lecture_23 valuation with financing effects

8/17/2019 Lecture_23 Valuation With Financing Effects

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Professor Sang Byung [email protected]

Valuation with financing effects



When Capital Structure Matters…

•

Capital structure affects capital allocationdecisions

• Financing is no longer zero NPV.

• For example, some projects may be worthwhile with

debt, but are not worthwhile with equity

• Tax shields, costs of financial distress, other frictions

come into play.



Two main methods

•

Two main methods1. Adjusted discount rate (WACC)

• Discount FCFs using (post-tax) WACC

1 −

2. Adjusted present value (APV)

tax shield − (Financial distress costs)

• Calculate the value of the project as if it is is unlevered (100% financed

by equity).

• Then take the PVs of these financing effects *separately*.

• We will also study

•

FTE (flow to equity) method.



WACC steps

1. Determine FCFs.

2. Compute the WACC.

3. Compute the value of the project (including

the tax benefit of leverage) by discounting

FCFs from the project using WACC.



Target capital structure

•

WACC is based on the assumption that capitalstructure is stable (i.e. it is at its “target” capitalstructure)

• / and / will always fluctuate to some degree, so at any point intime actual capital structure is likely to deviate from its target

•

The idea is that firms will rebalance towards target whenappropriate, so the long-run expected capital structure is the target.

• How do we figure out the target?

• Look at past capital structure to see if there’s a pattern

• Examine management pronouncements about target credit rating,

then convert to capital structure

• Not all firms have a target

• For example, young growth firms

• If true, don’t use WACC DCF, but APV instead



APV Method

• 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 imperfections, e.g.

− ( )

• When discounting FCFs here, you need to use the

discount rate for the unlevered firm (i.e. ), not

the WACC.

• This is because is the value of the project if it were

financed without leverage.



APV – discount rate for the tax shield

• Which discount rate we use for the tax shield

depends on what is happening to the firm’s

capital structure over time

1. If the level of debt a company has varies with the cash

flows or value of the firm, then the appropriate discountrate to use for the tax shield is . This is because the

variability of the firm’s underlying cash flows are

generating the uncertainty in the firm’s debt level.

2. If the level of debt of a company is not a function of theunderlying cash flows of the firm, the tax shield should

be discounted by the return on the company’s debt, .



APV – discount rate for unlevered firm

•If the discount rate for the tax shield is , thediscount rate for the unlevered firm is simply

the pretax WACC:

.




• A levered firm’s market value balance sheet

• Left hand side (assets)

• Value of unlevered firm

• () PV of interest tax shield

• Right hand side (financing sources)

• Value of debt

• Value of equity

• The CFs from assets should go to investors:



•If the discount rate for the tax shield () is

.

[ ]=+

.

.




Note: levering vs unlevering

•If you start from unlevered firm and calculatethe levered firm’s cost of equity, you use the

following formula:

1 − −

• If you start from levered firm and calculate the

unlevered firm’s cost of equity, you use thefollowing formula:

(1 − )

(1 − )

(1 − )



Example – WACC vs APV

•Cougar Printing is 100% equity financed nowand they are researching the possibility of

raising 50% in debt.

• Their pre-tax cash flows are a perpetuity of $10 per year,

and the discount rate on their assets is 10%.

• Assume their cost of debt is 5%.

• The only financing friction is the tax deductibility of

interest payments. Their tax rate is 30%.

• How does firm value change with each

valuation method?



WACC valuation

Their WACC changes. It started at 10%, but with50% debt it changes to:

1 − −

0.10 .5

.5 1 − .3 0.10 − 0.05

.10 .035 0.135

0.5 × 0.135 0.5 × 0.05 ∗ 1 − .3

. %



WACC valuation

•So the discount rate changed from 10% to 8.5%.

• We treat their cash flows the same- $10 per

year, of which they pay 30% taxes, so they keep$7/year forever. IGNORE INTEREST.

• Under old capital structure:

. $70

• Under new capital structure:

. $82.35

• Valuation increases from $70 to $82.35



FCFE

•Note two changes in the calculation of the FCF1. Interest expenses are deducted before taxes

2. The proceeds from the firm’s net borrowing activity are

added in — these are positive when the firm issues debt

and negative when it reduces debt by repaying

principal

− 1 − ∗



Example revisited – FTE method

•Calculate cash flow to equity holders. In thismethod, we take out interest payments before

discounting cash flows.

