 6. WACC | 12.21% | 12.00% | 11.83% | 11.75% | 12.02% | 12.76% | |||||||||||||
| 7. Vop | $2,457.00 | $2,500.00 | $2,535.93 | $2,553.19 | $2,495.84 | $2,351.10 | |||||||||||||
| 8. Debt | $0.00 | $250.00 | $507.19 | $765.96 | $998.34 | $1,175.55 | |||||||||||||
| 9. Equity | $2,457.00 | $2,250.00 | $2,028.74 | $1,787.23 | $1,497.50 | $1,175.55 | |||||||||||||
| 10. # Shares | 111.33 | 100.00 | 88.75 | 77.60 | 66.68 | 55.95 | |||||||||||||
| 11. Stock price | $22.07 | $22.50 | $22.86 | $23.03 | $22.46 | $21.011 | |||||||||||||
| 12. Net income | $300.00 | $285.00 | $268.81 | $250.02 | $224.38 | $192.44 | |||||||||||||
| 13. EPS | $2.69 | $2.85 | $3.03 | $3.22 | $3.37 | $3.44 | |||||||||||||
| Numbers are reported as rounded values for clarity but are calculated using Excel’s full precision unless otherwise noted. Thus, intermediate calculations using the figure’s rounded values will be inexact. | |||||||||||||||||||
| Notes: | |||||||||||||||||||
| 1. | The percent financed with equity is: ws = 1 − wd | ||||||||||||||||||
| 2. | The levered beta for each proposed capital structure is estimated by Hamada's formula with a 25% federal-plus-state tax rate, the unlevered beta (0.9323), and the propsed capital structure: b = bU [1 + (1-T) (wd/ws)] The unlevered beta is found by using a version of Hamada's formula with the current capital structure (wd = 10%) and current levered beta (1.01) as shown in the blue range of cells: bU = b/ [1 + (1-T) (wd/ws)]. | ||||||||||||||||||
| 3. | The cost of equity is estimated using the CAPM formula with a risk-free rate of 6.67% and a market risk premium of 5.94%: rs = rRF + (RPM)b. | ||||||||||||||||||
| 4. | The cost of debt, rd, is obtained from investment bankers. | ||||||||||||||||||
| 5. | The after-tax cost of debt is rd (1−T), where T = 25%. | ||||||||||||||||||
| 6. | The weighted average cost of capital is calculated as: WACC = ws rs + wd rd (1-T) and is rounded to 4 decimal places. | ||||||||||||||||||
| 7. | The value of the firm's operations is calculated as: Vop = [FCF(1+gL)] / (WACC − gL), where FCF = $300 million and gL = 0. | ||||||||||||||||||
| 8. | Debt = wd x Vop | ||||||||||||||||||
| 9. | The intrinsic value of equity after the recapitalization and repurchase is SPost = Vop − Debt = ws x Vop | ||||||||||||||||||
| 10. | The number of shares after the recap has been completed is found using: nPost = nPrior [(VopNew - DNew) / (VopNew-DOld)]. The subscript "Old" indicates values from the original capital structure where wd = 10%, the subscript "New" indicates values at the current capital structure after the recap & repurchase, and the subscript "Post" indicates values after the recap & repurchase. | ||||||||||||||||||
| 11. | The price after the recap & repurchase is: PPost = SPost/nPost. But we can also find the price as: PPost = (VopNew − DOld)/nPrior. | ||||||||||||||||||
| 12. | The EBIT is $400 million; see Figure 15-4. Net income is: NI = (EBIT − rdD)(1 − T). | ||||||||||||||||||
| 13. | Earnings per share: EPS = NI/nPost. | ||||||||||||||||||
| Data for Figure 15-7 | |||||||||||||||||||
| wd | 0% | 10% | 20% | 30% | 40% | 50% | |||||||||||||
| After-Tax Cost of Debt | 5.85% | 6.00% | 6.15% | 6.53% | 7.58% | 9.15% | |||||||||||||
| Cost of Equity | 12.21% | 12.67% | 13.25% | 13.99% | 14.98% | 16.36% | |||||||||||||
| WACC | 12.21% | 12.00% | 11.83% | 11.75% | 12.02% | 12.76% | |||||||||||||
| Figure 15-7 | |||||||||||||||||||
| Effects of Capital Structure on Cost of Capital | |||||||||||||||||||
| Data for Figure below | |||||||||||||||||||
| wd | 0% | 10% | 20% | 30% | 40% | 50% | |||||||||||||
| Vop | $2,457.00 | $2,500.00 | $2,535.93 | $2,553.19 | $2,495.84 | $2,351.10 | |||||||||||||
| Debt | $0.00 | $250.00 | $507.19 | $765.96 | $998.34 | $1,175.55 | |||||||||||||
| Equity (S) | $2,457.00 | $2,250.00 | $2,028.74 | $1,787.23 | $1,497.50 | $1,175.55 | |||||||||||||
