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VALUATION BASICS
There are three basic approaches to asset valuation in a free enterprise
economy. The first (the asset value) assumes the asset is worth its book value (what
shows on the annual report or other corporate financial reports), the cost of
recreating it (replacement value), or the returns from liquidating it (liquidation
value). The second (the market value) assumes that an asset is worth what someone
else will pay for it. The third (the income value) assumes that the asset’s value is the
sum of the benefits it will produce during its life. There are other ways of
evaluating the attractiveness of an asset, and these ways will be considered later.
We will not spend much time discussing the asset method except to note that,
in the case of companies, divisions, joint ventures, and the like, the asset value
includes the value of intangibles such as patents, copyrights, trademarks, and good
will as well as the value of tangible assets such as accounts receivable, inventory and
fixed assets. Both tangible and intangible assets are usually estimated at their market
or replacement values, but establishing market value for intangible assets represents
a significant challenge. In many cases, the income or market methods may be used
to value intangibles. In turnaround or bankruptcy situations, as well as some
ordinary lending situations, liquidation value is calculated.
THE INCOME METHOD
The present value (PV) model discounts (reduces) the free cash flow (FCF)
and terminal value (TV) expected from an investment. When net present value
(NPV) is wanted, the initial outlay (Co) is subtracted from the PV. FCF and TV are
discounted because the promise of future payments is worth less than cash in hand
now. If NPV > 0, or PV > Co, the asset will make an economic profit (called
economic rent or just rent) and is seen to be financially attractive although not
necessarily strategically appropriate.
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FCFs may take a number of forms with the PV calculated in different ways
(assuming end-of-period payment). The notations are as follows:
i = discount rate or cost of capital.
g = future growth rate of FCF
1. An annuity where a constant payment is offered in perpetuity: FCF / i
2. A growing annuity in perpetuity: FCF / (i – g)
3. An annuity in perpetuity beginning in some future period, say t = 4:
(FCF4 / i) / (1+i)3
FCF4 / i discounts the FCF to the beginning of period 4 / end of period 3.
(1 + i)3 discounts it back to the end of time period 0 / beginning of time
period 1.
4. A growing annuity in perpetuity starting in some future period, say t = 4:
FCF4 / (i – g) / (1 + i)3 OR FCF4 / (i * (1+i)3).
Often, FCF is forecast using the previous period’s FCF. Then [FCF3 *
(1+g)] = FCF4.
5. FCFs vary from time period to time period ending with a final value, the
terminal value (TV). This is called a two-stage model. Three and fourstage models may be constructed using different time periods and
different discount rates:
PV = FCF1 + FCF2 + FCF3 +….+ FCFn
(1 + i)
Where:
(1 + i)2 (1 + i)3
(1 + i)n
+ TVn
(1 + i)n
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FCF = free cash flow to capital consisting of earnings before interest and
after taxes (EBIAT) plus depreciation minus change in working
capital minus new investments. These are funds available to pay
suppliers of debt and equity during the period covered. An
alternative calculation is EBIAT minus change in working capital
minus change in net investments (change in investments after
accumulated depreciation is subtracted from the periods being
studied). The latter is helpful if the data do not show depreciation
and gross investment separately.
i
= cost of capital, opportunity cost of capital, hurdle rate, or discount
rate. The rate discounts FCF for liquidity preference (real rate of
interest), inflation, investment (or maturity) risk, and market risk.
1,2,3 = time, usually in years, beginning at time 0 with the designation Co.
Often, the assumption is made that all cash flows occur at the end of
the time period. However, you can calculate PV when the cash
flows occur at different time periods by manipulating the power. If
you use the more reasonable mid-year convention (all cash flows
occur during the middle of the year) and your beginning date is the
end of a year, you would take one plus the discount rate to the
power of 0.5, 1.5, 2.5 and so on.
n
= the last period of the planning horizon (often 5th or 10th year,
or when competition is expected to reduce future NPV to
zero).
TV
= terminal value; value at the end of the planning horizon. The
growing annuity in perpetuity discussed in (4) above is often used
to estimate this value. This perpetuity model is generally referred
to as the Gordon Growth Model.
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The strengths of this method are its emphasis on costs and benefits and its rigor. The
major weakness is the requirement for forecasting.
