Week 10 - Financing and Valuation

Introduction

• In capital budgeting, financing decisions are often simplified by assuming all-equity financing.

• In a Modigliani-Miller (MM) world, financing decisions are irrelevant, and real investment decisions can be analyzed as if they are all-equity financed.

• Under MM assumptions, spending decisions are separate from financing decisions.

• Reconsider capital budgeting when investment and financing decisions interact.

• A major adjustment is for value changes contributed by financing changes, like the debt tax shield.

Discount Rate vs. Cash Flow

• Two main ways to include value changes from financing decisions:

Adjust the Discount Rate

• Most common approach for handling interactions between investment & financing decisions.

• The adjusted discount rate r^* is usually calculated as the after-tax Weighted Average Cost of Capital (WACC).

Adjust the Cash Flow: Adjusted Present Value (APV)

• Value the project assuming all-equity financing (discount at the opportunity cost of capital r) and then add the present value of the tax shield.

• APV = Base case NPV + NPV of Financing Decisions

• Base-case NPV is net project value calculated in a pure MM world where financing is irrelevant. [value project as an all-equity mini-firm]

• Adjust the base-case NPV to account for the project’s impact on the firm’s capital structure.

After Tax WACC

• One reason that financing and investment decisions interact is taxes. Interest is a tax-deductible expense.

• If excluded from the cash flow, the tax benefit from interest expense deductibility must be included in the cost of capital.

• This tax benefit reduces the effective cost of debt by a factor of the marginal tax rate.

• Under a classical tax system, a simple adjustment to the cost of debt is all that is required.

• After-tax cost of debt = (1-Tc)r{debt}

• After-tax WACC: WACC = (1 - Tc)rD \frac{D}{V} + \frac{E}{V} \times r_E

After Tax WACC: Tax Adjusted Formula

• T_c = marginal corporate income tax rate

• rD = before-tax cost of debt capital; (1-Tc)r_D = after-tax cost of debt capital

• r_E = cost of equity capital

• D = market value of debt; E = market value of equity

• V = E + D = market value of firm

• The after-tax weighted-average cost of capital can be used as an adjusted discount rate

• WACC = (1 - Tc)rD \frac{D}{V} + \frac{E}{V} \times r_E

Properties and Limitations of After-Tax WACC

• After-tax WACC (r^*) is less than the opportunity cost of capital r, because ‘cost of debt’ is calculated as after-tax as rD(1-Tc)

• Tax advantages of debt financing are reflected in a lower discount rate.

• WACC gives the correct discount rate only for projects that are just like the firm undertaking them.

• WACC ‘works’ for the ‘average’ project.

• It is incorrect for projects that are safer or riskier than the average of the firm’s existing assets.

• It is incorrect for projects whose acceptance would lead to an increase or decrease in the firm’s debt ratio.

Example 18.1: Calculating Sangria’s WACC

• Sangria is a U.S.-based company whose products aim to promote happy, low-stress lifestyles.

• Use market values to calculate WACC.

Example 18.1 Calculating Sangria’s WACC 1

• The firm’s cost of debt is 6% and the cost of equity is 12.5%.

• The market-value balance sheet shows assets worth $1,250 million.

• WACC is the expected rate of return on a portfolio of the firm’s outstanding debt and equity. The portfolio weights depend on market values.

• Sangria’s true debt ratio is not 50% (the book ratio) but 40% because its assets are worth $1,250 million.

• The cost of equity, r_E = 0.125, is the expected rate of return from the purchase of stock at $7.50 per share, the current market price.

Example 18.1 Calculating Sangria’s WACC

• Sangria is consistently profitable and pays taxes at the marginal rate of 21%.

• The inputs for WACC are summarized below.

• True debt and equity ratios are determined by reference to market (not book) values.

• Sangria’s after-tax WACC is: \text{WACC} = (1 - Tc)rD \frac{D}{V} + r_E \frac{E}{V} = 0.06 \times (1 - 0.21) \times 0.4 + 0.125 \times 0.6 = 0.094, or 9.4%

Example 18.2: Using Sangria’s WACC to Value a Project

• Pretax cash flow: $1.487 million

• Tax at 21%: $0.312 million

• After-tax cash flow C = $1.175 million

• This after-tax cash flow does not account for interest tax shields on debt supported by the perpetual crusher project. The value of interest tax shields is picked up not as higher after-tax cash flows but in a lower discount rate, i.e., by Sangria’s after-tax WACC, in which the cost of debt is entered after tax.