| V for chart | $2,458.00 | $2,501.00 | $2,536.93 | $2,554.19 | $2,496.84 | $2,352.10 | |||||||||||||
| $1.00 | $1.00 | $1.00 | $1.00 | $1.00 | $1.00 | ||||||||||||||
| Figure 15-8 | |||||||||||||||||||
| Effects of Capital Structure on the Value of Operations | |||||||||||||||||||
| 15-6 Anatomy of a Recapitalization | |||||||||||||||||||
| Strasburg will issue additional debt and use the proceeds to repurchase stock. This is a recapitalization, often called a "recap." When Strasburg announces its planned recapitalization, investors realize that the company will be worth more after the recap because it will have a lower cost of capital. Therefore, the stock price will increase when the plans are announced, even though the actual repurchase has not yet occurred. If the stock price did not increase until after the actual repurchase, it would be possible for an investor to buy the stock immediately prior to the repurchase, and then reap a reward the next day when the repurchase occurred. Current stockholders realize this, and refuse to sell the stock unless they are paid the price that is expected immediately after the repurchase occurs. | |||||||||||||||||||
| Figure 15-9 | |||||||||||||||||||
| Anatomy of a Recapitalization (Millions, Except Per Share Data) | |||||||||||||||||||
| Before Issuing Additional Debt | After Debt Issue, but Prior to Repurchase | Post Repurchase | |||||||||||||||||
| (1) | (2) | (3) | |||||||||||||||||
| Percent financed with debt: wd | 10% | 30% | 30% | ||||||||||||||||
| Value of operations | $2,500.00 | $2,553.19 | $2,553.19 | ||||||||||||||||
| + Value of ST investments | $0.00 | $515.96 | $0.00 | ||||||||||||||||
| Estimated total intrinsic value | $2,500.00 | $3,069.15 | $2,553.19 | ||||||||||||||||
| − Debt | $250.00 | $765.96 | $765.96 | ||||||||||||||||
| Estimated intrinsic value of equity | $2,250.00 | $2,303.19 | $1,787.23 | ||||||||||||||||
| ÷ Number of shares | $100.00 | $100.00 | $77.60 | ||||||||||||||||
| Estimated intrinsic price per share | $22.50 | $23.03 | $23.03 | ||||||||||||||||
| Value of stock | $2,250.00 | $2,303.19 | $1,787.23 | ||||||||||||||||
| + Cash distributed in repurchase | $0.00 | $0.00 | $515.96 | ||||||||||||||||
| Wealth of shareholders | $2,250.00 | $2,303.19 | $2,303.19 | ||||||||||||||||
| Numbers in the figure are shown as rounded values for clarity in reporting. However, unrounded values are used for all calculations. | |||||||||||||||||||
| Notes: | 1. The value of ST investments in Column 2 is equal to the amount of cash raised by issuing additional debt but that has not been used to repurchase shares: ST investments = DNew − DOld. | ||||||||||||||||||
| 2. The value of ST investments in Column 3 is zero because the funds have been used to repurchase shares of stock. | |||||||||||||||||||
| 3. The number of shares in Column 3 reflects the shares repurchased: nPost = nPrior − (CashRep/PPrior) = nPrior − ([DNew − DOld]/PPrior). | |||||||||||||||||||
| Figure 15-10 | |||||||||||||||||||
| Effect of Capital Structure on Intrinsic Stock Price and Earnings per Share | |||||||||||||||||||
| Shortcut Formulas Applied to Change in Capital Structure: wd Prior = 10%, wd Post = 30% | |||||||||||||||||||
| Inputs: | |||||||||||||||||||
| wd = | 30% | ||||||||||||||||||
| VopNew = | $2,553.19 | ||||||||||||||||||
| nPrior = | 100.00 | ||||||||||||||||||
| DNew = | $765.96 | ||||||||||||||||||
| DOld = | $250.00 | ||||||||||||||||||
| Shortcuts: | |||||||||||||||||||
| SPost = VopNew (1-wd) = | $1,787.23 | ||||||||||||||||||
| nPost = nPrior (VopNew - DNew) / (VopNew - DOld) = | 77.60 | ||||||||||||||||||
| PPost = (VopNew - DOld) / nPrior = | $23.03 | ||||||||||||||||||
| 15-8 Risky Debt and Equity as an Option | |||||||||||||||||||
