VALUATION & LEVERAGE Capital budgeting considering risk and leverage

VALUATION & LEVERAGECapital budgeting considering risk and leverage

Introduction

Today we will discuss three approaches to valuing a risky asset for which both debt and equity financing are used.

Initial Simplifying Assumptions: The project has average (for the firm) risk.

For simplicity the betas or costs of capital used will be for the existing firm rather than being project specific. Often iffy but correctable.

The firm’s debt-equity ratio is held constant. This simplifies the application in that we don’t need to worry

about changing costs of capital over time and identifies the proper the adjustment of our risk measure for leverage. It is a realistic and common policy (at least in expectation).

Corporate taxes are the only relevant imperfection. No agency, bankruptcy or issuance costs to quantify. Clearly not!

The Weighted Average Cost of Capital Method

Because the WACC incorporates the tax savings from debt, we can compute the levered value (V for enterprise value, L for leverage, 0 for current or time 0) of an investment, by discounting its future expected free cash flow using the WACC.

(1 ) wacc E D c

E Dr r r

E D E D

31 20 2 3

1 (1 ) (1 )

L

wacc wacc wacc

FCFFCF FCFV

r r r

Valuing a Project using the WACC

Ralph Inc. is considering introducing a new type of chew toy for dogs. Ralph expects the toys to become obsolete after

five years when it will be confirmed that chew toys actually encourage dogs to eat shoes. However, the marketing group expects annual sales of $40 million for the first year, increasing by $10 million per year for the following four years.

Manufacturing costs and operating expenses (excluding depreciation) are expected to be 40% of sales and $7 million, respectively, each year.


Developing the product will require upfront R&D and marketing expenses of $8 million. The fixed assets necessary to produce the product will require an additional investment of $20 million. The equipment will be obsolete once production ceases

and (for simplicity) will be depreciated via the straight-line method over the five year period for tax purposes.

Ralph expects $1 million in new net working capital requirements for the years the project operates.

Ralph has a target of 60% equity financing, currently has $50 million in excess cash, and pays a 35% corporate tax rate.

Expected Future Free Cash Flow

"Income Statement:" Year 0 1 2 3 4 5Sales 40.00 50.00 60.00 70.00 80.00COGS 16.00 20.00 24.00 28.00 32.00Gross Profit 24.00 30.00 36.00 42.00 48.00Operating Expenses 8.00 7.00 7.00 7.00 7.00 7.00Depreciation Exp 4.00 4.00 4.00 4.00 4.00EBIT -8.00 13.00 19.00 25.00 31.00 37.00Tax (35%) -2.80 4.55 6.65 8.75 10.85 12.95Unlevered NI -5.20 8.45 12.35 16.25 20.15 24.05

Free Cash Flow:Unlevered NI -5.20 8.45 12.35 16.25 20.15 24.05Plus Deprecition Exp 0.00 4.00 4.00 4.00 4.00 4.00Less Net Cap Ex 20.00 0.00 0.00 0.00 0.00 0.00Less Changes in NWC 1.00 0.00 0.00 0.00 0.00 -1.00Free Cash Flow -26.20 12.45 16.35 20.25 24.15 29.05

“Market Value” Balance Sheet Before the project ($millions):

The firm is currently at its target leverage: Equity to Net Debt plus Equity (enterprise

value) ratio:$510.00/($510.00 + $390.00 - $50.00) =

60.0%

Excess Cash 50.00$ Debt 390.00$ Debt 5%Existing Assets 850.00$ Equity 510.00$ Equity 12%

Total Liabilities Risk Free 4%Total Assets 900.00$ and Equity 900.00$

Assets Liabilities Cost of Capital


Ralph intends to maintain a similar net debt-equity ratio for the foreseeable future, including any financing related to the project. Thus, Ralph’s WACC is:

(1 )

510 340 (12%) (5%)(1 0.35)850 850

8.5%

wacc E D c

E Dr r r

E D E D


The value of the project, including the tax shield from debt, is calculated as the present value of its future free cash flows discounted at the WACC.

The NPV (value added) of the project is $51.76 million

$77.96 million – $26.20 million = $51.76 million It is important to remember the difference between

value and value added (and cost).

0 2 3 4 5

12.45 16.35 20.25 24.15 29.05 +

1.085 1.085 1.085 1.085 1.085 $77.96 million

LV

Summary of the WACC Method1. Determine the incremental free cash flow of the

investment project.