• Sangria proposing to invest $12.5 million in a perpetual crushing machine that generates a perpetual pretax cash flow of $1.487 million per year. The project is average risk, so we can use WACC. The after-tax cash flow is:

Example 18.2: Using Sangria’s WACC to Value a Project

• NPV = 0 is a barely acceptable investment.

• The annual cash flow of $1.175 million p.a. implies a 9.4% pa. rate of return on investment (1.175/12.5 = 0.094), exactly equal to Sangria’s WACC.

• If project NPV = 0, the return to equity investors must be exactly equal to the cost of equity of 12.5%. Let’s confirm that Sangria shareholders can actually look forward to a 12.5% return on their investment in the perpetual crusher project.

• The crusher generates a perpetual after-tax cash flow of C = $1.175 million, so NPV is:

• NPV = \frac{C0 + C1}{r} = -12.5 + \frac{1.175}{0.094} = 0

Example 18.2: Using Sangria’s WACC to Value a Project

• Let’s confirm that Sangria shareholders can actually look forward to a 12.5% return on their investment in the perpetual crusher project.

• Suppose Sangria sets up this project as a mini-firm.

Example 18.2: Using Sangria’s WACC to Value a Project

• Calculate the expected dollar return to shareholders:

• The project’s earnings are level and perpetual, so the expected rate of return on equity is equal to the expected equity income divided by the equity value.

• The expected return on equity equals the cost of equity, so it makes sense that the project’s NPV is zero.

• \text{After tax interest} = (1 - Tc)rD D = (1 - 0.21) \times 0.06 \times 5 = 0.237

• \text{Expected equity income} = C - (1 - Tc)rD D = 1.175 - 0.237 = 0.938

• \text{Expected equity return} = \frac{\text{expected equity income}}{\text{equity value}} = \frac{0.938}{7.5} = 0.125 \text{ or } 12.5\% = r_E

Review of Assumptions

• Appropriate to discount the perpetual crusher’s cash flows at Sangria’s WACC only if:

  • The project’s business risks are the same as those of Sangria’s other assets and remain so for the life of the project.

  • Throughout its life, the project supports the same fraction of debt to value as in Sangria’s overall capital structure.

  • WACC formula works not only for projects with perpetual cash flows but for any cash-flow pattern as long as the firm adjusts its borrowing to maintain a constant debt ratio over time.

Valuing Businesses

• Demonstrate how WACC can be used for valuation of a company financed by a mixture of debt and equity.

• Important valuation exercises:

  • Valuation of takeover target company

  • Valuation of one of the company’s divisions being contemplated for sale

  • Valuation of firm going public in order to set the issue price for an IPO

  • Estimation of the fair value of mutual fund’s shares in a company that is not traded.

• In such valuations, treat the company as if it were one big project.

• Forecast the company’s free cash flows (the hardest part of the exercise) and discount back to present value using after-tax WACC.

Important Points to Remember

1. Treat the company as fully equity-financed – i.e., exclude interest payments. The value of interest tax shields is not ignored, as the after-tax cost of debt is used in the after-tax WACC used to discount cash flows.

2. Companies are long-lived => FMs need to forecast cash flows for the medium-term horizon & add carefully estimated terminal value to capture firm value beyond that horizon. Terminal value estimation requires careful attention as it often accounts for the majority of the company’s value.

3. 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 - then don’t forget to subtract the value of the company’s outstanding debt.

Valuing Businesses

• The value of a business or project is usually computed as the discounted value of Free Cash Flows (FCF) out to a valuation horizon (H).

• The horizon value is sometimes called the terminal value.

• The cash flows and horizon value are then discounted back to the present.

Example: Valuing Rio Corporation

• Sangria is considering acquiring Rio Corporation, a privately held US company (=> no stock market price to rely on).

• Rio is in the same line of business as Sangria => same business risk as Sangria.

• Rio, like Sangria, has debt capacity equal to 40% of firm value => we can use Sangria’s WACC.

• First task is to forecast Rio’s free cash flow (FCF) - the amount of cash that the firm can pay out to investors after making all investments necessary for growth.

• Free cash flow is calculated assuming the firm is all-equity-financed.

Example: Valuing Rio Corporation

• Discounting FCFs at the after-tax WACC gives the total value of Rio (debt plus equity).

• To find the value of Rio’s equity, you need to subtract the 40% of the firm that can be financed with debt.