| If we relax the MM assumption that debt is risk free, then we allow for management to make the decision of whether or not to default on the debt. This is like an option: If management decides NOT to default on the debt, i.e. if management decides to make a required interest or principal payment, then the stockholders get to keep the firm. If management defaults on the the interest or principal payment, then the stockholders lose the firm. | |||||||||||||||||||
| Kunkel's situation | |||||||||||||||||||
| Face value of zero coupon debt | $10,000,000 | ||||||||||||||||||
| Time to maturity (years) | 5 | ||||||||||||||||||
| When the debt comes due, Kunkel will repay the $10,000,000 only if the value of the firm exceeds $10,000,000 at the time the debt comes due. This is like exercising an option on the value of the firm with an exercise price equal to $10,000,000. Today, owning the equity in Kunkel is like owning a call option on the value of the firm that has five years to expiration and a strike price of $10 million. This can be valued using the Black-Scholes Option Pricing Model (BSOPM). See Chapter 8 for more details on the BSOPM. | |||||||||||||||||||
| Black-Scholes Option Pricing Model | |||||||||||||||||||
| Suppose the total value of the company at the time it issus the zero coupon debt is $20 million (this is the value of existing assets plus the proceeds raised when the debt is issued). | |||||||||||||||||||
| Total value of firm when debt is issued = | Value of operating assets + proceeds from issuing debt | ||||||||||||||||||
| = | Value of debt + value of equity | ||||||||||||||||||
| = | $20,000,000 | ||||||||||||||||||
| The inputs to the Black-Schole model are: | |||||||||||||||||||
| Total value of firm (P) | $20.00 | Analogous to the stock price from the BSOPM | |||||||||||||||||
| Face value of debt (X) | $10.00 | Analogous to the exercise price | |||||||||||||||||
| Risk free rate (rRF) | 6.0% | ||||||||||||||||||
| Maturity of debt in years (T) | 5.00 | Analogous to time to expiration of option | |||||||||||||||||
| Standard deviation of total value's return (σ) | 0.40 | This is the standard deviation of the total value of the firm's total value, not just the standard deviation of its stock. | |||||||||||||||||
| Applying the Black-Schole model: | |||||||||||||||||||
| d1 | 1.5576 | ||||||||||||||||||
| d2 | 0.6632 | ||||||||||||||||||
| N(d1) | 0.9403 | ||||||||||||||||||
| N(d2) | 0.7464 | ||||||||||||||||||
| Call Price = Equity Value = | $13.28 | ||||||||||||||||||
| How much did Kunkel receive for issuing face value $10 million in zero coupon debt? | |||||||||||||||||||
| If the total value of the firm is $20 million, and the equity is worth | $13.28 | million, | |||||||||||||||||
| then the value of the debt should be what is left over: | $6.72 | million. | |||||||||||||||||
| Therefore, the proceeds on the debt at the time it is issued are: | $6.72 | ||||||||||||||||||
| The yield on zero coupon debt is calculated like the rate on a single future value: | |||||||||||||||||||
| PV(1+I)N = FV | |||||||||||||||||||
| Soving for the rate, I: | |||||||||||||||||||
| I = | [(FV/PV)(1/N)]-1 | ||||||||||||||||||
| Therefore, the yield on the debt at the time it is issued is: | |||||||||||||||||||
| FV = Face value of debt | $10.00 | ||||||||||||||||||
| N = Number of years until maturity on date when issued = | $5.00 | ||||||||||||||||||
| PV = Present value of debt when issued = | $6.72 | ||||||||||||||||||
| Yield on Debt | 8.266% | ||||||||||||||||||
| If management can change the riskiness of its projects--i.e. change the volatility of the total company, then it can change the relative values of the debt, equity, and the yield on the debt. | |||||||||||||||||||
| Table 15-2 | |||||||||||||||||||
| The Value of Kunkel’s Debt and Equity for Various Levels of Volatility (Millions of Dollars) | |||||||||||||||||||
