Firm Valuation Methods

Firm Valuation Methods

Discounted Cash Flow Methods

There are four  DCF firm valuation methods

• The Weighted Average Cost of Capital Method (WACC)

• The Adjusted Present Value Method (APV)

• Cash Flow to Capital Method (CFC)

• Cash Flow to Shareholders Method (CFE)

• These different approaches use different cash flows and different discount rates

Firm Valuation Methods

• The first three methods value the firm

• I.e., WACC, APV, and  CCF value the firm,

• To find the value of the firm’s equity in these  three methods, one would need to subtract the value of the net debt from the firm value (i.e., subtract debt and add back excess cash)

• Cash flows to equity method directly gives the value of equity, and not firm value

• I.e., there is nothing to subtract or add

• In all the methods share price = E / #shares

The relevant cash flows in DCF valuation methods

• Both WACC and APV methods use unlevered cash flows in valuing firms

• CCF subtracts taxes calculated on (EBIT-interest expense) but does not subtract Interest expense

• The cash flows to Equity method uses the levered cash flows

What are the unlevered cash flows?

• Intuitively, one can think of the concept of unlevered cash flows in various ways

• It can be thought of as the cash flows that are potentially available to all the investors of the firm (both to bondholders and shareholders)

• Unlevered cash flows can also be thought of as the cash flows available to the shareholders of an all-equity firm

• Since this represents funds that are available to both SHs and BHs, interest expense is not deducted from the CFs

The construction of the unlevered cash flows

• Sales-COGS-Depreciation-Selling, administrative and other expenses = EBIT

• EBIT – taxes = EBIAT = NOPAT

• An important thing to remember is that taxes are calculated on EBIT. Alternatively, it can be thought of as taxes being calculated as if interest expenses are zero

• Interest tax shields are not accounted for in this definition of unlevered cash flows

Unlevered cash flows (cont’d)

• Unlevered cash flows = EBIAT + Depreciation Capital Expenditures – Change in Net Working Capital

• In calculating NWC (=CA – CL) both current assets and current liabilities should include only operating variables and not financing variables

• Financing variables,  i.e., interest bearing or interest earning items such as Bank notes, Excess cash, should be excluded from the NWC definition

The concept of cash flows

• The general principle is that cash flows represent the amount of cash that investors can walk away with at the end of the year

• The value of a walnut tree – the concept of liquidation vs. Market value

• Why is depreciation added back?

• It is a non cash charge but it is treated as an “expense” for tax purposes

• However, the firm doesn’t “spend” depreciation charges, and subtracting it would go against the concept of cash flow

Why Are capital expenditures and changes in NWC are  subtracted?

• Remember, the concept of cash flows is the money that investors can walk away with at the end of the year

• If you run a firm, but do not spend the necessary funds to make new investments, and, do the necessary annual maintenance,

• The value of a firm as a going concern  will decline

How are levered cash flows defined?

• The starting point would be Net Income

• I.e., funds available to the shareholders after taxes and after debt service payments are made

• The taxes are calculated in the standard accounting manner, i.e., taxable income is TI = EBIT-I

• T = TI x t

• Net Income = TI - T

What is the road map from NI to levered cash flows?

• Same as the map for the unlevered definition

• Thus: Sales – COGS –Depreciation and other expenses = EBIT

• EBIT – Interest expense – Taxes = Net Income (Earnings)

• Levered Cash Flows = Net Income + depreciation – Capx – change in NWC

Comparison of NI, “NI” and EBIAT

• Since levered CF, Unlevered CF, and Cash flows to capital all have +depreciation – Capital expenditures – ΔNWC ending,

• They only differ on the basis of NI, “NI”, and EBIAT

• How do these three concepts of “income” differ?  

An example: NI vs. “NI” vs.  EBIAT

• Assume, EBIT = $100, Int. exp = $10, t=0.4

• NI for Levered CF: 100-10 = 90(TI), T = 90x0.4 =36, NI =  90 -36 = $54

• EBIAT for unlevered CF: 100-0 = 100(TI), T=100x0.4 = 40, EBIAT=100 – 40 = $60

• “NI” for CCF: 100-10 = 90(TI), T=90x0.4 =36, “NI” = 100 -36 = $64

Example (cont’d)

• The difference between EBIAT and “NI” is that “NI” includes the interest tax shield of $4, while EBIAT doesn’t  ($60 vs. $64)

• Thus, when unlevered CF (EBIAT based) is used, interest tax shields are accounted for either

• By present valuing them (APV method)

• Or, in the discount rate (WACC discount rate in the WACC valuation method )

How can the cash flows in the CFC method be interpreted?

• It can be thought of as unlevered cash flows that also include interest tax shields. Thus, it is like APV except tax shield are discounted at reu instead of rd

• If you think risk of changing D/V is captured by reu  it is ideal for transactions where D/V is changing.

• Taxes in CFC method are calculated on EBIT-I

• CFE also calculates taxes this way, but it also subtracts interest expenses and arrives at Net Income

• In the CFC method I is not subtracted, i.e., it is not net income (which is EBIT – I – T), but it is “net income” that also includes interest tax shield                                                    

The road map from this “net income” to cash flows is same as the others

WACC valuation methodology

• In the WACC valuation approach, the unlevered cash flows are discounted at the WACC  

• WACC  = wd r d(1-t) +  we r eL  

• Where are the interest tax shields accounted for in this method?