• Two equivalent ways of calculating FCF:

  1. FCF = profit after tax + depreciation − investment in fixed assets − investment in working capital

  2. FCF = EBITDA – tax – investment in fixed assets and working capital

• EBIDTA \equiv \text{earnings before interest, taxes, depreciation, and amortization}

Example: Valuing Rio Corporation

• For example, FCF in year 1 is:

• Need to forecast cash flows for each of the first 6 years.

• Then we need to find the value for cash flows from year 7 onward (i.e., estimate horizon value).

• \text{Free Cash Flow} = \text{profit after tax} + \text{depreciation} - \text{investment in fixed assets} - \text{investment in working capital}

• \text{Year 1: } $9.9 + 5.0 - $11.6 - $11.1 = $5.3 \text{ million}

• \text{Free Cash Flow} = EBITDA - \text{tax} - \text{fixed assets} - \text{investment}

• 23.3 - 2.8 - $11.6 - $11.1 = $5.3 \text{ million}

Valuing Rio Corporation

Value of equity is $42.53 per share considering 1.5 million shares outstanding.
Sangria can bear to pay up to approximately $42 per share for Rio.

Valuation by Comparables

• Use ratios such as total company value (= D+E), often referred to as enterprise value, to EBIT or, more likely, EBITDA.

• For example, if companies similar to Rio are trading at a ratio of enterprise value to EBITDA of 4.8, then Sangria’s manager could estimate Rio’s horizon value at 4.8 × 27.9 = $133.9 million in year 6 and $78.1 million discounted to year 0. This would suggest that Rio is currently worth $29.0 + 78.1 = $107.1 million, a trifle higher than our initial DCF estimate.

• This is a hybrid valuation, with early free cash flow valued by DCF and horizon value by estimated via comparables.

• Possible to entirely bypass DCF. Rio could be valued by multiplying the enterprise value to EBITDA ratio by Rio’s EBITDA in year 1, which is $23.3 million . This gives a value of 4.8 × 23.3 = $111.8 million, a bit higher still than the DCF and hybrid approaches.

Liquidation Value

• Financial managers should also check whether a business is worth more dead than alive.

• Sometimes a company’s liquidation value exceeds its value as a going concern.

• Sometimes financial analysts can ferret out idle or underexploited assets that would be worth much more if sold to someone else.

• Such assets would be valued at their likely sale price, and the rest of the business valued without them.

WACC vs. the Flow-to-Equity Method

WACC Method

• Value firm by forecasting cash flows assuming all-equity financing and then use after-tax WACC to discount these cash flows. Equity value determined by subtracting the value of debt from the total value of the firm.

Flow-to-Equity Method

• Alternative to discounting the total cash flows at the firm’s WACC. Discount cash flows to equity after interest and after taxes at the cost of equity capital. If the company’s debt ratio is constant over time, the flow-to-equity method should give the same answer as discounting total cash flows at the WACC and then subtracting the value of the debt.

WACC vs. the Flow-to-Equity Method (Flow-to-Equity Method cont.)

• Each year’s interest payment depends on the amount of debt at the start of the year, and this depends in turn on Rio’s value at the start of the year (remember Rio’s debt is assumed to be a constant proportion of value).

•  ‘catch-22’ situation in which you first need to know Rio’s value each year before you can go on to calculate and discount the cash flows to equity.

• A simple formula allows you to solve simultaneously for the company’s value and the cash flow in each year.

Some Tricks of the Trade

• Sangria had just one asset and two sources of financing. A real company’s market-value balance sheet has many more entries, for example:

  • Current assets, including cash, inventory, and accounts receivable

  • Current liabilities, including accounts payable and short-term debt

  • Property, plant, and equipment

  • Long-term debt (D)

  • Preferred stock (P)

  • Growth opportunities

  • Equity (E)

  • Total assets

  • Total liabilities plus equity

Some Tricks of the Trade

• Several questions immediately arise:

  • How does the formula change when there are more than two sources of financing?

  • What about short-term debt?

  • What about other current liabilities?

  • How are the costs of financing calculated?

  • Should I use a company or industry WACC?

  • What tax rate should I use?

  • What if the company can’t use all its interest tax shields?

Some Tricks of the Trade: Multiple Financing Sources

• How does the formula change when there are more than two sources of financing?

• Weight each cost of financing by its relative proportion to the market value of the firm.

• For example, if the capital structure includes both preferred and common shares, where r_P is investors’ expected rate of return on the preferred stock, P is the amount of preferred stock outstanding, and V = D + P + E.

