Corporate Finance 2 - Week 3: Capital Budgeting

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Corporate Finance 2 - Week 3

• Capital Budgeting with Leverage is the topic for this week
• Readings for this week are in Chapter 18

Important Information

• Lecture Notes and all illustrations provided throughout the semester must be reviewed
• Tutorial Questions/Solutions must be reviewed
• Online-quiz Questions/Solutions must be reviewed
• Relevant Chapters in the textbook and any additional assigned readings must be reviewed
• All of the above materials are examinable

Introduction

• MM Proposition I: In a perfect capital market, the total value of a firm's securities is equal to the market value of the total cash flows generated by its assets and is not affected by its choice of capital structure
• MM Proposition II: The cost of capital of levered equity increases with the firm's market value debt-equity ratio
• Cost of Capital of Levered Equity can be calulcated as: rE = rU + (D/E)*(rU - rD)

Introduction

• Firms usually choose their optimal capital structure based on market imperfections like taxes, financial distress costs, agency costs (benefits), and asymmetric information

Capital Budgeting Decisions

• A levered firm should incorporate the costs and benefits associated with leverage into its Capital Budgeting Decisions

Three Main Methods

• Weighted Average Cost of Capital (WACC)
• Adjusted Present Value (APV)
• Flow-to-Equity (FTE)

Weighted Average Cost of Capital Method

• Free cash flow measures the after-tax cash flow of a project before considering how it is financed
• The WACC method uses the after-tax cost of capital as the discount rate
• The WACC method takes the interest tax shield into account
• When the market risk of the project is similar to the average market risk of the firm's investment, then its cost of capital equals the firm's WACC
• Under WACC method, a firm maintains a constant debt-equity ratio
• Under WACC method, the WACC remains constant over time

Calculate Free Cash Flow

• Start with Revenue, subtract Cost of Goods Sold to to achieve Gross Profit
• Subtract Selling, General and Admin Expenses and Depreciation from Gross Profit to achieve EBIT.
• Subtract Income tax from EBIT to get Incremental Earnings
• Add back Depreciation to Incremental Earnings
• Subract Capital Expenditure and change in Net Working Capital
• The result is Free Cash Flow

The Weighted Average Cost of Capital Method (cont'd)

• Calculate the Weighted Average Cost of Capital rWACC = (E/(E+D))*rE + (D/(E+D))rD(1-t)
• Because the WACC incorporates the tax savings from debt, the levered value of an investment can be computed by discounting its future free cash flow using the WACC
• Calculating Levered Value can be done by the following equation: V0L = FCF1/(1+rWACC) + FCF2/(1+rWACC)^2 + FCF3/(1+rWACC)^3

Using the WACC to Value a Project

• Avco is considering introducing a new line of packaging, the RFX Series
• The technology used in these products is expected to become obsolete after four years
• The marketing group expects annual sales of $60 million per year over the next four years for this product line
• Manufacturing costs are expected to be $25 million per year
• Operating expenses are expected to be $9 million per year

Using the WACC to Value a Project (cont'd)

• Developing the product will require upfront R&D and marketing expenses of $6.67 million, along with a $24 million equipment investment
• The equipment will be obsolete in four years and depreciated via the straight-line method
• Avco expects no net working capital requirements for the project
• Avco pays a corporate tax rate of 25%

Expected Free Cash Flow from Avco's RFX Project

• Sales are 60 million for years 1-4
• Cost of Goods sold is 25 million for years 1-4
• Gross profit is 35 million for year 1-4
• Operating expenses is 6.67 million for year 0 and 9 million for years 1-4
• Depreciation is 6 million for years 1-4
• EBIT is -6.67 in year 0 and 20 million for years 1-4
• Income Tax at 25% is 1.67 million in year 0 and and 5 million for years 1-4
• Unlevered Net Income is -5 million in year 0 and 15 million for years 1-4
• Depreciation is 6 million dollars for years 1-4
• Capital Expenditure is 24 million dollars in year 0
• Free Cash Flow is -29 million in year 0 and 21 million for years 1-4