| Standard Deviation Of Total Value | Total Value | Equity Value | Debt Value | Yield on Debt | Percentage Change in Equity Value from Base Case | ||||||||||||||
| Base Case values to right | $20 | $13.28 | $6.72 | $0.08 | Note: this row has the links to outputs for the data table below the row, but the font is yellow so you can't see them. This is a good way to "hide" material you don't want to show in a presentation. | ||||||||||||||
| 20% | $20 | $12.62 | $7.38 | 6.25% | -4.98% | ||||||||||||||
| 40% | 20 | 13.28 | 6.72 | 8.27% | 0.00% | ||||||||||||||
| 60% | 20 | 14.51 | 5.49 | 12.74% | 9.27% | ||||||||||||||
| 80% | 20 | 15.81 | 4.19 | 18.99% | 19.06% | ||||||||||||||
| 100% | 20 | 16.96 | 3.04 | 26.92% | 27.77% | ||||||||||||||
| Debt and Equity Values for Various Levels of Volatility When the Total Value is $11 Million | |||||||||||||||||||
| Total Value of Firm | $11.00 | Analogous to the stock price from the BSOPM | |||||||||||||||||
| Face Value of Debt | $10.00 | Analogous to the exercise price | |||||||||||||||||
| Risk Free rate | 0.06 | ||||||||||||||||||
| Maturity of debt (years) | 5.00 | Analogous to time to expiration of option | |||||||||||||||||
| Standard Dev. | 0.40 | This is the standard dev. of the total value of the firm, not just the stock. | |||||||||||||||||
| d1 | 0.8892 | ||||||||||||||||||
| d2 | -0.0052 | ||||||||||||||||||
| N(d1) | 0.8130 | ||||||||||||||||||
| N(d2) | 0.4979 | ||||||||||||||||||
| Call Price = Equity Value | $5.25 | ||||||||||||||||||
| If the total value of the firm is $10 million, and the equity is worth | $5.25 | million, | |||||||||||||||||
| then the value of the debt should be what is left over: | $5.75 | million. | |||||||||||||||||
| FV = Face value of debt | $10.00 | ||||||||||||||||||
| N = Number of years until maturity on date when issued = | 5.00 | ||||||||||||||||||
| PV = Present value of debt when issued = | $5.75 | ||||||||||||||||||
| Yield on Debt | 11.723% | ||||||||||||||||||
| Not Reported in Textbook | |||||||||||||||||||
| The Value of Kunkel’s Debt and Equity for Various Levels of Volatility if Total Value is $11 (Millions of Dollars) | |||||||||||||||||||
| Standard Deviation Of Total Value | |||||||||||||||||||
| Total Value | Equity Value | Debt Value | Yield on Debt | ||||||||||||||||
| Base Case values to right | $11 | $5.25 | $5.75 | 11.72% | Percentage Change in Equity Value from Base Case | ||||||||||||||
| 20% | $11 | $4.00 | $7.00 | 7.40% | -24% | ||||||||||||||
| 40% | 11 | 5.25 | 5.75 | 11.72% | 0% | ||||||||||||||
| 60% | 11 | 6.54 | 4.46 | 17.54% | 25% | ||||||||||||||
| 80% | 11 | 7.69 | 3.31 | 24.75% | 46% | ||||||||||||||
| 100% | 11 | 8.64 | 2.36 | 33.50% | 64% | ||||||||||||||
| Expected Return Compared to Yield to Maturity on Debt | |||||||||||||||||||
| Not Reported in Textbook | |||||||||||||||||||
| Yield to Maturity and Expected Return on Debt for Various Levels of Volatility and Debt. Total Value is $20 (Millions of Dollars) | |||||||||||||||||||
| Total Value of Firm | $20.00 | Analogous to the stock price from the BSOPM | |||||||||||||||||
| Face Value of Debt | $10.00 | Analogous to the exercise price | |||||||||||||||||
| Risk Free rate | 0.06 | ||||||||||||||||||
| Maturity of debt (years) | 5.00 | Analogous to time to expiration of option | |||||||||||||||||
| Standard Dev. | 0.40 | This is the standard dev. of the total value of the firm, not just the stock. | |||||||||||||||||
| d1 | 1.5576 | ||||||||||||||||||
| d2 | 0.6632 | ||||||||||||||||||
| N(d1) | 0.9403 | ||||||||||||||||||
| N(d2) | 0.7464 | ||||||||||||||||||
| Call Price = Equity Value | $13.28 | ||||||||||||||||||
| If the total value of the firm is $10 million, and the equity is worth | $13.28 | ||||||||||||||||||
| then the value of the debt should be what is left over: | $6.72 | ||||||||||||||||||
| FV = Face value of debt = | $10.00 | ||||||||||||||||||