• Step 1: calculate free cash flows to equity

(FCFE)

• FCF of 10, less $2.06 in interest, less taxes of .3*(10-

2.06)=2.382 => FCFE=5.558

• Step 2: discount FCFE by cost of equity

• .

. $41.17

• This is half of the firm value we calculated in previous

examples (because half the firm belongs to equity)



Another example - Avco

• Suppose Avco is considering introducing a new line of packaging,the RFX Series.

• Avco expects the technology used in these products to becomeobsolete after four years. However, the marketing group expectsannual sales of $60 million per year over the next four years forthis product line.

• Manufacturing costs and operating expenses are expected to be$25 million and $9 million, respectively, per year.

• Developing the product will require upfront R&D and marketingexpenses of $6.67 million, together with a $24 million investmentin equipment.

• The equipment will be obsolete in four years and will be depreciated via thestraight-line method over that period.

• Avco expects no net working capital requirements for the project.

• Avco pays a corporate tax rate of 40%.



FCF from Avco



Using the WACC

• Avco has $20 of cash and $320 of debt; since the cash couldbe used to pay off an equivalent amount of debt, we reducedebt by the amount of cash to get the net amount of debt.Hence Avco’s debt-value ratio is 300/600.

• Avco’s WACC can, therefore, be computed as

300 300 (1 ) (10%) (6%)(1 0.40)

600 600

6.8%

wacc E D c

E Dr r r

E D E D



Using the WACC

•The value of the project, including the taxshield from debt, is calculated as the present

value of its future free cash flows.

• The NPV of the project is $33.25 million

–$61.25 million – $28 million = $33.25 million

0 2 3 418 18 18 18 $61.25 million

1.068 1.068 1.068 1.068

LV



Implementing a constant debt-to-equity ratio

• The WACC method assumed that Avco would keep its debt-equity

ratio constant.

• This requires Avco to change the amount of its debt as its market value changes, as it will if it accepts the Avco project.

• How can we compute the additional debt to be issued each year?

•

To begin with, we note that Avco has a debt-value ratio of 0.5.• After Avco takes on the new project, its value will go up by the

amount of the value of the new assets added due to the project, viz.$61.25m.

• Hence Avco will have to issue 61.125/2 = 30.625 in net new debt.

•

We assume that Avco will do that by spending its $20m cash andissuing $10.625 in new debt.

• Since the firm only needs $28m for the RFX project, the additional$2.625m will be paid out as a dividend.

• Its balance sheet will now appears as follows:




• The firm’s debt capacity is defined as the total amount of debtrequired to maintain the firm’s target debt-value ratio. This equalsD = dVL , where d is the firm’s debt-value target ratio.

• We can now compute the increased debt capacity due to theproject at the different dates in the future by working backwards:

Value of in year 2 and beyond

1 1

1

FCF t

L

L t t

t

wacc

FCF V V

r




• This is computed as follows. The value at the end of year 3 of the

free cashflow of $18m in year 4 is 18/(1.068) = $16.854.• Hence the debt capacity at that point is 16.854/2 = $8.427m

• The value of this project at the end of year 2 is (18+16.854)/1.068 =$32.635.

• Hence the debt-capacity is 32.635/2 = 16.317m.

• Using the same procedure, we compute the debt capacity atprevious dates.

• In order for the WACC answer to be correct, we must assume that AVCO decreases its debt according to the schedule provided here.

• Thus, one year later, it must decrease debt by 30.62 – 23.71 or 6.91



WACC method with changing Debt levels

• Suppose we don’t want to modify debt levels each year tokeep a constant D/E ratio. How do we apply the WACCmethod?

• Clearly if the D/E ratio is changing, the WACC will bechanging because the WACC depends on the D/E.

• However, we cannot compute the D/E ratio for each yearwithout knowing the value of the project because the equity

value depends on the project value (assuming that we’reaccepting the project).

• Hence a trial-and-error method must be used to establishthe WACC for each period.

• On the other hand, unless we expect conditions to changeconstantly in a predictable fashion, we probably would wantto optimize the amount of debt at a specific debt-equityratio.

• Hence the assumption of a fixed D/E ratio is reasonable.