Avco's Current Market Value Balance Sheet ($ million) and Cost of Capital Without the RFX Project

• Cash is 20, and existing assets is 600, for total assets of 620
• Debt is 320 and Equity is 300 for total Liabilities and Equity of 620
• Cost of Debt is 6% and Cost of Equity is 10%
• Net debt is $320m-$20m = $300m

Using the WACC to Value a Project (cont'd)

• Avco intends to maintain a similar (net) debt-equity ratio for the foreseeable future, including any financing related to the RFX project, therefore Avco's WACC can be calculated as: rWACC = (E/(E+D))rE + (D/(E+D)rD(1-t) = (300/600)(10%) + (300/600)(6%)(1-.25) = 7.25%
• Note that net debt = D = $320-20 = $300 million

Using the WACC to Value a Project (cont'd)

• The value of the project, including the tax shield from debt, is calculated as the present value of its future free cash flows.
• Discount values for years 1 to 4 are calculated as 21/1.0725, 21/(1.0725^2), 21/(1.0725^3), 21/(1.0725^4)
• The project has an asset worth of $70.73 million
• The NPV of the project is $41.73 million (NPV = $70.73 million – $29 million = $41.73 million)

Summary of WACC Method

• Determine the free cash flow of the investment
• Compute the weighted average cost of capital
• Compute the value of the investment, including the tax benefit of leverage, by discounting the free cash flow of the investment using the WACC
• The WACC can be used throughout the firm as the companywide cost of capital for new investments that are of comparable risk to the rest of the firm and that will not alter the firm's debt-equity ratio

Implementing a Constant Debt-Equity Ratio

• Avco adds new assets with initial market value $70.73 million by undertaking the RFX project
• To maintain its debt-to-value ratio, Avco must add $35.365 million in new debt
• .50 * 70.73 million calculation
• Avco can add this debt either by reducing cash or by borrowing and increasing debt

Implementing a Constant Debt-Equity Ratio (cont'd) with NPV of New Project

• Avco decides to spend its $20 million in cash and borrow (and immediately spend) an additional $15.365 million
• So, the company has ($20m + $15.365m) = $35.365million cash with it
• Only $29 million is required to fund the project, therefore Avco will pay the remaining $6.365 million to shareholders through a dividend (or share repurchase)
• $35.365 million – $29 million = $6.365 million

Avco's Current Market Value Balance Sheet ($ million) with the RFX Project - Before Capital Structure change

• Asset side, cash 20, existing assets for 600, total 620
• Liability side, debt 320, equity 300, total 620
• Debt is 6% cost
• Equity is 10% cost

Avco's Current Market Value Balance Sheet ($ million) with the RFX Project - After Capital Structure change

• Asset side, existing assets for 600, RFX project for 70.73 total 670.73, zero cash, and a total of 670.73
• Liability side, debt 335.365, equity 335.365 and total liabilities and Equity are also 670.73

Implementing a Constant Debt-Equity Ratio (cont'd)

• The market value of Avco's equity increases by $35.365 million (335.365 – $300 = $35.365 million)
• Adding the dividend of $6.365 million, the shareholders' total gain is $41.73 million including both the increase in equity and the dividend, which matches the NPV calculated for the RFX project

Implementing a Constant Debt-Equity Ratio (cont'd) Debt Capacity

• Debt Capacity is the amount of debt at a particular date that is required to maintain the firm's target debt-to-value ratio
• The debt capacity at date t can be calculated as: Dt = d * VLt where d is the firm's target debt-to-value ratio and VLt is the levered continuation value on date t

Implementing a Constant Debt-Equity Ratio (cont'd) Debt Capacity VL

• Value of FCF in year t +2 and beyond V¹t = FCF+1 / 1 + rWACC + VL/ 1 + rWACC

Value and Debt Capacity of the RFX Project over Time

• Free Cash Flow at Year 0 is (29.00), and other years are 21.00, 21.00, 21.00 and 21.00.
• Levered Value, VL at Value, VL (at rwacc = 7.25%) at Year 0 is 70.73, Year 1 is 54.86 Year 2 is 37.84, and Year 3 is 19.58.
• Debt Capacity, D₁ (at d = 50%) at Year 0 is 35.37, Year 1 is 27.43, Year 2 is 18.92, Year 3 is 9.79.