MORE ON FREE CASH FLOW
FCF for debt is the interest paid on a periodic basis—monthly, quarterly, biannually, or annually. FCF to equity holders (common and preferred stock) is the
dividend payment plus or minus the capital gains or losses in the market value of the
stock over the given time period. You must also account for stock splits when they
occur by multiplying the dividend and the stock price after the split by the amount of
the split. If the stock were split two for one during the period measured but prior to
the dividend being issued, you would multiply the dividend and the end-of-period
stock value by two. If the dividend had already been paid, you would only multiply
the stock value by two.
Developing a forecast of company FCF requires an understanding of what
income statements, balance sheets, and cash flow statements really mean, how they
are constructed, and how they are forecast. An income statement calculated on the
accrual basis shows how much it costs to produce goods and services that are
shipped (producing revenues) during a specific period of time. Typically, the
moment a product leaves the shipping dock (or a service is provided), or the product
arrives at its destination (FOB Destination) a sale is recorded. If the sale is on credit,
an account receivable is created. Exceptions to the shipped assumption include
progress payments on large items under construction (such as airplanes) and on
services provided over time.
Income Statement Items
The income statement used for financial analysis differs somewhat from the
income statement found on the usual annual report. For purposes of discounting,
financial analysts often use earnings before interest after taxes (EBIAT) rather than
net income. They separate operating cash flow from financing cash flow, while the
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preparers of the income statement do not. Financial analysts separate operations and
finance because the effect of interest is accounted for in the discount rate (discussed
below) and should not be double counted. Table 1 demonstrates the difference.
TABLE 1. ACCOUNTING AND FINANCE DIFFERENCES
Time Period
Time Period
1
1
Accounting
Finance
Revenue (Net Sales)
1,000
1,000
Cost of Goods Sold
(500)
(500)
500
500
(150)
(150)
350
350
(100)
(100)
250
250
Gross Profit
Operating Expenses
EBITDA
Depreciation/Amortization
EBIT
Corporate Taxes @ .40
(100)
EBIAT
150
Interest
(50)
Profit Before Taxes
200
Corporate Taxes @ .40
(80)
Interest Tax Shield
Net Income (PAT)
(50)
20
120
120
The interest tax shield (ITS) is found by multiplying interest bearing debt * cost
of debt * marginal tax rate. The marginal tax rate is the incremental tax you pay
(expressed as a percentage) because you choose to make the investment. In the
above illustration, it is 40%.
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Balance Sheet Items
The balance sheet shows the book value of assets required to support the
sales revenues and how those revenues are financed by liabilities and equity (net
worth).
In finance, working capital is the difference between current operating assets
(usually required operating cash, accounts receivable, and inventory) and current
operating liabilities (usually accounts payable to vendors or ‘the trade’, accrued
expenses such as payroll expenses and other costs that have been incurred but not yet
paid, and accrued taxes). Excess cash is excluded since it is not essential for
operations and it is the operating entity that is being valued. Current interest-bearing
debt usually is not included since it is not part of the operations of the company
(although, as mentioned above, there is significant disagreement about whether all
current interest bearing debt should be excluded). For our purposes, we will assume
that all interest-bearing debt is excluded. Non-operating assets and liabilities are
valued separately and added to the value of operating assets.
Tangible assets with a life of more than a year are depreciated as of the time
they are put into use. (However, current tax law allows you to expense up to
$500,000 in tangible assets per year.) Intangible assets such as patents, copyrights,
trademarks, and service marks are amortized. Goodwill is the difference between
the firm or project’s market value and the tangible and intangible assets that can be
valued individually. Depreciation and amortization may be deduced for tax purposes
with the exception of goodwill. Net tangible assets are assets after accumulated
depreciation and amortization.
The book value of an asset, liability, or equity is not usually the same as the
real or market value. Adjustments need to be made before an analysis is undertaken.
Accountants usually value balance sheet items at cost or market; whichever is
lower—although this is changing. Financial analysts use the market values of these
items.
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Sometimes, it is enough to assume that book values equal market values, but
exceptions occur when, for example, some accounts receivable are not collectable,
inventories are outdated or damaged, fixed assets are rapidly depreciated below their
actual market value or have become obsolete. On the opposite side of the balance
sheet, bond and preferred stock values change with the market. Book values of
common stocks are often significantly different from their market values.
