0. Valuation and Capital Budgeting for the Levered Firm
Valuating the levered firm
Valuation and Capital Budgeting for the Levered Firm

1. Introduction
In a strict MM world, firms can analyze real investments as if they are all-equity-financed.
Under MM assumptions, decisions to spend money can be separated from decisions to raise money.
How to do capital budgeting when investment and financing decisions interact and cannot be wholly separated?

2. Simplifying assumption
Project has average risk: (scale enhancing project) the project’s cost of capital is equivalent to that of the firm.
The D/E ratio of the firm is constant
Corporate taxes are the only imperfection:
Ignoring personal taxes, insurance costs, financial distress costs or agency costs.

3. Outline The Adjusted Present Value approach Flows to Equity Approach
Evaluating a firm with leverage and its project
The Adjusted Present Value approach
Flows to Equity Approach
Weighted Average Cost of Capital Method
Comparison of the APV, FTE, and WACC

4. 1. Adjusted Present Value Approach
APV = NPVU + 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 net present value of the financing side effects (NPVF).
NPVU= PV of unlevered cash flow- investment
Discount rate: R0 (unlevered cost of capital)

5. NPV of financing side-effects
There are four side effects of financing:
The Tax Subsidy to Debt
VL = VU + TC B (for perpetual debt)
The Costs of Issuing New Debt and Equity Securities (e.g. payments to investment bankers)
The Costs of Financial Distress arising from the use of debt
Subsidies to Debt Financing: obtaining debt from a municipality at a low interest rate.

6. Example of PMM Inc. Suppose the company has a project
investment costs $10,000,000
expected EBIT: $3,030,303 per year forever
The unlevered cost of equity: R0 = 20%
The firm’s marginal tax rate: TC = 34%
Should the firm accept the project
If the project is all financed with equity?
If it is financed with $ 5,000,000 of 10% perpetual debt and the rest with internal equity?

7. NPV to unlevered firm Annual after‑tax cash flows :
EBIT (1‑ Tc) = ($3,030,303)(1‑.34)=$2,000,000.
NPV = ($2,000,000 / .2) – $10,000,000 = $0
The all‑equity firm should be indifferent to accepting or rejecting the project.

8. NPVF: Tax Subsidy The present value of tax shield subsidy: Remark
NPVF=TC×B =0.34×$ 5,000,000= 1,700,000.
Remark
In the MM world
All cash flows are perpetual and even debt does not have a maturity date.
No bankruptcy cost
Noting that some papers see the tax shield cash flow as the same cash flow generated by the firm. All these CF are denoted by capital cash flows (CCF= Free CF+ Interest tax shield). Therefore, they use R0 as the TS discount rate. See textbook of Berk & Demarzo 2014.

9. The value of the project with leverage
The Adjusted Present Value of the project is
APV = NPV + NPVF = $ 1,700,000
The firm should accept the project
VU = $1,000,000 (the value of the investment)
VL = VU + TCB = $10,000,000 + $1,700,000.
VB = $5,000,000 VS = $6,700,000.
The entire tax shield subsidy is captured by stockholders.
The D/E ratio is based on the value of the project (50/67) not on the initial investment (1:1)

10. 2. 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 (LCFs)
Step Two: Calculate RS.
Step Three: Value the levered cash flows at RS.

11. Example of PMM Inc. Step1: Cash Flows to Levered Equity
(EBIT– B×RB) (1 – TC)
= ($3,030,303 – $500,000)(1 – .34) = $1,670,000
Step 2: Calculating RS. Assuming B/SL=50/67
Rs = R0 + (B/SL) (1 –tC) (R0 – RB)
= 20% + (50/67) (1 – .34) (20% – 10%)
= %
Step 3: Valuation
NPV= LCF/ RS – Equity Investment
= $1,670,000 / – $5,000, 000 = $1,700,000.

12. Remark The D/E ratio is 50/67 instead of 1.
To determine RS , we need to know SL. However SL=PV(LCF) discounted at RS. => simultaneity problem that does not have an easy solution.
In practice, we use target D/E ratio.