2. Compute the weighted average cost of capital.

3. Compute the value of the investment, including the tax benefit of leverage, by discounting the free cash flow of the investment using the WACC.

a. Note that only the tax benefit of debt is explicitly valued via this method.

4. The WACC can be used throughout the firm as the companywide cost of capital for new investments that are of comparable risk to the firm itself and that will adopt the firm’s debt-equity ratio.

Implementing a Constant Debt-Equity Ratio

By undertaking the project, Ralph adds new assets to the firm with an initial market value of $77.96 million. Therefore, to maintain the target debt-to-

value ratio, Ralph must initially add $31.19 million in new net debt. 40% × $77.96 = $31.19 ($31.185, rounding) 60% × $77.96 = $46.78 (compare to $51.76)


Ralph can add (net) debt in this amount either by reducing cash and/or by borrowing and increasing actual debt. Suppose Ralph decides to spend $26.20 million

(the negative FCF in year 0) of its excess cash to initiate the project. This increases net debt by $26.20 million

Excess Cash 23.80$ Debt 390.00$ Net Debt 39.5%Existing Assets 850.00$ Equity 561.76$ Equity 60.5%New Project 77.96$

Total LiabilitiesTotal Assets 951.76$ and Equity 951.76$

Assets Liabilities % of Total Value

New Market Value Balance Sheet We need an initial increase in net debt of

$31.19 and equity of $46.78. So… Spend $26.20 million on the project and

pay a $4.99 million dividend so $31.19 million in cash goes out (the dividend further increases net debt and reduces equity to achieve the desired ratio).

Excess Cash 18.81$ Debt 390.00$ Debt 40.0%Existing Assets 850.00$ Equity 556.78$ Equity 60.0%New Project 77.96$

Total LiabilitiesTotal Assets 946.78$ and Equity 946.78$

Assets Liabilities % of Total Value


The market value of Ralph’s equity increases by $46.78 million. $556.78 − $510.00 = $46.78 (60% of $77.96)

Adding the dividend of $4.99 million into the mix, the shareholders’ total gain is $51.76 million. $46.78 + 4.99 = $51.76 (rounding) Which is exactly the NPV calculated for the project The first try: without the dividend the equity value

increased by the project’s NPV of $51.76 = $561.76 - $510.00. This was too large an increase in equity (with an increase in net debt of $26.20) since Ralph seeks to maintain 60% equity financing.


Debt Capacity The amount of debt at a particular date

that is required to maintain the firm’s target debt-to-value ratio

The debt capacity at date t is calculated as:

Where d is the firm’s target debt-to-value ratio and VL

t is the project’s levered continuation value on date t (i.e. the present value of all future FCF from time t).

Lt tD d V

Debt Capacity

In order to maintain the target financing, the amount of new debt must fall over the life of the project.

This is true because the value of the project depends upon the future cash flow at each point in time. Since the project ends, value decreases. Since value decreases, debt must also decrease.

year 0 1 2 3 4 5Free Cash Flow (26.20)$ 12.45$ 16.35$ 20.25$ 24.15$ 29.05$ Levered Value 77.96$ 72.14$ 61.92$ 46.93$ 26.77$ -$ Debt Capacity d = 40% 31.19$ 28.86$ 24.77$ 18.77$ 10.71$ -$

The Adjusted Present Value Method

Adjusted Present Value (APV) A valuation method to determine the

levered value of an investment by first calculating its unlevered value and then adding the value of the interest tax shield and deducting any costs that arise from other market imperfections0 0 (Interest Tax Shield)

(Financial Distress, Agency, and Issuance Costs)

L UV APV V PV

PV

The Unlevered Value of the Project The first step in the APV method is to

calculate the value of the free cash flows using the project’s cost of capital if it were financed without leverage.

The Unlevered Value of the Project

Unlevered Cost of Capital The cost of capital of a firm, were it unlevered:

If the firm maintains a target leverage ratio, rU can be estimated (recall the picture) as the weighted average cost of capital computed without taking into account taxes (pre-tax WACC).

This is, strictly speaking, only true for firms that adjust their debt to maintain a target leverage ratio, a common but not universal policy.

