Capital budgeting with the Net Present Value rule
3. Impact of financing
Professor André Farber
Solvay Business School
University of Brussels, Belgium
Hanoi April 2000
1
Capital budgeting for the levered firm
• With debt and equity, decision depends on financing mix.
• Why?
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Tax subsidy to debt
Cost of issuing new securities
Subsidies to debt financing
Cost of financial distress
• 3 methods:
– Adjusted-Present Value
– Flow-to-equity
– Weighted-average cost of capital
Hanoi April 2000
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Adjusted-Present-Value
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Divide and conquer!
Step 1: Calculate NPV for unlevered project NPV
Step 2: Calculate NPV of financing side NPVF
Step 3: Add up.
APV = NPV + NPVF
Hanoi April 2000
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APV - example
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Initial investment = 500
Expected future EBIT = 140 per year for indefinite future
Corporate tax rate = 40%
Cost of capital, all equity r0 = 20%
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Unlevered cash flow (UCF) = 140 (1 - 0.40) = 84
Present value of UCF = 84 / 0.20 = 420
NPV = -500 + 420 = -80
Unlevered project would be rejected!
Hanoi April 2000
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APV example: Introducing debt
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Now imagine the company borrows 300
Remaining investment (500 - 300 = 200) financed with equity.
Borrowing rate = 10%
Income statement
unlevered
levered
EBIT
140
140
Interest
0
30
Tax saving
Taxes
56
44
= 56 - 44 = 12
= 40% x 30
Earnings
84
66
Cash to investors
84
Hanoi April 2000
96
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Valuing the Tax Shield
• Annual tax shield from debt
= TaxRate  Interest rate  Value of debt
= TC rB B
• Present value (perpetuity)
= (TC rB B)/rB
=TC B
• In our example: PV(TaxShield) = 0.40  300 = 120
Hanoi April 2000
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APV calculation (finished)
• We now have the following for our project:
• Net Present Value (all equity)
• Present Value of Tax Shield
• Adjusted Present Value
- 80
+120
+ 40
•
Hanoi April 2000
7
Flow-to-Equity Approach
• Valuation of cash flows from the project to the
equityholders of levered firm (levered cash flow LCF).
• LCF = UCF - (1-TC) x rB x B
= UCF - rB x B + TC x rB x B
Interest
TaxShield
• In our example: LCF = 84 - 30 + 12 = 66
Hanoi April 2000
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Discounting Levered Equity Cash Flows
• Because of debt, equity is more risky. Discount rate should
take this additional risk into account.
• The formula for the discount rate is:
rS = r0 + (r0 - rB) x L/(1-L)
• with L : debt-to-value ratio
• In our example: L = 300 /(420 + 120) = 0.5555
• rS = 0.20 + (0.20 - 0.10) x 0.60 x 1.25 = 27.50%
• Present value of levered cash flows = 66/.275 = 240
• NPVfor stockholders = 240 - 200 = 40 … same as APV
Hanoi April 2000
9
Weighted-Average-Cost-of-Capital Approach
• Discount unlevered cash flow using adjusted cost of
capital.
• rWACC = rs (1-L) + rB(1-TC) L
• (Remember: L = B/V
so 1-L = S/V)
• In our example:
• rWACC = 0.275 x 0.445 + 0.10 x 0.60 x .555 = 15.57%
• Net present value = -500 + 84 / 0.1557 = 40
Hanoi April 2000
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Alternative WACC formulas
• Modigliani Miller : rWACC = r0 (1-TCL)
– perpetuity
– debt level constant
• Miles-Ezzel: rWACC = r0 - L rB TC (1+r0)/(1+rB)
– any set of cash flows
– debt ratio constant Bt = L x Vt
Hanoi April 2000
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Comparing APV, FTE and WACC
• Which approach is best?
• APV
– any type of side effect
– unbundles present value
– use APV when level of debt known
• WACC, FTSE
– takes into account interest tax shield
– use WACC or FTSE when debt ratio constant
Hanoi April 2000
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