Free Cash Flow (FCF)
A cash flow statement shows how cash flows into and out of an organization
over a time period. Financial analysts are interested in cash flow because only cash
can be used to pay bills, purchase assets, pay dividends and interest, or pay off debt
and repurchase equity. You cannot pay shareholders, creditors, or anyone else with
profits.
There is a difference between profits and cash flow. Not appreciating this
difference has cost many people their businesses. Just because the company is
making an adequate profit does not mean that it will survive and prosper. It must
also provide for new capital investment (CAPX), working capital (the difference
between current operating assets and current operating liabilities), interest and
dividends.
Cash flow is a general term with several definitions. FCF is Earnings before
interest after taxes (EBIAT) + Depreciation, Amortization of intangibles except good
will, Deferred Taxes, Write-downs, and Other Non-Cash Charges – Periodic
(annual) change in operating working capital – Periodic (annual) change in gross
investments (CAPX) - Periodic (annual) changes in capitalized operating leases –
Investment in Goodwill. The worth of capitalized leases is found by calculating the
present value of future lease payments.
Depreciation, amortization of intangibles except good will, and other noncash charges, being tax deductible, are subtracted from revenues just like other costs
to get EBIAT. However, they must be added back because they are non-cash. An
alternative when only net investment is available is: EBIAT – Periodic change in
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operating working capital – Periodic change in net investments (after accumulated
depreciation, amortization, and other noncash charges) – Periodic changes in
capitalized operating leases – Investment in Goodwill. Textbook writers usually
simplify the free cash flow items by limiting them to EBIAT + depreciation –
changes in operating working capital – CAPX.
An example calculation of FCF is shown in Table 2, beginning with the
calculations of change in working capital and CAPX.
TABLE 2. CALCULATING FREE CASH FLOW
Time Periods
0
1
2
Operating Cash
25
30
Accounts Receivable
80
90
Inventory
70
80
0
0
Accounts Payable
35
40
Accrued Expenses
45
50
Accrued Taxes
8
10
Other Non-Interest Liabilities
0
0
Current Operating Assets
Other Operating Assets
Current Operating Liabilities
Operating Working Capital
40
87
100
Change in Working Capital
40
47
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(500)
(100)
(50)
500
600
650
(100)
(225)
500
425
CAPX (Capital Expenditure)
Total Capital Expenditure
Accumulated Depreciation
Net Capital Expenditure
500
9
EBIAT
0
*150
200
*100
125
(40)
(47)
(13)
Minus Change in CAPX
(500)
(100)
(50)
Equals Free Cash Flow
(540)
103
262
Add Back Depreciation
Minus Change in Working Capital
*From Table 1
ALTERNATIVE FREE CASH FLOW CALCULATION
Time Periods
0
1
2
EBIAT
0
*150
200
(40)
(47)
(13)
Minus Change in Net CAPX
(500)
0
75
Equals Free Cash Flow
(540)
103
262
Minus Change in Working Capital
Things to Remember in Calculating FCF
Some of the challenges and important points to remember in forecasting and
evaluating FCF include the following:
1. Separate fixed costs from variable and semi-variable costs if possible.
Variable costs can often be forecast using ratios from past data. Sometimes fixed
costs can be forecast with ratios if you make the assumption that the company is
always working up to capacity.
2. Use iteration (including Solver) to estimate borrowing requirements and
interest costs.
3. Add profit after taxes to retained earnings to get next period’s equity.
Actually, other factors such as gains or losses in the sale of assets (including
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currency transactions) and dividend payments will affect retained earnings also.
Using the profit to sales ratio to forecast changes in retained earnings seems to be a
common mistake with those new to forecasting.
4. Use only relevant costs and benefits when estimating free cash flow.
Relevant costs and benefits are future costs and benefits that come about only
because an investment opportunity is chosen. Past costs and benefits are sunk—the
money is already spent (benefit received) and cannot be retrieved by choosing one
alternative over another. Those costs and benefits that will occur whether an
alternative is chosen or rejected cannot be relevant to that alternative. Ask yourself:
what changes in the flow of cash will come about if I select this alternative? Those
changes should include opportunities created (opportunity benefits such as options to
invest in other markets that wouldn’t be available otherwise) and opportunities lost
(opportunity costs such as cannibalizing the market share of products already
produced by your company or the opportunity to use existing assets in more
profitable ways than your alternative provides.)