Pretax WACC U E D

E Dr r r

E D E D

The Unlevered Value of the Project

For Ralph, the unlevered cost of capital is:

The project’s value without leverage is:

340

850

0.60 12.0% 0.40 5.0%

9.2%

8.5% 0.35 5% 9.2%

U

DE Dwacc c D

r

r r

2 3 4 5

12.45 16.35 20.25 24.15 29.05 +

1.092 1.092 1.092 1.092 1.092 $76.35 million

UV

Valuing the Interest Tax Shield The $76.35 million is the value of the

unlevered project and does not include the value of the tax shield provided by the interest payments on any incremental debt associated with the project.

The interest tax shield is equal to the interest paid multiplied by the corporate tax rate.

1Interest paid in year D tt r D

1Interest tax shield for year c D tt r D

Interest Tax Shield

From the debt capacity calculation we can find the interest associated with the project if the financing is kept on target.

year 0 1 2 3 4 5Free Cash Flow (26.20)$ 12.45$ 16.35$ 20.25$ 24.15$ 29.05$ Levered Value (WACC) 77.96$ 72.14$ 61.92$ 46.93$ 26.77$ -$ Debt Capacity d = 40% 31.19$ 28.86$ 24.77$ 18.77$ 10.71$ -$ Interest -$ 1.56$ 1.44$ 1.24$ 0.94$ 0.54$ Interest Tax Shield -$ 0.55$ 0.50$ 0.43$ 0.33$ 0.19$

Valuing the Interest Tax Shield

The next step is to find the present value of the annual interest tax shields created by the borrowing associated with the project. When the firm maintains a target leverage

ratio, its future interest tax shields have similar risk to the project’s cash flows, therefore they should be discounted at the project’s unlevered cost of capital.2 3 4 5

0.55 0.50 0.43 0.33 0.19(interest tax shield) +

1.092 1.092 1.092 1.092 1.092 $1.61 million

PV

Valuing the Project with Leverage

The total value of the project with leverage is the sum of the value of the interest tax shield and the value of the unlevered project.

The NPV of the project is $51.76 million $77.96 million – $26.20 million = $51.76 million

These are exactly the same values found using the WACC approach.

(interest tax shield)

76.35 1.61 $77.96 million

L UV V PV

Summary of the APV Method1. Determine the investment’s value

without leverage.

2. Determine the present value of the interest tax shield.a. Determine the expected interest tax shield.

b. Discount the interest tax shield.

3. Add the unlevered value to the present value of the interest tax shield to determine the value of the investment with leverage.

4. Could subtract the costs associated with debt as well if there is a reasonable way to quantify them.

Summary of the APV Method

The APV method has some advantages. It can be easier to apply than the WACC

method when the firm does not maintain a constant debt-equity ratio.

The APV approach also explicitly values market imperfections and therefore allows managers to measure their contribution to value. Note that but for the tax shield the WACC

method may also do this.

The Flow-to-Equity Method

Flow-to-Equity A valuation method that calculates the free

cash flow available to equity holders taking into account all payments to and from debt holders. Free Cash Flow to Equity (FCFE), the free cash

flow that remains after providing for interest payments, debt issuance and debt repayments

The cash flows to equity holders are then discounted using the cost of (levered) equity capital.

Free Cash Flow to Equity

Recall, this is the actual cash flow to levered equity.

Free Cash Flow to EquityYear 0 1 2 3 4 5

Unlevered NI (5.20)$ 8.45$ 12.35$ 16.25$ 20.15$ 24.05$ Less After Tax Interest -$ 1.01$ 0.94$ 0.80$ 0.61$ 0.35$ Plus Depr -$ 4.00$ 4.00$ 4.00$ 4.00$ 4.00$ Less Net Cap Ex 20.00$ -$ -$ -$ -$ -$ Less Change in NWC 1.00$ -$ -$ -$ -$ (1.00)$ Plus Net Borrowing 31.19$ (2.33)$ (4.09)$ (5.99)$ (8.06)$ (10.71)$ Free Cash Flow to Equity 4.99$ 9.11$ 11.32$ 13.45$ 15.48$ 17.99$

Valuing the Equity Cash Flows Because the FCFE represents expected payments

to equity holders, they should be discounted at the project’s cost of equity capital. Given that the risk and leverage of the project are the

same as for Ralph Inc. overall, we can use the firm’s cost of levered equity capital of 12.0% to discount the project’s FCFE.

