Prof. Ken Shah MBA 515 Financial Management

Prof. Ken Shah MBA 515 Financial Management

Notes on Valuation

1.  Cash Flows & WACC

In a world with corporate taxes,

·  When discounting the cash flows at (after tax) WACC, always estimate the cash flows to the firm (all capital providers) AS IF the firm were all equity financed.

·  Using WACC as the discount rate is only appropriate for (unlevered) firm cash flows. If the objective is to find the value of the firm’s equity, subtract the value of debt.

·  It is possible to value a firm’s equity directly by estimating the cash flows accruing only to shareholders (FCFE). However, you CANNOT use the WACC to discount equity cash flows. You must use the required return on equity to discount the cash flows.

·  If using FCFE method, the valuation is strictly correct only if the debt ratio can be assumed to be relatively constant. If the debt ratio varies widely in the future, FCFE will not give the correct answer if a single Re is used. This is because Re changes as leverage changes.

·  One-shot change in leverage is not a problem. We can always unlever, and relever the Re and WACC, and then discount the cash flows at the proposed leverage.

·  Short term debt is included in computing WACC if it is a permanent, long term source of financing. If the ST debt is offset by an equivalent amount of short term income generating investments (e.g. marketable securities), then do not include it

·  Current liabilities: Usually, we net out current liabilities against current assets (net working capital) and treat NWC as an asset. In cash flow calculations, increases in NWC is outflow, decreases in NWC is inflow. However, this results in netting out short term debt. As noted above, when ST Debt is an important permanent source of financing, it should not be netted out in NWC. Instead, treat ST Debt as a separate source of (long term) financing, and show it explicitly on the right hand side of the balance sheet. The after tax interest cost of ST Debt is then one more element of the weighted average cost of capital.

·  There is nothing fundamentally different between a firm and a project. A firm is simply one big project.

2.  Estimation of Cash Flows

Free cash flow to equity (FCFE/Direct) v/s the Free cash flow to firm (FCFF/Indirect) approach:

FCFE (Direct Model): / FCFF (Indirect Model):
Revenue / Revenue
- Operating Exp. / - Operating Exp.
- Depr. Exp / - Depr. Exp.

Operating Profit

/

Operating Profit

+/- Non-Operating Rev (Exp.) / +/- Non-Operating Rev (Exp.)
= EBIT / = EBIT
- interest exp / - Taxes** (based on EBIT)
= EBT / = After-Tax EBIT
- Taxes* (based on EBT) / + Depr. Exp.
= Net Income / - Change in W/C
+ Depr. Exp / - Change in LT Assets (Capital Exp., etc.)
- Change in W/Capital / = Free Cash Flow to Firm
(All investors: Bond and Stockholders)
- Change in LT Assets (Capital Exp., etc.)
+ Change in Interest Bearing Liabilities (addition or redemption of debt) /
= Free Cash Flow to Equity

Notes:

* Taxes here are taxes on EBT, i.e., amount actually owed/paid: (EBT x T)

** Taxes here are computed on EBIT: (EBIT x T), not the actual taxes owed/paid based on EBT

If firm has excess cash and marketable securities, (i.e., more than that required for working capital/running the business), it is necessary to remove that from working capital calculation. Any income from excess cash or marketable securities is considered as non-operating income.

Non-operating income is income from any asset that is not the core business of the firm.

As noted before, if all or part of the Short Term Debt is permanent, and used to finance long term assets, it is necessary to exclude that portion of ST Debt from working capital calculation; however, include that portion in WACC calculation.

Use WACC to discount FCFF

Use cost of equity (levered Re) to discount FCFE

3.  Unlevering, relevering betas:

The unlevering and relevering of betas depend on the assumptions about i) corporate taxes, ii) whether or not debt beta is zero, and iii) whether the firm maintains a constant level of debt or a constant debt ratio. Different formulas need to be used depending on your assumptions.

In a world with corporate taxes,

VL = B + S = VU + T · B = A + T · B

Assets / Liabilities and Owner’s Equity
(Unlevered) Assets (β= βA) / A / B / Liabilities (β= βB)
Tax Shield (β = βTS) / T · B / S / Equity (β= βS)
(Levered)Total Assets
(β= βVl) / A + T · B = VL / B + S = VL / Liabilities + Equity
(β= βVl)

If you assume that the β of the tax shield, βTS = 0 and the βB = 0, then, (and only then) we can get the result,

Assuming βTS = 0 is saying that the firm will maintain a constant dollar amount of debt. However this must mean that the debt ratio (B/VL in market value terms) varies over time.

If the firm instead keeps the debt ratio constant, then we get the result,

because it would be appropriate that βTS = βA . This is because a firm that keeps constant debt as a percentage of its total assets will find that the value of its debt also varies with the market in the same way as the value of the assets. Note that in this case (1-T) term disappears.

Throughout so far, we have assumed that βB = 0, i.e., debt is ‘risk-free’.[1]

3.1. Unlevering and relevering beta when βB ≠ 0

If we assume that debt level (B) is constant, the formula is:

If we assume that debt ratio (B/S) is constant, i.e., βTS = βA, then the formula is:

The definition of assets (VL) in the above equation is the value of levered firm’s assets (including the value of tax shields). This is not the same as unlevered assets (A) on the previous page; A is the value of unlevered firm. In fact, in this case, it turns out that βVL = βA.[2]

Both of the above methods works in a world with and without corporate taxes. In a world without corporate taxes TC is zero, so just input zeros in the equations as required.

4.  Required return on firm’s levered assets:

If you want to directly estimate the required return on levered firm’s total assets (VL), you can always use:

RVL = + (B/V) x RB + (P/V) x RP + (S/V) x RS

Or

RVL = + (B/V) x RB + (S/V) x RS (if no preferred stock)

Note that this is NOT the same was WACC. It omits the (1-tax) term.

5.  An alternative way to calculate WACC at different leverage ratios: (Relevering cost of equity directly):

Step 1: Find the return on levered assets using:

RVL = + (B/VL) x RB + (S/VL) x RS

RVL is also referred to as opportunity cost of capital. Again, this is not the same as WACC.

Step 2: Estimate the cost of debt, RB at the new debt ratio and calculate the new cost of equity as:

RE(New) = RVL + (RVL – RB(New)) B/S(New)

Step 3: Calculate the WACC at the new financing weights using new RB(New) and RE(New).

Notes:

The above method does not require the explicit unlevering and relevering of equity beta.

This method does not require the assumption that beta of debt is zero.

This method does require that leverage (B/S) is constant.

This method works in a world with and without corporate taxes. In a world without corporate taxes, VL = A.

6.  A Brief Clarification on Notation:

Different textbooks use alternative notations for debt, common stock, etc.:

B = Debt = D

S = Common Stock = E

And similarly, RE = RS and RD = RB, etc.

The notation for unlevered assets, A in this document, is often represented by VU:

A = VU

[1] Strictly speaking, βB = 0 does not necessarily imply that variance of debt’s return is zero. In other words, we are not saying that the debt is totally risk-free.

[2] To see this, remember that when B/S is constant, tax shield varies with the value of unlevered assets. Hence the covariability (with the market return) of unlevered assets (A) is the same as that for levered assets (VL).