13. 3. WACC Method
To find the value of the project, discount the unlevered cash flows at the weighted average cost of capital.
Note that the weight S/ (S+B) and B/ (S+B) are target ratios, expressed in terms of market values.

14. Example of PMM Inc. B = $5,000,000 S = $6,700,000
RB = 10% RS = % TC = 34%
RWACC = (5,000,000/11,700,000)(.10)(.64) + (6,700,000/11,700,000)(.24925) = %
PVWACC = ($3,030,303)(1 –.34)/ = $11,700,000
NPVWACC = $11,700,000 – $10,000,000 = $1,700,000.
RS, is the same as in the FTE approach (D/E=50/67). =>Simultaneity problem

15. Remarks
WACC is only appropriate as a discount rate for a project when:
The project has similar systematic business risk as the firm, e.g. scale ‑ enhancing firm
The project and firm have the same debt capacity.
In practice, each project should be treated as if it were a mini‑firm, with its own proportion of debt and equity and its own capital costs. 
A convenient feature of the WACC approach is that it is often easy to obtain estimates of RS, RB, B and S. (e.g., the Wall Street Journal).

16. Example: Finite life project
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 $ $ $ $500
The unlevered cost of equity is R0 = 10%
The corporate tax rate TC = 40%
Should the firm accept the project
If it is an all-equity firm?
if the firm finances the project with $600 of debt at RB = 8%?

17. APV The project should be rejected by an all-equity firm:
With $ 600 debt: Pearson’s interest tax shield worth
TCBRB = .40×$600×.08 = $19.20 each year.
The net present value of the project under leverage is:
In the real world, the interest expense on debt is tax deductible but repayment of principal is not.
Note, the example in the text assumes a perpetual project, so the PV of the tax shield is calculated assuming a perpetuity. The approach in this slide is comparable, but for a finite life project.
So, Pearson should accept the project with debt.

18. FTE—Step One: Levered Cash Flows
Since the firm is using $600 of debt, the equity holders only have to provide $400 of the initial $1,000 investment.
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
This example assumes an interest only loan.

19. Step One: Levered Cash Flows
–$400
$221.20
CF2 = $250 – 28.80
$346.20
CF3 = $375 – 28.80
–$128.80
CF4 = $500 – – 600
CF1 = $125 – 28.80
$96.20

20. Step Two: Calculate RS B S V
To calculate the debt to equity ratio, , start with
This assumes we know the value created by the project. A more straightforward assumption is to assume that the ratio is 600/400, based on the amount provided by each source to fund the project. With these values, RS=11.80%.
PV = $ $63.59 = $1,007.09
B = $600 when V = $1, so S = $

21. Step Three: Valuation
Discount the cash flows to equity holders at RS = 11.77% 1 2 3 4
–$400
$96.20
$221.20
$346.20
–$128.80
Note that the chapter examples work out nicely with the perpetuity assumption, in that each approach provides the same value. With a finite life project, the values will deviate based on assumptions made, for example, the repayment of the $600.

22. WACC Method
Suppose Pearson’s target debt to equity ratio is 1.5.

23. WACC Method
To find the value of the project, discount the unlevered cash flows at the weighted average cost of capital
The differences among these three methods is due to the brutal treatment about the debt financing.
Indeed, for WACC and FTE to be applied, one should keep a constant D/E ratio. This means that the debt capacity of the project throughout all these years are different and interest payments are also different.
Thus in order to derive the same result, one should calculate the D/E of each period and the associated interest tax shield, treating the project as a finite life project.
To see more in details, cf. Berk and Demarzo 2014.
NPV7.58% = $6.68

24. Summary The APV formula can be written as:
The FTE formula can be written as:
The WACC formula can be written as
All three approaches attempt the same task: valuation in the presence of debt financing.
APV vs WACC: both uses UCF.
APV discounted at R0 and adjusting the tax benefit directly.
WACC adjusting the benefit by discounting the UCF at a lower rate.
FTE: uses LCF: CF to levered equity holders
The effect is reflected by a smaller CF (interest payment exempt from tax) and less investment (reduced by debt financing)

