Valuation and Evaluation

Basic Valuation

• Assets have value by virtue of being expected to produce cash flows

• Cash flows to equity holders are “dividends” – including repurchases (even buyouts)– net of stock issuance (“negative dividends”)

• typically assumed to be zero

• The value of the firm’s equity can be expressed as the present value of expected future dividends

Dividend Discount Model

• Like any other asset, stock value is the present value of future cash flows

Vt = E(Dt+1)/(1+r) + E(Dt+2)/(1+r)2 + …

where: Vt ≡ equity value at time t

Dt ≡ div. (including repurchases)

E ≡ expected value operatorr ≡ discount rate

• Discount rate is equity “cost of capital”– amount the firm “promises” to attract capital– amount investors could earn in alternative

investments of similar risk– assumes you can borrow and lend at same rate

• Dividend discount model underpins all other valuation approaches

Vcoke= $3,980/(1+7%)+$4,261/(1+7%)2+…

where: dividends are 45% of forecast NI ($4,353 in ’03)repurchases are the use of excess cash’03: Div. = 45% x $4,353 = $1,959

Repurch. = $2,021; $2,021+$1,959=$3,980’04: $4,261discount rate is based on CAPM

Problems with Dividend Discount

• Dividends reflect distribution of value not creation• Dividend pay-outs are arbitrary and hard to predict• Earnings are often retained in the firm and allowed

to accumulate• Much of value comes far in the future• Therefore, often focus on ability to pay dividends

rather than dividends themselves

Savings Account Example

• Assume:– Invest $100 in a savings account with expected

return of 10%– Cost of capital is 10%– Expect to withdraw $110 in one year

• Then,

Vt = $110/1.1 = $100It is worth what you put into it

• Now assume 12% expected return– e.g., mutual fund has locked in 12% one year

bonds before rates fell

Vt = $112/1.1 = $102

• Now assume 8% expected return– e.g., mutual fund has locked in 8% one year

bonds before rates rose

Vt = $108/1.1 = $98

Other Valuation Approaches

• The firm’s ability to pay dividends is based on its cash inflows

• Therefore, other valuation approaches focus on likely cash inflows into the firm

Free Cash Flows

• Under reasonable assumptions value can be expressed in terms of expected free cash flows to the firm

• Free Cash Flows = Cash from Operations + Cash from Investing

• Free cash flows capture amount left over after covering investing

Practical Consideration

• Ultimately care about value of equity

• One way to get at that is to directly estimate cash flows available to equity; after interest

• In practice, often easier to: – estimate PV of cash flows to assets– subtract off value of debt– implies value for equity since A = L + OE

Implementation

• Assets:– Asset value is PV of free cash flows, before

interest– Use free cash flows (operating minus investing)– Add back after tax interest (like ROA)

• Asset values setting aside financing choices

– Discount rate is technically weighted average cost of capital—more on that in finance

• Liabilities:– PV of cash flows to existing debt = book value – PV of cash flows on future debt = 0 forecast cash flows to assets

• subtract BV of existing interest-bearing debt

Vt = E(AFCFt+1)/(1+r)+E(AFCFt+2)/(1+r)2+…- Existing Debtwhere: AFCF is FCF adjusted for after-tax interest on

existing debt existing interest-paying debt is subtracted

•In the preceding example expected dividends = expected cash flows

Vt = $110/1.1 = $100

• E.g., you invest $100 in a mutual fund which invests for 2 years at 10%

• At the end of year 1, the fund borrows $110 and pays you a dividend of $110– dividends = $110– free cash flows = $0

• At the end of year 2, the investment pays off $121 and the fund repays the debt– dividends = $0– free cash flows = $121

• Dividend approach

Vt = $110/1.1 + $0/1.21 = $100

• Free cash flow approach

Vt = $0/1.1 + $121/1.21 = $100

Vcoke= $4,232/(1+7%)+$4,507/(1+7%)2+… - $5,356where expected free cash flows are from pro forma and existing

debt from balance sheetNI 4,353 4,556

+ Depr. 760 880 Working Cap. (CA-CL) -210 -100- Cap. Exp. -950 -1,100+ Change in Other Liab. +113 +107+ Change in Def. Taxes + 20 + 19 + Adj. Int. (.77 x 199) +145 + 145

4,232 4,507

Problems with Free Cash Flows

• Free cash flow forecasts are generally not available

• Generally must compute statement of cash flows from:– earnings forecasts– balance sheet assumptions

• Much of value comes far in the future

Balance Sheet Valuation

• If estimated values of assets (& liab.) are available, they equal PV of expected cash flow

• Then, can use asset and liability values to value of the firm

Vt = Asset Value - Liability Value

• E.g., invest in a mutual fund holding an asset returning 10% and no liabilities

• Market value of the asset being held is $100 if it is expected to pay out $110 in one year

• Therefore, you can rely on the market value of the asset held to value the firm

Approach

• Start with existing balance sheet• Revalue assets that are likely misvalued

– E.g., Coke’s investment in bottling companies

• Add assets that have been excluded– E.g., Coke’s brand

• Do the same with liabilities– Typically less of an issue

• Back into the equity value

Vcoke= (Asset book values + investment security additional values + brand values) - Liability book values

Vcoke = ($24.5B + $3.5B + $70.5B) - $12.7B

= $85.8B

Problems with Balance Sheet Method

• Many assets don’t have ascertainable values – PP&E, Intangibles, etc.

• Many assets have higher values to that firm than to other firms– Customized PP&E, Inventory, etc.

• Doesn’t work well for Coke– Too many hard-to-value assets