| N = Number of years until maturity on date when issued = | 5.00 | ||||||||||||||||||
| PV = Present value of debt when issued = | $6.72 | ||||||||||||||||||
| Yield to Maturity on Debt = | 8.266% | ||||||||||||||||||
| The yield to maturity above is not equal to the expected (or required) return on the debt. Rather, the YTM is the maximum return the bondholders will get, and they will only get that if the company doesn't default. If the company does default, the bondholders will get less. Thus the expected return is less than the YTM. Option pricing theory says that the expected return can be calculated from the inputs to the option pricing model, but using the unlevered expected return on the stock (that is, the expected return on the entire company, not just the equity) rather than the risk free rate to calculate the actual expected returns on the debt. | |||||||||||||||||||
| Options pricing theory shows that (expected payoff from zero coupon debt) = (face value of debt) x (probability the equity holders fully pay back the debt) + (expected payoff if the equity holders default on the debt). These amounts are functions of N(d1*) and N(d2*) where d1* and d2* are the same as d1 and d2 calculated with the regular Black Scholes Option Pricing Model, but with the risk free rate replaced by the unlevered expected return on the stock. | |||||||||||||||||||
| N(d2*) = probability of stockholders fully paying off the debt. (S0ert-S0ertN(d1*)) = expected payoff to bondholders if the stockholders default where S0 is the total value of the firm at time zero. So the overall expected payoff to bondholders is XN(d2*)+(S0ert-S0ertN(d1*)) where X is the face value of the debt and r is the unlevered expected rate of return on the total value of the company rather than the risk free rate. The expected rate of return is the return calculated from investing the value of debt from the option pricing model and receiving the expected payoff. | |||||||||||||||||||
| Expected unlevered return on stock = | 9% | ||||||||||||||||||
| d1* = | 1.7253 | This uses the expected unlevered return on the stock in the calculation rather than the risk free rate. | |||||||||||||||||
| d2* = | 0.8309 | This uses the expected unlevered return on the stock in the calculation rather than the risk free rate. | |||||||||||||||||
| N(d1*) = | 0.9578 | ||||||||||||||||||
| N(d2*) = | 0.7970 | = Probability of fully retiring the debt (probability of exercise) | |||||||||||||||||
| Face Value of Debt | X | Probability of retiring debt | + | Expected payoff if stockholders default | = | Expected payoff from bond | |||||||||||||
| N(d2*) | (S0ert-S0ertN(d1*)) | ||||||||||||||||||
| $10.00 | X | 0.7970 | + | $1.32483 | = | $9.2946 | |||||||||||||
| Price of bond = | $6.72 | ||||||||||||||||||
| Face value of bond = | $10.00 | YTM = | 8.266% | ||||||||||||||||
| Expected payoff = | $9.295 | Expected Return = | 6.693% | Note that Expected return will always be less than YTM. | |||||||||||||||
| Yield to maturity and expected return on debt for different levels of standard deviation of total value. | |||||||||||||||||||
| Standard Deviation of Total Value | Total Value | Equity Value | Debt Value | Debt YTM | Expected Return on Debt | ||||||||||||||
| Base Case values to right | $20.00 | $13.28 | $6.72 | 8.27% | 6.69% | ||||||||||||||
| 10% | $20.00 | $12.59 | $7.41 | 6.18% | 6.18% | ||||||||||||||
| 20% | $20.00 | $12.62 | $7.38 | 6.25% | 6.23% | ||||||||||||||
| 30% | $20.00 | $12.83 | $7.17 | 6.89% | 6.44% | ||||||||||||||
| 40% | $20.00 | $13.28 | $6.72 | 8.27% | 6.69% | ||||||||||||||
| 50% | $20.00 | $13.86 | $6.14 | 10.25% | 6.90% | ||||||||||||||
| 60% | $20.00 | $14.51 | $5.49 | 12.74% | 7.06% | ||||||||||||||
| 70% | $20.00 | $15.17 | $4.83 | 15.66% | 7.18% | ||||||||||||||
| 80% | $20.00 | $15.81 | $4.19 | 18.99% | 7.27% | ||||||||||||||