25. Which approach to choose?
These three methods should be viewed as complementary.
Use WACC or FTE if the firm’s target debt-to-value ratio applies to the project over the life of the project.
If D/E remains constant, so do RS and RWACC .
In real world situation, WACC or FTE applies to firms with target D/E.
WACC is the most widely used method.
In the real company, if the firm plans significant change in capital structure, WACC won’t work. => APV
APV is based on the level of debt in each future period.
Use the APV if the project’s level of debt is known over the life of the project.
eg. Leverage buyout: easily forecast the tax shield.
Interest subsidies and flotation costs

26. In real world Measuring the discount rate
What if the discount rate must be measured?
What if the debt ratio and business risks of project differ from that of the firm?
How to value the other financing-side effects?
How about other sources of financing?
=>
Measuring the discount rate
Determine the risk of the project
Other sources of financing
Other financial side effects

27. Measuring the discount rate
Ex Discount rate(WACC) of World-Wide Widgets
AW WWE
B/S 4/6 1/3
RB 12% 10%
βEquity 1.5
RF 8%
MRP 8.5%
Tc 40%
What is the discount rate for WWE (RWACC) to use for its business?

28. Measuring the discount rate
Using the equity β of the existing company with the same risk to determine its RS .
CAPM: RS = RF + β (RM - RF ).
RF is the risk free (riskless) rate
RM: Expected return on the market portfolio
Using RS of the existing company to determine a hypothetical R0
Under MM II: RS = R0 + B/S (1 -TC) (R0  -RB).
B/S: ratio for the company with the same risk
Using R0 and the firm’s target D/E to determine RS of the project
Computing RWACC

29. Measuring discount Rate of a scale- enhancing project
A scale-enhancing project is one where the project is similar to those of the existing firms.
In the real world, executives would make the assumption that the business risk of the non-scale-enhancing project would be about equal to the business risk of firms already in the business.
No exact formula exists for this. Some executives might select a discount rate slightly higher on the assumption that the new project is somewhat riskier since it is a new entrant.

30. How to determine the risk (β)?
Recall that the risk of a security can be measured by
The risk of a project can be measured by
β of firm with similar business if the project is scale-enhancing
Taking into account the financing side effect.

31. Determine the levered β
The leverage increases the risk of equity.
However, leverage increases the equity beta less rapidly under corporate taxes.
Leverage creates a riskless tax shield, thereby lowering the risk of entire firm.

32. Measuring the risk for scale-enhancing projects
E.g β for scale-enhancing project of CFL. Inc.
Capital structure of CFL.Inc.
B= $100 Riskless debt TC=0.34
S= $200 βequity =2.0 (regression analysis)
What is the risk of the scale-enhancing project if it is all equity financed? (Hint: βProject = βUnlevered firm )
What is the discount rate of the project, providing that RF =10% and MRP=8.5%?

33. What if the project is not scale enhancing?
If project is not scale enhancing : the risk is not comparable to the existing firms of the industry.
We would begin with an average beta of the new industry to compute the R0 , instead of referring to the beta of a specific firm. (Ex. 17)

34. Other sources of financing
Market value balance sheet may has more entries
Current assets Current liabilities
cash, Inventory accounts payable
accounts receivable short-term debt
Property, plants, equipmt Long-term debt (D)
Preferred stock(P)
Growth opportunities Equity (E)
Total assets Liabilities + equity

35. How to discount when there are more than two sources of financing
There is one cost for each element.
The weight for each element is proportional to its market value.
Eg. In the presence of preferred stocks
RWACC = RB (1-TC ) B/V + RP P/V + RE E/V
R is the rate of return on the preferred stock.
P is the value of preferred stock outstanding
V= D+P+E.