5. Use only changes in working capital and fixed assets. Financial analysts
are interested only in cash inflow and outflow for each period being forecast.
6. Make comparisons among projects only when the discounted costs are
equal among them or the discounted benefits are equal. It is misleading to compare
the return from an investment costing $1 million and returning a NPV of $200,000
with an investment costing $2 million and an NPV of $250,000 unless you know
what the return will be from an additional $1 million spent in conjunction with the
first investment.
7. Avoid consistent bias in the forecast. Behavioral finance teaches that
there are many human factors that may bias a forecast so that it is no longer a true
estimate. Some of these ways include:
A. Risk aversion to a sure loss (taking big risks to avoid a sure loss).
B. Excessive optimism or pessimism.
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C. Too much or too little confidence in your ability, knowledge,
information, or control over future events and conditions.
D. Confirmation bias: recognizing only events and conditions that
confirm your original assumption.
E. Representativeness: assuming that the average of the past is
representative of the future. This is really important. You use past actual data to
forecast your expected result, and then assume that the expected result is the
required result. In all of this you imply that the market values of the past data
are correct, when, as Franciso de Orsuna (1497–1541) said in the Third Spiritual
Alphabet: "…value reflects only our opinions and not the true worth of the things
themselves." Representativeness stretches credibility, but it may be the only thing
you have unless you can adjust future expectations and requirements using your
experience and common sense and the views of others you respect.
F. Anchoring and adjustment: placing too much emphasis on one
piece of information—an event or statistic (the anchor). You interpret or adjust
other information in light of that event or statistic. An example is using your
company’s overall cost of capital as a basis from which to adjust upward or
downward the risk factor for a project.
G. Over/under reliance on intuition.
THE DISCOUNT RATE
Discounting FCF by the cost of capital or hurdle rate percentage lowers the firm’s
best estimate of an asset’s cash flow to account for four factors that do not appear on
the financial statement of the firm. These factors include the preference investors
have to remain liquid (liquidity preference), inflation, maturity risk, and market risk.
Maturity Risk, Liquidity Preference, and Inflation
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The financial theory used in practice measures the discount rate as the sum of
a risk-free rate plus a percentage factor for market risk. Analysts usually assume
that the “risk free” rate is the yield of a constant maturity 20-year U. S. Treasury
bond. Twenty years is used because many investments have long lives and the bond
accounts for that fact. However, the bond is not completely risk-free because its
value can vary with changes in the economy. Variations in the bond’s value are
referred to as either investment or maturity risk.
Liquidity preference (often referred to as the real rate of interest) exists for a
number of reasons: the possibility of more attractive opportunities appearing in the
future; the wish to save; or the desire to spend funds now on attractive consumer
items. An investment must promise some return to encourage investors to provide
capital in light of these factors. The required return is relatively low and stable over
time but varies among countries with differing propensities to save.
Inflation reduces the purchasing power of the currency. A dollar today is
worth more than the valid promise of a dollar one year from now because that future
dollar will buy fewer goods and services. Financial managers usually approximate
inflation and liquidity preference by using the U. S. Treasury bill or bond yield as a
risk-free rate.
The two influence one another and therefore cannot be added together along
with maturity risk to obtain the risk free rate of interest. To find the risk free rate of
interest, multiply 1 + the real rate of interest times 1 + the expected inflation rate and
subtract 1. Multiplying the two rates together (simply multiplying fractions), results
in an erroneous number. For example, suppose the real rate of interest is 2% and the
expected inflation rate is 3%. You would expect the combination to be around 5%.
If you multiply .02 * .03, you get .0006 or .06%. If you multiply 1.02 * 1.03 and
subtract 1, you get .0506 or 5.06%. To that, you add the maturity risk.
Companies and investors discount cash flows for maturity risk, liquidity
preference and inflation because money has a time value. If a company must invest
$1 million in the project at the end of time 0, it cannot use the funds for any other
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purpose. If it may invest instead at the end of year 1, it can purchase a safe U.S.