| 90% | $20.00 | $16.41 | $3.59 | 22.74% | 7.35% | ||||||||||||||
| 100% | $20.00 | $16.96 | $3.04 | 26.92% | 7.41% | ||||||||||||||
| Yield to maturity and expected return on debt for different face values of debt. | |||||||||||||||||||
| Face Value of Debt | Standard Deviation of Total Value | Total Value | Equity Value | Debt Value | Debt YTM | Expected Return on Debt | |||||||||||||
| Base Case values to right | 40% | $20.00 | $13.28 | $6.72 | 8.27% | 6.69% | |||||||||||||
| $2.00 | 40% | $20.00 | $18.52 | $1.48 | 6.22% | 6.20% | |||||||||||||
| $4.00 | 40% | $20.00 | $17.07 | $2.93 | 6.45% | 6.27% | |||||||||||||
| $6.00 | 40% | $20.00 | $15.70 | $4.30 | 6.91% | 6.40% | |||||||||||||
| $8.00 | 40% | $20.00 | $14.44 | $5.56 | 7.54% | 6.54% | |||||||||||||
| $10.00 | 40% | $20.00 | $13.28 | $6.72 | 8.27% | 6.69% | |||||||||||||
| $12.00 | 40% | $20.00 | $12.22 | $7.78 | 9.06% | 6.84% | |||||||||||||
| $14.00 | 40% | $20.00 | $11.27 | $8.73 | 9.90% | 6.98% | |||||||||||||
| $16.00 | 40% | $20.00 | $10.40 | $9.60 | 10.77% | 7.11% | |||||||||||||
| $18.00 | 40% | $20.00 | $9.62 | $10.38 | 11.64% | 7.24% | |||||||||||||
| $20.00 | 40% | $20.00 | $8.91 | $11.09 | 12.52% | 7.35% | |||||||||||||
| $25.00 | 40% | $20.00 | $7.41 | $12.59 | 14.71% | 7.61% | |||||||||||||
| $30.00 | 40% | $20.00 | $6.22 | $13.78 | 16.84% | 7.82% | |||||||||||||
| $35.00 | 40% | $20.00 | $5.27 | $14.73 | 18.90% | 8.01% | |||||||||||||
| $40.00 | 40% | $20.00 | $4.50 | $15.50 | 20.88% | 8.16% | |||||||||||||
| $45.00 | 40% | $20.00 | $3.87 | $16.13 | 22.78% | 8.29% | |||||||||||||
| $50.00 | 40% | $20.00 | $3.35 | $16.65 | 24.60% | 8.41% | |||||||||||||
| $55.00 | 40% | $20.00 | $2.92 | $17.08 | 26.35% | 8.51% | |||||||||||||
| $60.00 | 40% | $20.00 | $2.55 | $17.45 | 28.02% | 8.59% | |||||||||||||
| $65.00 | 40% | $20.00 | $2.25 | $17.75 | 29.63% | 8.67% | |||||||||||||
| Note that as the face value of debt increases, the expected return on the debt approaches the unlevered expected return on the stock. This is because as the face value of debt increases, the probability that the stockholders will default on the debt and turn the company over to the bondholders approaches 1 and the debt's payoffs approach those of simply owning the company without any debt at all. | |||||||||||||||||||
[SERIES NAME]
After-Tax
Cost of Debt
0 0.1 0.2 0.3 0.4 0.5 5.8499999999999996E-2 0.06 6.1499999999999999E-2 6.5250000000000002E-2 7.5750000000000012E-2 9.1499999999999998E-2 Cost of Equity[SERIES NAME]
0 0.1 0.2 0.3 0.4 0.5 0.12207907692307693 0.126694 0.13246265384615385 0.13987949450549453 0.14976861538461539 0.1636133846153846 WACC[SERIES NAME] 0 0.1 0.2 0.3 0.4 0.5 0.1221 0.12 0.1183 0.11749999999999999 0.1202 0.12759999999999999 Percent Financed with Debt Cost of Capital Debt 0 0.1 0.2 0.3 0.4 0.5 0 250 507.18512256973793 765.95744680851067 998.33610648918477 1175.5485893416928 Equity 0 0.1 0.2 0.3 0.4 0.5 2457.002457002457 2250 2028.7404902789517 1787.2340425531916 1497.5041597337772 1175.5485893416928 0 0.1 0.2 0.3 0.4 0.5 1 1 1 1 1 1 Percent Financed with Debt Price 0 0.1 0.2 0.3 0.4 0.5 22.070024570024568 22.5 22.859256128486894 23.031914893617024 22.458402662229616 21.010971786833856 EPS 0 0.1 0.2 0.3 0.4 0.5 2.69475 2.85 3.0288514370245139 3.2220003799392098 3.3650173322240704 3.4394960815047018 Percent Financed with Debt Stock Price EPS Panel A: Operating Leverage Plan A 0 20 40 60 64 76 80 100 120 140 -7.4999999999999997E-2 -3.7499999999999999E-2 0 3.7499999999999999E-2 4.4999999999999998E-2 6.7500000000000004E-2 7.4999999999999997E-2 0.1125 0.15 0.1875 Plan B Plan U 0 20 40 60 64 76 80 100 120 140 -0.22500000000000001 -0.15 -7.4999999999999997E-2 0 1.4999999999999999E-2 0.06 7.4999999999999997E-2 0.15 0.22500000000000001 0.3 0 20 40 60 64 76 80 100 120 140 0 0 0 0 0 0 0 0 0 0 Units Sold Millions ROE rRF 