36. Other financing side effects
Subsidized financing
Flotation cost
Cost of financial distress
In these cases, the firm’s D/E is not necessarily to be constant.
=> APV is a preferred approach.

37. Example of PPM The company has a project Annual after‑tax cash flows :
investment costs $10,000,000
expected EBIT: $3,030,303 per year forever
The unlevered cost of equity: R0 = 20%
The firm’s marginal tax rate: TC = 34%
Annual after‑tax cash flows :
EBIT (1‑ Tc) = ($3,030,303)(1‑.34)=$2,000,000.
NPV = ($2,000,000 / .2) – $10,000,000 = $0

38. Subsidized financing
Suppose a municipal government decides that the investment is socially (or politically) desirable and agrees to raise the $5,000,000 debt financing as a municipal bond, at the municipality's borrowing rate, RB = 7%.
Interest income on a muni is exempt from Federal tax, so the muni rate is typically below the rate on corporate debt (10%).
Assuming the muni is a perpetual debt.

39. = PV(tax shield) + PV(interest rate subsidy)
Subsidized financing
Good news: the firm is able to borrow at a below market rate (cheaper way of financing).
Bad news: the value of the tax shield on debt financing is reduced.
The total present value of both subsidies:
NPVF(Municipal Loan)
= PV(tax shield) + PV(interest rate subsidy)

40. = PV(tax subsidy) + PV(interest rate subsidy)
Subsidized financing
NPVF(Municipal Loan)
= PV(tax subsidy) + PV(interest rate subsidy)
PV(tax shield)= ($350,000)(.34)/(0.10) = $1,190,000. (Note: the tax subsidy is smaller than in the original example, i.e., $1,700,000)
PV(interest rate subsidy)
= V of debt -V of municipal bond
= $5,000,000 - $350,000 / (0.1) = $1,500,000
NPVF(Municipal Loan) = $1,190,000 + $1,500,000 = $2,690,000.

41. Subsidized financing NPVF(Municipal Loan)
= Amount borrowed – PV(after‑tax interest payments) – PV(loan repayments)
= $5,000,000 – (1 –.34)(.07)($5,000,000)/(.10) – $0
= $5,000,000 – $2,310,000 – $0 = $2,690,000

42. Flotation costs
When a company raises funds through external debt or equity, it must incur flotation costs.
Assume that the municipal government no longer sponsored the project and PPM, Inc. must obtain $5,000,000 with new debt at the market interest rate of 10%. Flotation costs are 12.5% of gross proceeds.
Assuming the flotation cost can be amortized over five years on the straight-line bases.

43. Flotation cost
To get $5,000,000 in net proceed, the company must raise $5,000,000/(1 –0.125) = $5,714,286.
Flotation cost = $5,714,286- $5,000,000= $714,286
Amortization/year = ($714,286/5 years) = $142,857
Annual tax shields from amort
= (.34)($142,857) = $48,571
NPV(FC) = –$714,286 + $48,571 × [1 – (1/1.1)5]/.1
= –$714,286 + $184,124 = –$530,162

44. Flotation cost
Interest is paid on gross proceeds, although flotation costs are paid to intermediaries.
PV (interest TS) = PV (GP ×RB × TC )=GP × TC
= $5,714,286 × 0.34
= $1,942,857
APV = NPV + NPVF(tax shield) + NPVF(issue costs)
= $0 + $1,942,857– $530,162
=$ 1,142,695

45. Cost of financial distress
Firms should continue to exploit tax shields on interest until the benefits are offset by the marginal costs of financial distress.
This means that financial distress costs are likely to be non‑trivial for an optimally‑financed firm.
Unfortunately, financial economists are no help here.  

46. Mini case: Homework Ch. 18 the leveraged buyout of cheek products Inc.
In book of Ross, Westerfield and Jaffe, “Corporate Finance”, 9th edition.
Chapter 17—Questions and problems: 7, 9, 10
Chapter 18—Questions and problems: 2, 3, 4, 14, 17
To be submitted no later than 13:55 Thursday 3 November.
No electronic version is accepted.