Treasury security at the beginning of the year and earn “risk-free” interest before
investing. If Treasuries yield 5.5%, the company would need to set aside only
$947,867 in the project at the beginning of year 0, since that amount at interest
would provide the $1 million at the end of the year:
$1 million / (1 + .055) = $947,867
$947,867 + ($947,867 * .055) = $1,000,000
$947,867 X (1 + .055) = $1,000,000
FCF is often forecast on a real or non-inflationary basis. If inflation is not
removed from the discount rate, the FCF will be discounted more than is warranted.
To remove the effect of inflation, divide the risk free rate by 1 + expected inflation.
If the risk free rate is 5.5% and the expected inflation is 3%, divide 1.055 by 1.03
and subtract 1 to obtain 0.0243. The 0.0243 (2.43%) is the rate of interest that
accounts for liquidity preference and the maturity risk. Note that (1+. 0243) * (1 +
.03) minus 1 is equal to 0.055.
Dealing with Risk
Managers generally create a “best estimate” forecast of sales, profits, and
cash flow for operating and capital budgeting purposes. They forecast on the belief
that there will be a 50% chance that the actual numbers will be greater (or less) than
the forecast. Risk is generally defined as the extent of expected variation around the
forecast. The more the variation, the greater is the risk. It is measured by the
variance or standard deviation using data from the past experience of the company or
similar companies, past projects, or by intuition.
Most managers and firms are risk averse. To bet large sums on a coin toss is
considered imprudent. Furthermore, companies operate in an uncertain world where
projects, like tosses of unfair coins, have outcomes impossible to predict with
statistical precision.
Equity Risk
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The textbooks and industry practice indicate that investors usually develop
percentage factors for discounting using the capital asset pricing model (CAPM) or
similar build-up models. A factor for risk is added to the rate being used as the
measure of future liquidity preference and inflation to “build it up”. It is found by
comparing company returns to the returns of a large number of firms such as those
represented in the Standard and Poor’s (S & P) 500. The S & P 500 firms act as a
proxy variable for risk in the market.
Beta (β) measures the extent to which a firm’s periodic shareholder returns—
dividends and stock splits plus capital gains or losses divided by first-of-period stock
prices—relate to and vary with the average periodic shareholder returns of the
representative market (proxy variable). If a company’s stock varies more than the
average of the proxy, β is greater than one. The firm is riskier than average. A β of
one indicates that the firm is of average risk compared with the proxy; a β of less
than one indicates less than average risk. Beta is multiplied by the risk factor in the
Capital Asset Pricing Model (CAPM) and the result is added to the risk free rate to
obtain the cost of equity capital.
The β accounts for systematic risks only—those ups and downs in value
caused by business cycles, interest rates, foreign exchange fluctuations, and sociopolitical changes that are reflected in the proxy. Those factors can affect most or all
firms for good or ill.
Unsystematic risks—risks such as the company’s loss or gain of a major
customer, loss of a key employee or serious competitor, or a boom or bust in the
firm’s industry—are ignored. The idea is that, in general, most investors are well
diversified so that these unsystematic losses encountered by one firm or industry in
their portfolios are offset by unsystematic gains in others. Be careful; it is tempting
to include non-systematic risk factors in the discount rate. Bad practice. It should
be calculated separately when appropriate. Unsystematic risks include country
risks—those special risks associated with doing business in a country outside the
U.S.
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Consistent negative or positive forecasting bias discussed above is also
ignored and should be dealt with in the FCF rather than the discount rate. To do
otherwise is to violate the assumption that the FCF is a 50-50 estimate and the
discount rate measures only systematic risk.
Entrepreneurs and others whose entire net worth is invested in one or a few
companies are clear exceptions to the rule as they face systematic and unsystematic
risk as well as possible consistent forecasting bias. The message is clear: don’t put
all your eggs in one basket. But sometimes diversification is not possible and a
company specific risk premium (CSRP) should be added to the discount rate.
Finally, smaller companies and companies in riskier industries tend to have
higher capital costs than large companies in stable industries. Additional percentage
points should be added to the discount rate in most firms to account for size.
The Treasury rate plus beta times market risk is the “i” or cost of equity (Ke)
in the PV model above when the firm is financed entirely by common stock. If the
risk free rate is 5.5%, the average return on S&P stocks is 11.5%, and the company’s
beta is 1.2, the “i” or Ke would be 5.5% + 1.2 * (11.5% - 5.5%) or 12.7%. In this
case the equity beta is also called the asset beta. Since there is no debt involved it
measures the total systematic risk associated with the assets. Size and unsystematic
risk factors are added to the “i” to calculate the Ke where appropriate.