• WACC = (1 - Tc) \times rD \times (\frac{D}{V}) + rP \times (\frac{P}{V}) + rE \times (\frac{E}{V})

Short-Term Debt Considerations

• What about short-term debt?

• Many companies consider only long-term financing when calculating WACC; the cost of short-term debt is left out. In principle, this is incorrect. Ignoring the claim of lenders who hold short-term debt will misstate the required return on capital investments.

• “Zeroing out” short-term debt is not a serious error if the debt is only temporary, seasonal, or incidental financing, or if it is offset by holdings of cash and marketable securities.

Current Liabilities

• What about other current liabilities?

• Current liabilities are usually “netted out” by subtracting them from current assets. The difference is entered as net working capital on the left-hand side of the balance sheet. The sum of long-term financing on the right is called total capitalization.

• As current liabilities include short-term debt, netting them out against current assets excludes the cost of short-term debt from WACC. (This can be an acceptable approximation as discussed in the previous slide).

Other Current Liabilities (cont.)

• If short-term debt is an important, permanent source of financing, it should be shown explicitly on the RHS of the balance sheet, not netted out against current assets. The interest cost of short-term debt is then one element of the WACC.

• Financial practitioners use rules of thumb for deciding whether short-term debt is worth including in WACC. One rule checks whether short-term debt is at least 10% of total liabilities and net working capital is negative. If so, then short-term debt is almost surely being used to finance long-term assets and is explicitly included in WACC.

Determining Financing Costs

• How are costs of financing determined?

• Return on equity, r_E, can be derived from market data (e.g., using the CAPM).

• The borrowing rate r_D and the debt and equity ratios, D/V & E/V, can be directly observed or estimated without too much trouble.

• Most corporate debt is not actively traded => market value cannot be observed directly. Nontraded debt can usually be valued by looking to other debt securities that are traded and that have approximately the same default risk and maturity.

• For healthy firms, the market value of debt is usually not too far from the book value, so many managers and analysts use the book value for D in the WACC formula. However, be sure to use market, not book, values for E.

Company-Wide vs. Industry WACC

• Should a diversified company use a single, companywide WACC?

• Depends on whether the divisions of the diversified company differ significantly in business risk. If different, the higher-risk divisions should be assigned higher WACCs, and the lower-risk divisions should be assigned lower WACCs.

• Ideally want to know company’s WACC; yet industry WACCs are sometimes more useful.

• Example: A company is viewed as a portfolio of two dissimilar business lines, say railroads and investment management. The company’s overall WACC would not be right for either business line. Instead, the company should use a railroad industry WACC for its railroad operations and an investment management industry WACC for investment management operations.

Company-Wide vs. Industry WACC

• Another Example: Large electric utilities typically operate in both regulated & unregulated markets. The regulation stabilizes prices and provides a “floor” on profitability. Applying a single WACC for both businesses would underestimate the required return for the unregulated merchant business and lead to overinvestment and would result in an overestimate of the required return and, therefore, inadequate investment in regulated activities. Such companies typically set two WACCs: a lower one for the safer regulated market and a higher one for the riskier merchant business.

• Use of an industry WACC for a particular company’s investments assumes that the company and industry have approximately the same business risk and financing.

• Industry WACCs need to be adjusted if industry-average debt ratios differ from the target debt ratio for the project to be valued.

Tax Rate Considerations

• What tax rate should I use?

• The WACC formula calls for the marginal tax rate — i.e., cash taxes paid as a percentage of each dollar of additional income generated by a capital-investment project.

• Need to take into account not only corporate income tax but also other taxes that need to be paid (e.g., state income taxes).

• US corporations operating nationwide would add three or four percentage points over the corporate income tax rate of 21% to cover state taxation => might use a 24% or 25% tax rate for the calculation of WACC.

Interest Tax Shields

• What if the company can’t use all its interest tax shields?

• Sometimes, interest tax shields from new debt cannot be captured immediately because (1) the company is suffering losses overall or (2) its total interest payments exceed some max allowable threshold (e.g., 30% of EBIT in the US).

• Should the company change its WACC if it finds itself in one or both of these unfortunate states?

• Answer: Probably not if the losses or constraint are temporary. Tax losses and non-deductible interest can be carried forward and used to shield future income.

Adjusting WACC

• The WACC formula assumes that the project or business to be valued will be financed in the same debt–equity proportions as the company (or industry) as a whole.

• What if that is not true?

• For example, what if Sangria’s perpetual crusher project supports only 20% debt versus 40% for Sangria overall?