0 0.1 0.2 0.3 0.4 0.5 6.6699999999999995E-2 6.6699999999999995E-2 6.6699999999999995E-2 6.6699999999999995E-2 6.6699999999999995E-2 6.6699999999999995E-2 bU ´ RPM 0 0.1 0.2 0.3 0.4 0.5 5.5379076923076927E-2 5.5379076923076927E-2 5.5379076923076927E-2 5.5379076923076927E-2 5.5379076923076927E-2 5.5379076923076927E-2 (b − bU)´ RPM 0 0.1 0.2 0.3 0.4 0.5 0 4.6149230769230729E-3 1.0383576923076924E-2 1.7800417582417585E-2 2.7689538461538467E-2 4.153430769230769E-2 Percent Financed with Debt Required Return on Equity Panel B: Financial Leverage Plan B Plan U 0 20 40 60 64 76 80 100 120 140 -0.22500000000000001 -0.15 -7.4999999999999997E-2 0 1.4999999999999999E-2 0.06 7.4999999999999997E-2 0.15 0.22500000000000001 0.3 Plan L 0 20 40 60 64 76 80 100 120 140 -0.32 -0.22 -0.12 -0.02 0 0.06 0.08 0.18 0.28000000000000003 0.38 0 20 40 60 64 76 80 100 120 140 0 0 0 0 0 0 0 0 0 0 Units Sold (Millions) ROE Miller with Corporate and Personal Taxes VU VU 0 10 20 30 40 50 100 100 100 100 100 100 VL VL 0 10 20 30 40 50 100 100.29411764705883 100.58823529411765 100.88235294117646 101.17647058823529 101.47058823529412 Pre-TCJA VL Pre-TCJA VL 0 10 20 30 40 50 100 102.11940298507463 104.23880597014926 106.35820895522389 108.4776119402985 110.59701492537313 Debt Value of Firm M&M with Corporate Taxes VU 0 15 30 45 60 100 100 100 100 100 VL 0 15 30 45 60 100 103.75 107.5 111.25 115 Pre-TCJA VL 0 15 30 45 60 100 106 112 118 124 Leverage Value VU 0 6 12 18 24 30 36 42 48 54 100 100 100 100 100 100 100 100 100 100 M & M II 0 6 12 18 24 30 36 42 48 54 100 101.5 103 104.5 106 107.5 109 110.5 112 113.5 Actual Value 0 6 12 18 24 30 36 42 48 54 100 101.3 102.4 103.5 104.28399313781514 104.55532044893448 103.94690968343613 101.82886234153655 97.120268275127174 87.966278252648479 0 Leverage 0 6 12 18 24 30 36 42 48 54 60 60 60 60 60 60 60 60 60 60 Value
15-2
| SECTION 15-2 | ||
| SOLUTIONS TO SELF-TEST | ||
| A firm has fixed operating costs of $100,000 and variable costs of $4 per unit. If it sells the product for $6 per unit, what is the breakeven quantity? | ||
| F = | $100,000 | |
| V = | $4 | |
| P = | $6 | |
| QBE | 50,000 | |
15-6
| SECTION 15-6 | ||
| SOLUTIONS TO SELF-TEST | ||
| JAB Industry's capital structure 20% debt. Use the following data to calculate its cost of equity: bL = 1.4; rRF = 6% and RPM = 5%. | ||
| bL | 1.10 | |
| rRF | 6% | |
| RPM | 5% | |
| rs = | 11.50% | |
| Use the Hamada equation to calculate JAB's unlevered beta and unlevered cost of equity. The tax rate is 20%. | ||
| Tax rate | 25% | |
| wd | 20% | |
| ws | 80% | |
| bU | 0.9263 | |
| rs,U | 10.63% | |
| What would the cost of equity be if JAB changes its capital structure to 35% debt? | ||
| wd = | 35% | |
| ws = | 65% | |
| bL = | 1.30 | |
| rs,L | 12.50% | |
15-7
| SECTION 15-7 | ||
| SOLUTIONS TO SELF-TEST | ||
| A firm’s value of operations is equal to $800 million after a recapitalization (the firm had no debt before the recap). It raised $200 million in new debt and used this to buy back stock. The firm had no short-term investments before or after the recap. After the recap, wd = 25%. The firm had 10 million shares before the recap. Its federal-plus-state tax rate is 25%. What is S (the value of equity after the recap)? What is PPost (the stock price) after the recap? What is nPost (the number of remaining shares) after the recap? | ||
| Vop | $800 | |
| D | $200 | |
| wd | 25% | |
| nPrior | 10 | |
| S = | $600 | |
| PPost = | $80.00 | |
| nPost = | 7.5 | |
Web 15B
| WEB EXTENSION 15B | 11/21/18 | |||||
| BOND REFUNDING | ||||||
| This example examines the issue of replacing existing debt with newly issued debt. First, is it profitable to call an outstanding issue and replace it with a new issue? Second, even if refunding now is profitable, would the firm's expected value be further increased if the refunding were postponed until a later date? | ||||||
