Net Present Value and Cash Flows Essay

Week 9
Capital structure and capital budgeting

Topics
 First segment of the course: capital budgeting
 Second segment of the course: capital structure (theory)
 Chapter 18: Capital budgeting after accounting for capital structure considerations
 The impact of leverage on capital budgeting





Tax shield
Issuance cost
Cost of financial distress
Financing specific subsidy

 Here we incorporate these effects in the capital budgeting decision – emphasis on problem solving

Outline
 APV, FTE, WACC as three approaches to the problem  When do we use which:
 APV when we know the $ value of debt
 FTE or WACC when we know a D/E ratio

 Other issues:
 Quantifying the impact of leverage on risk
 Scale enhancing projects vs. projects in a new industry
(revisited - Chapter 13)

Adjusted Present Value Approach
APV = NPV + NPVF

 The value of a project to the firm can be thought of as the value of the project to an unlevered firm (NPV) plus the present value of the financing side effects (NPVF):
 Four possible side effects of financing:





The Tax Subsidy to Debt
The Costs of Issuing New Securities
The Costs of Financial Distress
Subsidies to Debt Financing

APV Example
Consider a project of the Pearson Company, the timing and size of the incremental after-tax cash flows for an all-equity firm are:
-$1,000 $125
0

1

$250
2

$375
3

$500

4

The unlevered cost of equity is r0 = 10%:

NPV10%
NPV10%

$125
$250
$375
$500
 $1,000 



2
3
(1.10) (1.10) (1.10) (1.10) 4
 $56.50

The project would be rejected by an all-equity firm: NPV < 0.

APV Example (continued)
 Now, imagine that the firm finances the project with $600 of debt at rB = 8%.
 Pearson’s tax rate is 40%, so they have an interest tax shield worth TCBrB = .40×$600×.08
= $19.20 each year.

 The net present value of the project under leverage is:

APV  NPV  NPVF
4
$19.20
APV  $56.50   t (
1
.
08
) t 1
APV  $56.50  63.59 $7.09
 So, Pearson should accept the project with debt.

APV Example (continued)
 Note that there are two ways to calculate the
NPV of the loan. Previously, we calculated the
PV of the interest tax shields. Now, let’s calculate the actual NPV of the loan:
4

$600 .08 (1  .4) $600
NPVloan $600  

t
4
(
1
.
08
)
(
1
.
08
)
t 1
NPVloan $63.59

APV  NPV  NPVF
APV  $56.50  63.59 $7.09
 Which is the same answer as before.

The APV approach
 Find r0
 Find unlevered cash flow
 Use these to get NPV without debt

 Find tax shield benefit of debt by either
 Tax shield present value (easier calculation)
 Debt present value (works better for some more complex situations)  May need to add other effects of debt
 APV = NPV + Effects of debt

Reminders
 Proposition I (with Corporate Taxes)
 The APV relation
VL = VU + TC B

 Proposition II (with Corporate Taxes)
 Calculation of rS and r0 rS = r0 + (B/S)×(1-TC)×(r0 - rB) rB is the interest rate (cost of debt) rS is the return on equity (cost of equity) r0 is the return on unlevered equity (cost of capital)
B is the value of debt
S is the value of levered equity

Flow to Equity Approach
 Discount the cash flow from the project to the equity holders of the levered firm at the cost of levered equity capital, rS.
 There are three steps in the FTE Approach:
 Step One: Calculate the levered cash flows
 Step Two: Calculate rS.
 Step Three: Valuation of the levered cash flows at rS.

Step One: Levered Cash Flows for
Pearson

 Since the firm is using $600 of debt, the equity holders only have to come up with $400 of the initial $1,000.
 Thus, CF0 = -$400
 Each period, the equity holders must pay interest expense. The after-tax cost of the interest is B×rB×(1-TC) = $600×.08×(1-.40) =
$28.80

CF3 = $375 -28.80
CF2 = $250 -28.80
CF1 = $125-28.80
-$400
0

$96.20
1

2

CF4 = $500 -28.80 -600

$221.20
3

$346.20
4

-$128.80

Step Two: Calculate rS for
Pearson
B rS r0 

S

(1  TC )( r0  rB )

 To calculate the debt-to-equity ratio, B/S, start with the

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