Example

• A company has a market value of equity of $600 million and a market value of debt of $400 million
• The company intends to maintain its debt ratio for the foreseeable future
• It is considering a project with a present value of cash flows of $40 million and an initial investment of $30 million
• Need to show the market value balance sheet for the company soon after investing in this project
• Need to reconcile the value of equity in new balance sheet with that of the old balance sheet

Solution

• The company has $600 million equity and $400 million debt with a market value of assets of $1,000 million
• The company's debt ratio is [400/1,000] = 40%
• The project has a present value (levered value) of $40 million. So, the company's market value of assets will increase by this amount
• To maintain the above debt ratio, the company should add (40 x 0.40) = $16 million debt
• This will increase the amount of debt to $416 million

Solution - New market value balance sheet

• Assets are divided into two sections, existing assets and PV of New Project.
• Total Assets = 1000 of existing assets PLUS 40 worth of PV of Project, therefore 1040.
• Liabilities and Equity: debt is 416, Equity is 624, total 1040
• In the start, value or equity before project = $600
• During the project, new equity capital raised = $30 invested less 16 added dept = 14
• Project will increase value of equity. NPV = $40 projected future profits and only 30 of new required assets means NPV = $10 increase to equity
• After all transactions, value of equity with project = Old value of Equity 600 + capital raised during process + new value created by project = $624

Adjusted Present Value

• A valuation method that is aimed at determining the levered value of an investment by first calculating its unlevered value and then adding the value of the interest tax shield
• VL = APV = VU + PV(Interest Tax Shield)

The Unlevered Value of the Project

• The first step is to calculate the value of the free cash flows using the project's cost of capital as if it were financed without leverage
• Discounting the cash flows at a rate that only reflects the firm's business risk is required.
• Its cost of equity cannot be an appropriate rate, because it only captures the cash flows available to equity holders

The Unlevered Value of the Project (cont'd)

• To capture the total cash flows available to the firm, need to consider the cash flows available to the debtholders, using the cost of debt
• the discount rate should be the weighted average cost of capital, except that dont take into account the taxes. rU = E/(E+D)rE + D/(E+D)rD
• rU now captures cash flows at the firm level.

The Unlevered Value of the Project (cont'd)

• For Avco the unlevered cost of capital is calculated as: rU = .50 * 10% + .50 * 6% = 8.0%
• The project has a value without leverage, and can be calculated as: VU = 21/1.08 + 21/1.08^2 + 21/1.08^3 + 21/1.08^4 = $69.55 million

Target Leverage Ratio

• When a firm adjusts its debt proportionally to a project's value or its cash flows (where the proportion needs not remain constant) represents target leverage ratio of firm.
• A constant market debt-equity ratio is a special case.

Valuing the Interest Tax Shield

• The value of $69.55 million is the value of the unlevered project and does not include the value of the tax shield provided by the interest payments on debt
• Interest paid in year t = rD xt - 1
• The interest tax shield is equal to the interest paid multiplied by the corporate tax rate

Expected Debt Capacity, Interest Payments, and Tax Shield for Avco's RFX Project

• Debt Capacity, D₁ (at d = 50%)at Year 0 is 35.37, at Year 1 is 27.43, Year 2 is 18.92, and Year 3 is 9.79.
• Interest Paid (at rp = 6%)at Year 1 is 2.12, Year 2 is 1.65, Year 3 is 1.14, and Year 4 is 0.59.
• Interest Tax Shield (at т = 25%)at Year 1 is 0.53, Year 2 is 0.41, Year 3 is 0.28 and Year 4 is 0.15
• The interest paid in year 1 can be calculated as 35.37 * 0.06 = 2.12

Valuing the Interest Tax Shield cont'd

• The next step is to find the present value of the intrest tax shield
• When the firm maintains a target leverage ratio, its future interest tax shields have similar risk to the project's cash flows, so they can be discounted at unlevered cost of capital PV (interest tax shield) = .53/1.08 + .41/1.08^2 + .28/1.08^3 + .15 /1.08^4 = $1.18 million

