NPV and Debt. Assume: Long-term debt at 4.25% = $2,000 A/P = $300 N/P = $ shares selling for $25 each. A 3-year project

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1 NPV and Debt Assume: Long-term debt at 4.25% = $2,000 A/P = $300 N/P = $ shares selling for $25 each A 3-year project Pro forma income statement for a 3-year project (S = $2,000) Sales $0.00 $5, $5, $5, (Costs) $0.00 $3, $3, $3, (Depreciation) $ $ $ $ EBIT -$ $ $1, $1, (Interest) $0.00 $85.00 $85.00 $85.00 EBT -$ $ $ $1, (Tax) $0.00 $ $ $ Net income -$ $ $ $1, Addition to RE -$ $ $ $ Dividend $0.00 $ $ $

2 Pro forma income statement for a 3-year project (S = $2,000) Cash $ $1, $1, $0.00 Inventory $ $ $ $0.00 A/R $ $ $ $0.00 Current assets $1, $1, $2, $0.00 Gross fixed assets $3, $3, $3, $1, Depreciation $ $ $1, $1, Net fixed assets $2, $2, $1, $0.00 Total assets $3, $4, $4, $0.00 A/P $ $ $ $0.00 N/P $ $ $ $0.00 Current liabilities $ $ $ $0.00 Long-term debt $2, $2, $2, $0.00 Outstanding shares $1, $1, $1, $0.00 Retained earnings ($300.00) $75.38 $ ($0.00) Owner's equity $1, $1, $1, ($0.00) Total L&E $3, $4, $4, ($0.00) 2

3 Cash flow projection for a 3-year project (S = $2,000) Unlevered Net Income -$ $ $ $1, Depreciation $ $ $ $ OCF $0.00 $1, $1, $ Sales $0.00 $5, $5, $5, Costs $0.00 $3, $3, $3, Tax** $0.00 $ $ $ OCF $0.00 $1, $1, $ ATNOR $0.00 $ $ $ DeprTS $0.00 $ $ $92.48 OCF $0.00 $1, $1, $ OCF $0.00 $1, $1, $ Net Capital Spending -$3, $0.00 $0.00 $2, Investment in CA net of A/P -$ $ $ $2, Unlevered Cash Flow -$3, $ $ $5, Interest tax shield $0.00 $28.90 $28.90 $28.90 CF from assets -$3, $ $ $5, CF to creditors -$2, $85.00 $85.00 $2, CF to shareholders -$1, $ $ $2, CF to stakeholders -$3, $ $ $5,

4 Things to note: Notes payable carry very low interest, almost zero. For the purpose of this exercise we will assume to be equal to zero. The cost of long-term borrowing is 4.25%. The effective cost of borrowing, however, becomes: Effective cost of borrowing = Interest paid/all liabilities Effective cost of borrowing = $85/($2,000 + $400 + $300) = 3.15% At t= 0, Toy Inc requires $3,000 worth of plant and equipment and $1,000 worth of current assets. Since current assets are partially financed with accounts payable ($300), the total initial investment outlay that needs debt and equity financing is: Initial investment outlay = $3,000 + $1,000 - $300 = $3,700 OCF requires the estimation of unlevered net income. For example, in year 1, net income is equal to $577.5 as shown in the pro-forma income statement. One would have to estimate unlevered net income in the following way: UNI = EBIT(1-Tax%) - $960(1-0.34) = $633.6 The tax shield is equal to: Annual tax shield = Annual interest(tax%) = $85(0.34) = $28.9 4

5 M&M NPV M&M states that: Total market value of project = PV(unlevered cash flow) + PV(debt tax shield) or Market value of equity + Market value of liabilities = PV(unlevered cash flow) + PV(debt tax shield) or Market value of equity = - Market value of liabilities + PV(unlevered cash flow) + PV(debt tax shield) M&M NPV can be derived from above: NPV = Total market value of project Initial cost NPV = PV(unlevered cash flow) + PV(debt tax shield) Initial cost In this case, NPV is calculated by discounting unlevered cash flows using the unlevered cost of equity; and by discounting the annual tax shield at the effective cost of debt. PV(debt tax shield at 3.15%) = $81.51 M&M NPV = $258.23/(1.05) + $283.17/(1.05) 2 + $5,366.61/(1.05) 3 + $ $3,700 = $1, Further implications: Fair market value of equity = PV(unlevered cash flow) + PV(debt tax shield) - Total liabilities = $258.23/(1.05) + $283.17/(1.05) 2 + $5,366.61/(1.05) 3 + $ $2,700 = $2,

6 Flow to equity NPV = PV(cash flow to shareholders) Initial equity investment Note that PV(cash flow to shareholders) is estimated using the levered cost of equity Levered cost of equity = Unlevered cost of equity +Risk premium(financial leverage) Which financial leverage? Book value leverage = $2,700/$1,000 = 2.7 Market value leverage (current prices) = $2,700/$2,500 = 1.08 or Market value leverage (estimated fair value) = $2,700/ 2,520.17= 1.07 Hypothetical levered cost of equity = 6.32% Flow to equity NPV = $202.13/(1.0632) +$227.07/(1.0632) 2 +$2,910.15/(1.0632) 3 - $1,300 = $1,512.7 WACC NPV NPV = PV(unlevered CF) Initial cost Note: In this case, the present value of the project is found by discounting unlevered cash flow using the wacc. Wacc = (Levered cost of equity)(weight of equity) + (Effective cost of debt)(1-tax%)(weight of debt) Assume weights are given by market prices: wacc = 6.32%(0.4808) %(0.5192)(1-0.34) = 4.12% WACC NPV = $258.23/(1.0412) + $283.17/(1.0412) 2 + $5,366.61/(1.0412) 3 - $3,700 = $1,