• In the discount rate: cost of debt is on an after tax basis, i.e., (1-t) in front of rd

• Cost of equity is the “levered” cost of equity  

Advantages of the WACC method

• Well-known, commonly understood

• Computationally efficient when D/V is known

• Suggested application: Standard transactions.  

• When firms intend to stick to their  target capital structure

• i.e., when their equity value increases they borrow incremental debt to keep D/V constant

• Similarly, rebalancing D/V when E declines (e.g., by retiring debt or issuing equity)

APV method of Valuing Firms 

• PV of Unlevered cash flows (i.e., the same cash flows as those used in the WACC method)    

• These UCFs are discounted at the unlevered cost of equity

• PV of the unlevered CFs are added together with

• The present value of interest tax shields, to find firm value

• It is in this latter term that the tax benefits of debt are acknowledged

• Typically, interest tax shields are discounted at the cost of debt

Advantages of APV

• Decomposes the sources of value

• Shows how much of the value comes from financing and how much from operations

• This could be very important in determining what price to bid

• When should it be used?

• APV is the correct method when D is known even if D/V varies

• Thus, ideally suited for firms where managers formulate their policies in terms of changing D during the finite period and terminal D (constant or growing perpetuity) beyond the finite period

• It may be best to use APV for the finite period and WACC for the terminal period since firms may have target D/V rather than target D

Cash flows to capital (CFC) method

• The discount rate used is the unlevered cost of equity

• Advantages:

• May be ideally suited for transactions where D/V will be changing over time and risk of tax shields can be represented by reu

• Can be used in valuing

• Leveraged Buyouts

• Project Finance transactions

Unlevered and levered cost  of equity?

• Unlevered cost of equity is the RRR of shareholders from an all-equity firm

• Levered cost of equity is the return required by the shareholders if the same firm has debt

• The beta, as calculated on the basis of stock returns, is the levered beta, and it determines the levered cost of equity via the SML equation

The connection between the unlevered and levered cost of equity

• rel = reu + D/E (reu – rd)

• rel is the levered cost of equity

• reu is the unlevered (I.e., without debt) cost of equity

• rd is the before-tax cost of debt

• D and E are debt and equity, respectively

• We have seen this equation as well as the its solution for reu  in Midland Energy Resources

• Used the equations in question for levering and unlevering of the cost of equity

What price would the buyer pay for the target if either WACC, CFC or APV is used in valuing the firm?

• Since all 3 methods finds  firm value

• As a buyer, you are buying the assets of the target, but, you are also assuming its debt

• I.e., you are buying the equity of the firm

• Thus, the most you will pay for the target is the value of the firm minus net debt it has in its balance sheet at the time of the purchase

• Debt in question is both long and short-term, but not operating liabilities (such as AP, accruals, etc.)  

• If the firm has net excess cash.  This needs to be added to the firm value to find the value of the equity

Should debt be subtracted from the value found in CFE?

• No.

• CFE already finds the value of the firm’s equity 

• And not the value of the firm

• Thus, neither the value of debt should be subtracted

• Nor the value of excess cash should be added (levered cash flows account for net interest expense (income))

The typical time horizon in DCF valuation methods

• The time horizon needs to be infinite since the maturity is of firms is undefined

• In practice, typically, near-term cash flows are estimated year-by-year and discounted to present for 5-6 years

• Or for a time period that matches the buyers’ investment horizon

• How about cash flows of years 6 to infinity?

• We find the value of future CFs beyond year 5-6, by present valuing these CFs as a growing perpetuity

Terminal value

• This is called the terminal value, and it needs to be brought from year 5-6 to present

• In any valuation the terminal value represents a significant proportion of the present value

• Thus, the buyer needs to be careful and make assumptions that are on the conservative side

• In APV, the terminal value of interest tax shields also need to be calculated and discounted to present

A valuation example using the  WACC method

• Value of the firm today = V0

•  V0 = UCF1 discounted at the WACC rate for 1 yr. + UCF2 discounted at the WACC rate for 2 yrs.+ …+ UCF5 discounted at the WACC rate for 5 yrs + (UCF6 /(WACC – g)) discounted back at WACC for 5 years

• i.e., (UCF6 /(WACC – g)) / (1 + WACC)5

Capital structure changes and CFE & WACC

• When capital structure changes, using WACC or CFE is likely to involve circularity

• As capital structure changes so does rel, (both in CFE and WACC) and weights (in WACC)

• Thus, while WACC is the most popular valuation method it has some serious shortcomings when D/V changes

• Either resulting from changes in D or due to changes in market value of E

• Of course this is not an issue if the firm constantly rebalances

Capital structure changes (cont’d)

• Furthermore, the formula that shows the connection between levered and unlevered cost of equity is true only for perpetual cash flows

• Thus, it is not useful in finding the year to year WACC and rel   

• Additional issues that should be accounted for in valuing firms

• Strategic investments – real options

• Financing or other subsidies