Valuing the Interest Tax Shield cont'd

• The total value of the project with leverage is the sum of the value of the interest tax shield and the value of the unlevered project
• VL = VU + PV(interest tax shield) = 69.55 + 1.18 = $70.73 million
• this is also the NPV of the project and is $41.73
• can be calculated as $70.73 million - $29 million = $41.73 million

Expected Debt Capacity, Intrest Payments and Tax Shield for Avco's RFX project

• The first line is Debt Capacity D_t at d= 50%, the numbers are 35.37, 27.43, 18.92, and 9.79
• The second line is Interest Paid and numbers are 2.12, 1.65, 1.14, and 0.59

Pre Determined Debt Levels

• Rather than set debt to meet target debt-equity ratio, the firm may change debt and equity on a fixed schedule in advanced and can be known

Pre Determined Debt Levels cont'd

• When debt lavels are set to meet fixed schedule, interest tax shields discount through the debt cost of the capital
• Project Value is calculated by adding Free Cash Flows and PV Investment tax shield

Summary of the APV Method

• Determine the investment's value without leverage
• Determine the present value of the interest tax shield, which consists of determining the expected interest tax shield, and discounting the interest tax shield.
• Add the unlevered value to the present value of the interest tax shield to determine the value of the investment with leverage

Summary of the APV Method (cont'd)

• The APV method may be easier to apply than the WACC method when the firm does not maintain a constant debt-equity ratio
• The APV approach also explicitly values market imperfections; therefore, it allows managers to measure their contribution to value

The Flow-to-Equity Method

• A valuation method that calculates the free cash flow available to equity holders considering debt to equity holders
• The cash flow to equity holders are then discounted using the equity cost of capital

Calculating the Free Cash Flow to Equity

• The free cash flow that remains after adjusting for interest payments, debt issuance, and debt repayments is used for free cash flow to equity.
• The first step in the FTE method is to determine the project's free cash flow to equity

Spreadsheet Expected Free Cash Flows to Equity from Avco's RFX Project

• Sales $60 million for years 1 through 4
• Cost of Goods Sold: $25 million for years 1 through 4
• Gross Profit: $35 million for years 1 through 4
• The rest of numbers are documented on the spreadsheet

Calculating the Free Cash Flow to Equity (cont'd)

• The calculation of FCF has two notes that need to make attention:
• Interest expenses are subtracted before taxes
• Borrowing and the proceeds are included from all activities and can be expressed as: net borrowing at date t=Dt – Dt-1.

Expected Debt Capacity and the Interest and Tex Shield

• The same chart shown above here

Calculating the Free Cash Flow to Equity (cont'd)

FCFE=FCF - (1 - Tc) X ( interest payments) + net borrowing

Computing FCFE from FCF for Avco's RFX Project

• From the spreadsheet, the after tax intrest expenses in year 1 can be presented as $53.7 *6% * (1 - .25) = $ 1.59 where the chart has been documented above.

Valuing Equity Cash Flow

• Since FCFE represents payment to equity holders, it is considered for discounting through equity cost of capital

Valuing Equity Cash Flows (cont'd)

• The value of the project's FCFE represents the gain to shareholders from the project and it is identical to the NPV computed using the WACC and APV methods

Summary of the Flow-to-Equity Method

• Determine the free cash flow to equity of the investment
• Determine the equity cost of capital
• Compute the equity value by discounting the free cash flow to equity using the equity cost of capital

Summary of the Flow-to-Equity Method (cont'd)

• The FTE method offers some advantages like when the firm capital structure is complex or not know.
• The FTE method has a disadvantage: compute the project's debt capacity to determine the interest before decision can be made.

A Comparison of Methods

• WACC method is the optimal when the firm will maintain a fixed debt to value ratio over the investment
• APV method is the optimal when alternative leverage policies is usually the simplest approach
• FTE method are used only in complicated settings or hard to determine the values.