7 Perpetual project Toy Inc.: Sales projection with debt financing Sales $0.00 $5, $5, $5, (Costs) $0.00 $3, $3, $3, (Depreciation) $ $ $ $ EBIT -$ $ $1, $1, (Interest) $0.00 $85.00 $85.00 $85.00 EBT -$ $ $ $1, (Tax) $0.00 $ $ $ Net income -$ $ $ $ Addition to RE -$ $ $ $ Dividend $0.00 $ $ $

8 Toy Inc pro-forma balance sheet with $2,000 long-term debt, $300 A/P, and $400 N/P Cash $ $1, $1, $2, Inventory $ $ $ $ A/R $ $ $ $ Current assets $1, $1, $2, $3, Gross fixed assets $3, $3, $3, $3, Depreciation $ $ $1, $1, Net fixed assets $2, $2, $1, $1, Total assets $3, $4, $4, $4, A/P $ $ $ $ N/P $ $ $ $ Current liabilities $ $ $ $ Long-term debt $2, $2, $2, $2, Outstanding shares $1, $1, $1, $1, Retained earnings ($300.00) $75.38 $ $ Owner's equity $1, $1, $1, $2, Total L&E $3, $4, $4, $4,

9 Toy Inc.: Cash flows with debt Unlevered Net Income -$ $ $ $ Depreciation $ $ $ $ OCF $0.00 $1, $1, $1, Sales $0.00 $5, $5, $5, Costs $0.00 $3, $3, $3, Tax** $0.00 $ $ $ OCF $0.00 $1, $1, $1, ATNOR $0.00 $ $ $ DeprTS $0.00 $ $ $ OCF $0.00 $1, $1, $1, OCF $0.00 $1, $1, $1, Net Capital Spending -$3, $0.00 $0.00 $0.00 Investment in CA net of A/P -$ $ $ $ Unlevered Cash Flow -$3, $ $ $ Interest tax shield $0.00 $28.90 $28.90 $28.90 CF from assets -$3, $ $ $ CF to creditors -$2, $85.00 $85.00 $85.00 CF to shareholders -$1, $ $ $ CF to stakeholders -$3, $ $ $

10 M&M NPV M&M states that: Total market value of project = PV(unlevered cash flow) + PV(debt tax shield) or Market value of equity + Market value of liabilities = PV(unlevered cash flow) + PV(debt tax shield) or Market value of equity = - Market value of liabilities + PV(unlevered cash flow) + PV(debt tax shield) M&M NPV can be derived from above: NPV = Total market value of project Initial cost NPV = PV(unlevered cash flow) + PV(debt tax shield) Initial cost In this case, NPV is calculated by discounting unlevered cash flows using the unlevered cost of equity; and by discounting the annual tax shield at the effective cost of debt. PV(UCF) = $258.23/(1.05) + $283.17/(1.05) 2 + $303.13/(1.05) 3 + $303.13(1.03)/( )(1.05) 3 PV(UCF) = $14, PV(debt tax shield) = $28.9/(0.0315) = $ M&M NPV = $14, $916 - $3,700 =$ or if we want to include A/P as part of the initial cash outlay: M&M NPV = $14, $916 - $4,000 = $11, Further implications: The market value of equity = - Market value of liabilities + PV(unlevered cash flow) + PV(debt tax shield) The fair market value of equity = -$2,700 + $14, $916 = $12, Since the current price per share is $25, it follows that the firm is significantly undervalued ($2,500 vs $12,466.17) Note that: NPV = Market value of equity Initial equity investment = $12, $1,300 = $11, A/P lay in a grey area as they represent neither financial debt nor equity. 10

11 Flow to equity NPV NPV = PV(cash flow to shareholders) Initial equity investment Note that PV(cash flow to shareholders) is estimated using the levered cost of equity Levered cost of equity = Unlevered cost of equity +Risk premium(financial leverage) Which financial leverage? Book value leverage = $2,700/$1,000 = 2.7 Market value leverage (current prices) = $2,700/$2,500 = 1.08 Market value leverage (estimated fair value) = $2,700/$12, = We are at a loss to estimate even a simple metric such as financial leverage! Hypothetical levered cost of equity = 6.32% NPV=$202.13/(1.0632) +$227.07/(1.0632) 2 +$247.03/(1.0632) 3 +$247.03(1.03)/( )(1.0632) 3 - $1,300 NPV = $5, Why such a huge discrepancy? Arbitrary leverage Inconsistent assumptions about debt levels and leverage ratios Lack of a reliable model to estimate discount rates Arbitrary growth rate in cash flows Had we assumed 4.5% growth rate in CF to shareholders, the results would have been very close. 11

12 WACC NPV NPV = PV(unlevered CF) Initial cost Note: In this case, the present value of the project is found by discounting unlevered cash flow using the wacc. Wacc = (Levered cost of equity)(weight of equity) + (Effective cost of debt)(1-tax%)(weight of debt) Assume weights are given by market prices: wacc = 6.32%(0.4808) %(0.5192)(1-0.34) = 4.12% NPV = $258.23/(1.0412) + $283.17/(1.0412) 2 + $303.13/(1.0412) 3 + $303.13(1.03)/( ) (1.0412) 3 - $3,700 NPV = $21, NPV: A summary NPV is a great tool for analysing and evaluating projects; in theory, that is. In practice, it has several formidable challenges: Inability to project cash flows in the long-term Lack of a reliable model for predicting risk and estimating required returns Extreme sensitivity of NPV estimations to small changes in input variables For short-term projections, however, NPV does a decent job. 12