### Valuation and Evaluation

```Valuation and Evaluation
Basic Valuation
• Assets have value by virtue of being expected to
produce cash flows
• Cash flows to equity holders are “dividends”
– 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 operator
r ≡ 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: \$4,261
discount 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 = \$100
It 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 Debt
where: 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
• Free cash flow approach
Vt = \$0/1.1 + \$121/1.21
= \$100
= \$100
Vcoke= \$4,232/(1+7%)+\$4,507/(1+7%)2+… - \$5,356
where expected free cash flows are from pro forma and
existing debt from balance sheet
NI
4,353
4,556
+ Depr.
760
880
 DWorking 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
• 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
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