• Moving from 40% to 20% debt may change all the inputs to the WACC formula. The financing weights will change; the cost of equity r_E is lower because financial risk is reduced; the cost of debt may be lower, too.

Three-Step Procedure for Finding WACCs at Different Debt Ratios

1. Calculate the opportunity cost of capital – i.e., calculate WACC and the cost of equity at zero debt. This step is called unlevering the WACC. The simplest unlevering formula is:

   • Opportunity cost of capital = rA = rD\frac{D}{V} + r_E\frac{E}{V}

2. Estimate the cost of debt, r_D, at the new debt ratio, and calculate the new cost of equity.

   • rE = r + (r − rD)\frac{D}{E}

3. Recalculate the weighted-average cost of capital at the new financing weights.

   • WACC = rD(1 − Tc)(\frac{D}{V}) + r_E (\frac{E}{V})

Three-Step Procedure for Finding WACCs at Different Debt Ratios

• Step 1 – Calculate the opportunity cost of capital. This step is called unlevering the WACC. Sangria’s current debt ratio is D/V = 0.4 => company cost of capital r_A is:

• Step 2 – Estimate the cost of debt at the new debt ratio and calculate the new cost of equity. We will assume that the debt cost stays at 6% when the debt ratio is 20%.

• Step 3 – Recalculate WACC at the new financing weights.

• r_A = 0.06 × (0.4) + 0.125 × (0.6) = 0.099, or 9.9%

• r_E = 0.099 + (0.099 − 0.06) × (0.25) = 0.109, or 10.9%

• WACC = 0.06(1 − 0.21)(0.2) + 0.109(0.8) = 0.097, or 9.7%

Unlevering and Relevering Betas

• Three-step procedure (1) unlevers and then (2) relevers the cost of equity.

• Some financial managers find it convenient to (1) unlever and then (2) relever the equity beta.

• Given the beta of equity at the new debt ratio, the cost of equity is determined from the capital asset pricing model. Then WACC is recalculated.

• The formula for unlevering beta is given by:

  • \betaA = \betaD (\frac{D}{V}) +\beta_E(\frac{E}{V})

• The formula for relevering equity beta is given by:

  • \beta’E = \betaA + (\betaA − \betaD)(\frac{D}{E})

• Re-calculate the cost of equity, using this new re-levered beta:

  • r’E = rf + (rm − rf)\beta’_E

Unlevering and Relevering Betas

• Suppose Sangria’s debt and equity betas in our example are \betaD = 0.135 and \betaE = 1.07.

• If the risk-free rate is 5%, and the market risk premium is 7.0%, then Sangria’s cost of equity is rE = rf + (rm − rf)\beta_E = 0.05 + (0.07) 1.07 = 0.125, or 12.5%

• Matches the cost of equity in our example at a 40/60 debt-equity ratio.

• To find Sangria’s WACC at a 20% debt ratio, we can follow a similar three-step procedure.

• Step 1 – Unlever beta.

• Step 2 – Estimate betas of debt and equity at the new debt ratio.

• Step 3 – Recalculate the cost of equity and the WACC at the new financing weights.

Unlevering and Relevering Betas

• Step 1 – Unlever beta.

• Step 2 – Estimate the betas of the debt and equity at the new debt ratio.

• Step 3 – Recalculate the cost of equity and the WACC at the new financing weights.

• Most important point to remember is rebalancing.

• Companies must rebalance their capital structure to maintain the same market-value debt ratio for the relevant future.

Unlevering and Relevering Betas

• Step 1 – Unlever beta. The unlevered beta is the asset beta: the beta of the equity if the company had zero debt.

• Step 2 – Estimate the betas of the debt and equity at the new debt ratio. If the beta of Sangria’s debt stays at 0.135 at the new debt-equity ratio of 0.2/0.8 = 0.25, then:

• Step 3 – Recalculate the cost of equity and the WACC at the new financing weights.

• \betaA = \betaD (\frac{D}{V}) +\beta_E(\frac{E}{V}) = 0.135 \times0.4 + 1.07 \times0.6 = 0.696

• \betaE = \betaA + (\betaA − \betaD) (\frac{D}{E}) = 0.696 + (0.696 - 0.135) 0.25 = 0.836

• rE = rf + (rm - rf) \beta_E = 0.05 + 0.836 \times 0.07 = 0.109 or 10.9\%

• WACC = 0.06(1 - 0.21) + 0.109 \times 0.8 = 0.097 or 9.7\%

Constant Debt Ratio Assumption

• Using a company’s after-tax WACC to discount future cash flows assumes that the existing debt ratio and capital structure do not change in the future.