The value of the project’s FCFE represents the gain to shareholders from the project and it is identical to the NPV computed using the WACC and APV methods. (Assumes the debt is sold at a fair price.)

2 3 4 5

9.11 11.32 13.45 15.48 17.99( ) 4.99 +

1.12 1.12 1.12 1.12 1.12 $51.76 million

NPV FCFE

Project-Based Costs of Capital

Any specific project may have different systematic risk than the average project for the firm.

In addition, different projects will may also vary in the amount of leverage they will support.

In other words, let’s relax those initial simplifying assumptions.

Estimating the Unlevered Cost of Capital

Suppose the project Ralph launches faces different market risks than its main business. The unlevered cost of capital for the new

project can be estimated by looking at publicly traded, pure play firms that have similar business risk.


Assume two firms are comparable to the chew toy project in terms of basic business risk and have the following observable characteristics:Firm Equity Beta Debt Beta Net Debt-to-

Enterprise Value Ratio

Firm A 1.7 0.05 40%

Firm B 1.9 0.10 50%

Estimating the Unlevered Cost of Capital using Betas

We now find their unlevered or asset betas:

An average of these unlevered betas is 1.02.

Note, an unlevered beta estimate for the project of 1.02 gives an unlevered cost of equity capital of:

0.6 0.41.7 0.05 1.04

0.6 0.4 0.6 0.4

0.5 0.51.9 0.1 1.0

0.5 0.5 0.5 0.5

A AA A AU E DA A A A

B BB B BU E DB B B B

E D

E D E D

E D

E D E D

( ) 4% 1.02(6%) 10.12% 9.2%U f Ur r RP

Project Leverage and the Equity Cost of Capital

Assume that Ralph plans to maintain a 20% net debt to enterprise value ratio for its chew toy project, and it expects its borrowing cost for the project to be 4%.

We now “relever” the unlevered beta estimate of 1.02 and using the SML we find the cost of levered equity:

A cost of debt capital of 4% is consistent with the low leverage chosen and a debt beta of 0.

0.2( ) 1.02 (1.02 0.0) 1.275

0.8

( ) 4% 1.275(6%) 11.65%

E U U D

E f E

D

E

r r RP

Project Leverage and the Weighted Average Cost of Capital

With a 20% debt to value ratio, a cost of equity capital of 11.65%, and a cost of debt capital of 4% we can now estimate the WACC for the project.

0.8 0.211.65% 4%(1 0.35) 9.84

0.8 0.2 0.8 0.2WACCr

An Alternate Approach

From the observable (or measurable) data we can get estimates of the cost of equity capital and the cost of debt capital:

Firm A:

Firm B:

4% 1.7 6% 14.2%

4% 0.05 6% 4.3%E

D

r

r

4% 1.9 6% 15.4%

4% 0.1 6% 4.6%E

D

r

r

An Alternate Approach

Recall the relation between the levered cost of equity capital and the unlevered cost of equity capital:

Rearranging this we find:

In other words, (as we saw before) the unlevered cost of equity capital equals the pre-tax WACC

( )E U U D

Dr r r r

E

pre-tax WACCU E D

E Dr r r

E D E D


If both firms are maintaining a target leverage ratio, the unlevered cost of capital for each competitor can be estimated by calculating their pretax WACC.

Based on these comparable firms, we estimate an unlevered cost of capital for the project that is approximately 10.12%.

Firm A: 0.60 14.2% 0.40 4.3% 10.24%

Firm B: 0.50 15.4% 0.50 4.6% 10.0%U

U

r

r

Project Leverage and the Equity Cost of Capital

Because Ralph plans to maintain a 20% debt to value ratio for its chew toy project, and it expects its borrowing cost to be 4%. Given the unlevered cost of capital

estimate of 10.12%, the chew toy division’s equity cost of capital can be estimated to be:

0.20 10.12% (10.12% 4%)

0.80 11.65%

Er

Project Leverage and the Weighted Average Cost of Capital

The division’s WACC can now be estimated to be:

An alternate method for calculating the chew toy division’s WACC is:

0.80 11.65% 0.20 4.0% (1 0.35)

9.84%WACCr

10.12% 0.20 0.35 4%

9.84%

WACC U c Dr r d r

Documents

VALUATION & LEVERAGE Capital budgeting considering risk and leverage