Using the APV

• Since the RFX project has risk similar to that of the firm’s other projects,

the discount rate to be used in valuing the RFX project is the required rateof return on the firm’s assets.

• This can be computed by taking a weighted average of the cost of thefirm’s securities.

• We do not take into account the tax shield from debt because we areinitially valuing the project as if there were no debt at all. That is, we use

the pretax WACC:

We assume that effective personal taxes on debt income and equityincome are the same; else the pre-tax WACC could not be computed byusing the rD that is observed when there is debt.

Thus, if interest income were taxed at a higher rate than equity income,then the actual rD would contain a penalty due to the tax disadvantage ofdebt income for the investor. Hence in the absence of debt, the unleveredcost of capital would be lower than the pre-tax WACC.

Pretax WACC

U E D

E Dr r r

E D E D



Using the APV

• The unlevered cost of equity works out to (0.5)(10) + (0.5)(6) = 8%

• We first compute the project’s value without leverage:

• Next we find the present value of the firm’s additional tax shields due tothe project.

• Since we have already computed the firm’s debt capacity previously, wecan compute the tax shields each period as debt capacity times theinterest rate of 6% times the tax rate of 40%:

2 3 4

18 18 18 18 $59.62 million

1.08 1.08 1.08 1.08

U V



Using the APV

• In order to obtain the present value of the taxshields, we need to know the required rate ofreturn on the firm’s tax shields.

• In our case, we are assuming that the firmmaintains a constant debt-to-value ratio.

• This means that the tax shield at any point equals(Firm Value) x (target debt ratio) x (int rate) x

c

• We see from this that the risk of the firm’s taxshield is the same as the risk of the firm itself andhence the appropriate discount rate to value the tax

shields is rU.



Using the APV

• The tax shields, discounted at rU = 8% are worth

$1.63m.

• The unlevered project value is $59.62m for a

total of $61.25m.

• The present value is $61.25m - $28m = $33.25mas before.

2 3 4

0.73 0.57 0.39 0.20(interest tax shield) $1.63 million

1.08 1.08 1.08 1.08PV



Using the FTE

•

In the WACC method, we compute the value of thefirm and then subtract the value of debt, in order toobtain the value of equity.

• When valuing a project, the WACC methodimplicitly assumes that if firm value goes up, sodoes equity value. This is true in most cases, butnot in all cases.

• The FTE method values equity directly bycomputing the free cash flows to equity holders(FCFE) and discounting them at the cost of equity.

• We now use Avco’s RFX project to show that we getthe same values with the FTE method as with theother methods.

U i h FTE



Using the FTE

U i th FTE



Using the FTE

• In computing the FCFE, we note that interest payments have to be

deducted.

• Furthermore, we have to adjust cashflows by the change in debt.

• This is because if money is required to be paid out to debt-holders, it isnot available to be paid out to equity-holders.

• Similarly, if additional debt is issued, that can be used for payouts toequity-holders.

• In our example, debt capacity dropped from $30.625 in year 0 to $23.71min year 1. Hence Net Borrowing is 23.71-30.625 = -$6.915, i.e. a netpayment to debt-holders of $6.915m.

• Discounting FCFE at 10%, we get an NPV of $33.25 as before:

2 3 4

9.98 9.76 9.52 9.27( ) 2.62 $33.25 million

1.10 1.10 1.10 1.10 NPV FCFE

P j t b d t f it l



Project-based cost of capital

• If the new project has the same riskiness as theaverage projects undertaken by the firm, then theappropriate discount rate for valuing the project issimply the WACC of the firm, as discussed above.

• What if the new project has a different risk?

• In this case, we would need to find other firmswhose riskiness is similar to the riskiness of the

new project.

• We could then take the average WACC for thosefirms to estimate the discount rate for our project.

Summary: three NPV methods to account



Summary: three NPV methods to account

for financing

• Adjusted discount rate (WACC)

• Use after-tax unlevered free cash flows (with no financing effects)

• Adjust the discount rate for financing effects

• Puts everything in discount rate (usually inflexible)

• Adjusted present value (APV)• Explicitly identify the cash flows associated with financing

• Take the PV of these financing cash flows *separately*

• Add them to the “no-financing” valuation, e.g.:

ℎ − ( )

• Flow to equity

• Use cash flows to equity holders only (include financing effects)

•

U th t it th di t t

lecture_23 valuation with financing effects

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