• Requires company to rebalance its capital structure to maintain the same market-value debt ratio for the relevant future.

• The three-step procedure for recalculating WACC with a different debt ratio makes a similar rebalancing assumption. Whatever the starting debt ratio, the firm is assumed to rebalance its capital structure to maintain that ratio in the future.

Miles and Ezzell Formula

• Suppose a firm undertakes annual rebalancing to a constant debt ratio (i.e., a firm rebalances once a year, so that next year’s interest tax shield, which depends on this year’s debt, is known).

• Then you can use a formula developed by Miles and Ezzell.

• But first, we need the opportunity cost of capitalr_A and the debt to value ratioD/V

• Miles - Ezzell formula can be used to adjust WACC to find the adjusted cost of capital at any debt level.

• r^* = WACC = rA - \frac{D}{V} rD Tc \frac{1 + rA}{1 + r_D}

Modigliani-Miller Formula

• Modigliani and Miller (MM) suggested an alternative formula for adjusting the WACC.

• MM considered a company or project generating a level perpetual stream of cash flows financed with fixed, perpetual debt and derived a simple relationship between the after-tax discount rate (r{MM}) and the company cost of capital (rA):

• r^* = WACC = rA[1 – Tc(\frac{D}{V})]

• This formula applies to a company or project generating a level, perpetual stream of cash flows financed with fixed, perpetual debt.

• Not a bad approximation for projects that are not perpetual as long as debt is issued in a fixed amount.

Adjusted Present Value (APV)

• An alternative way to take account of financing decisions is to calculate an Adjusted Present Value or APV.

• APV = Base-case NPV + PV of financing decisions

  • Base-case NPV, calculated as though the entire project were all-equity financed; i.e., the NPV is calculated using a discount rate equal to the opportunity cost of capital for the project being valued, which equals the company cost of capital if the project is average-risk for the company. (The discount rate is not “levered up” to account for the financial risk created by borrowing. It is an “all-equity” rate).

  • PV of financing decisions caused by project acceptance. Common financing side effects include interest tax shields, issue costs, and special financing packages offered by suppliers or governments.

Adjusted Present Value

• APV gives the financial manager an explicit view of the factors that are adding or subtracting value.

• In the APV method, the user traces out all incremental effects of accepting a project, including effects on financing decisions. If the financing effects matter, then add their value (or subtract their cost) from project NPV.

• When used correctly, both WACC and APV give the same result.

• The APV method is very useful in analyzing international projects.

Adjusted Present Value

• APV = Base Case NPV + PV Side-effects

• Accept project if APV is positive.

  • Base Case = Project NPV assuming an all equity “mini-firm.”

  • PV Side-effects = Costs and benefits arising from financing side-effects

• The most important financing side effect is the interest tax shield on the debt supported by the project (a plus). Other possible side effects are the issue costs of securities (a minus) or financing packages subsidized by a supplier or government (a plus).

Adjusted Present Value

Example
Project A has an NPV of $150,000. In order to finance the project we must issue shares, with issue costs of $200,000.
Project NPV = 150,000, Shares issue cost = -200,000, Adjusted NPV = - 50,000
APV = Base Case NPV + PV Side-effects
APV = +150,000 + (-200,000) = -50,000
Conclusion: Don’t do the project!

Adjusted Present Value

• Example

• Project B has −$20,000 NPV. Firm can issue debt at 8% to finance the project. New debt has PV tax shield of $60,000. Assume Project B is the only option.

• Base-case Project NPV = −20,000

• PV of tax shield from debt financing = + 60,000

• APV = base case NPV + PV side-effects

• Adjusted NPV = 40,000

• Conclusion: Invest in Project B

APV to the Perpetual Crusher Project

• Start by showing that APV is equivalent to discounting at WACC if we make the same assumptions about debt policy and taxes.

• Earlier, we used Sangria’s WACC as the discount rate for the crusher’s projected cash flows.

• The WACC calculation assumed that debt will be maintained at a constant 40% of the future value of the project or firm. In this case, the risk of interest tax shields is the same as the risk of the project i.e., \betaA = \beta{\text{tax shields}}. Therefore, we can discount the tax shields at the company cost of capital (r_A).

• We calculated rA previously by unlevering Sangria’s WACC to obtain rA = 9.9\%.

Applying APV to Sangria's Perpetual Crusher

Step 1: Calculate the base-case NPV
- Discount after-tax project cash flows of $1.175 million at company cost of capital (or cost of equity