| The firm should refund only if the present value of the savings exceeds the cost of the refunding. The after-tax cost of debt should be used as the discount rate, since there is relative certainty to the cash flows to be received. Using the example laid out in the chapter, we will now evaluate such a scenario. | ||||||
| Figure 15B-1 | ||||||
| Spreadsheet for the Bond Refunding Decision | ||||||
| Panel A: Input Data | ||||||
| Existing bond issue = | $60,000,000 | Years since old debt issued = | 5 | |||
| Original flotation cost = | $3,000,000 | Current call premium (%) = | 10.0% | |||
| Maturity of original debt = | 25 | New bond issue = | $60,000,000 | |||
| Original coupon rate = | 12.0% | New flotation cost = | $2,650,000 | |||
| Call protection period = | 5 | New bond maturity = | 20 | |||
| Initial call premium (%) = | 10.0% | New cost of debt = | 9.0% | |||
| Tax rate = | 25.0% | ST interest rate = | 6.0% | |||
| Panel B: Investment Outlay | Before-tax | After-tax | ||||
| 1: | Call premium on the old bond | −$6,000,000 | −$4,500,000 | |||
| 2: | Flotation costs on new issue | −$2,650,000 | −$2,650,000 | |||
| 3: | Immediate tax savings on old flotation expense | $2,400,000 | $600,000 | |||
| 4: | Extra interest paid on old issue | −$600,000 | −$450,000 | |||
| 5: | Interest earned on short-term investment | $300,000 | $225,000 | |||
| 6: | Total after-tax initial outlay | −$6,775,000 | ||||
| Panel C: Present Value of Annual Flotation Cost Tax Effects: t = 1 to 20 | ||||||
| Before-tax | After-tax | |||||
| 7: | Annual tax savings from new-issue flotation | $132,500 | $33,125 | |||
| 8: | Annual lost tax savings from old-issue flotation | −$120,000 | −$30,000 | |||
| 9: | Net flotation cost tax savings | $12,500 | $3,125 | Since the annual flotation cost tax effects and interest savings occur for the next 20 years, they represent annuities. To evaluate this project, we must find the present values of these savings. | ||
| 10: | Maturity of the new bond (Nper) | 20 | ||||
| 11: | After-tax cost of new debt (Rate) | 6.75% | ||||
| 12: | PV of annual after-tax flotation cost savings | $33,759 | ||||
| Panel D: Present Value of Annual Interest Savings Due to Refunding: t = 1 to 20 | ||||||
| Before-tax | After-tax | |||||
| 13: | Interest on old bond | $7,200,000 | $5,400,000 | |||
| 14: | Interest on new bond | −$5,400,000 | −$4,050,000 | |||
| 15: | Net interest savings | $1,800,000 | $1,350,000 | Since the annual flotation cost tax effects and interest savings occur for the next 20 years, they represent annuities. To evaluate this project, we must find the present values of these savings. | ||
| 16: | Maturity of the new bond (Nper) | 20 | ||||
| 17: | After-tax cost of new debt (Rate) | 6.75% | ||||
| 18: | PV of annual after-tax interest savings | $14,584,079 | ||||
| Panel E: Total Net Present Value of the Refunding | After-tax | |||||
| 19: | Total after-tax initial outlay | −$6,775,000 | ||||
| 20: | PV of annual after-tax flotation cost savings | $33,759 | ||||
| 21: | PV of annual after-tax interest savings | $14,584,079 | ||||
| 22: | Total NPV of Bond Refunding | $7,842,838 | ||||
| Our refunding analysis tells us that should the firm proceed with the bond refunding, the project will have a positive net present value. However, unlike traditional capital budgeting decisions, the positive NPV does not tell the firm if it should refund the bond issue. That decision is dependent upon several external factors, including interest rate expectations. | ||||||
| Scenario Analysis | ||||||
| Rates fall | Rates stay the same | Rates go up | ||||
| Probability | 25% | 50% | 25% | |||
| Rate | 7% | 9% | 11% | |||
| NPV of refunding | $20,049,044 | $7,842,838 | ($2,214,092) | |||
| Expected NPV | $8,933,680 | |||||
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