Debt Risk
Debt, like equity, can be measured by CAPM. However, debt usually is
measured by its yield to maturity, the internal rate of return (IRR). The price of the
bond is the initial outlay, interest payments represent the FCF, and the principal is
the terminal value. The rate that equates the outlay with the inflow from interest and
principal repayment is the IRR. It is found by iteration, which requires a calculator,
a computer, or a great deal of patience.
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The value of a debt security will vary over time depending upon market
interest rates. If market interest rates on a similar security change, you substitute the
new interest rate for the old and recalculate the PV. If the new interest rate is higher,
the value of the bond (PV) will decrease; if lower, the value will increase. For
example, if you bought a three year $1,000 bond last year with an interest rate of
4%, and sellers are now offering 5% returns on two year bonds similar to yours, your
bond would be worth [$40 / (1 + .05)] + [($1000 + $40) / (1 + .05)2] = $981.41.
In addition, it is usually the case that the longer the maturity period, the
higher is its interest rate because the risk of default (non-payment) is greater and
because interest rates are more likely to change over a longer time period than a
shorter period. This is why interest rates increase at a geometric rate rather than an
arithmetic rate. However, the yield on short-term bonds may exceed the yield on
long-term bonds if investors think interest rates will drop sufficiently in the more
distant future. Bonds that are not secured by the assets of the firm carry a higher
interest rate because unsecured creditors are paid only after secured creditors in the
event of bankruptcy. Bankruptcy lawyers and consultants, employees, and the
government are paid first; common shareholders are paid last.
Organizations such as Moody’s and Standard and Poor’s (S&P) rate the risk
of bonds using grades. These range from Aaa (Moody’s) and AAA (S&P) to C, with
triple A being the highest. Bonds rated triple B and above are considered investment
grade; those below, as speculative or junk bonds. As a rule, the higher the rating the
lower is the yield. Incidentally, bonds are usually sold in units of $1,000, but are
quoted with the last zero removed. Interest is usually paid bi-annually.
Weighted Average Cost of Capital and Other Adjustments
When debt is used as part of the company’s financing, its cost (Kd) is
included on a weighted average basis. The percentage of debt times its after-tax cost
is added to the percentage of equity times its cost (Ke) to develop a weighted
average cost of capital (WACC). The after tax cost of debt is used because debt,
unlike equity, is tax deductible. Therefore, the actual cost of debt to a company is
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not what the lender charges, but what the company actually pays after the tax
deduction (1 – T) is taken. The formula is shown as:
i = WACC = [Kd * (1 – T) * %d] + (Ke * %e)
Again, the “1 + i” is compounded to account for the belief that risk grows
geometrically over time rather than arithmetically. For example, period 2’s discount
factor would be (1 + i)2 or (1 + i) * (1 + i). Given a discount rate of 10%, year 2’s
discount factor would be multiplicative (1 + .21) rather than additive (1 + .20).
It is entirely possible that risk associated with expenditures will change at
various times during an investment. An initial investment in research and
development and plant and equipment may occur over a long time period and be
unaffected by systematic risk. In that case, the proper discount rate for the
investment and its depreciation is the riskless rate of interest. If systematic risk is
involved, the riskless rate should be reduced, possibly even to less than one, since
the cash flows involved are outlays. When the project is underway and FCFs are
positive, the discount rate should change to reflect market risk. Finally, the
systematic risk associated with the terminal value may be altogether different and
require another discount rate especially for it.
If risk or inflation is expected to be different in subsequent periods, say .10 for
period one and .15 and .09 for periods two and three, the discount factor for period
two will be (1 + .10) * (1 + .15) = 1.265 and for period three (1 + .10) * (1 + .15) *
(1 + .09) = 1.379.
It is generally assumed that all cash flows occur at the end of the period
being measured, including the cash flow in time period 0. A more realistic
assumption is that cash flows occur in the middle of the year. To account for this,
cash flows are discounted using different powers. If the investment is made at the
end of time period 0 and you are measuring as of that time period, time period one’s
discount would be (1+i)0.5, time period two’s would be (1 + I)1.5, and so on. If the
investment were made at the end of September/beginning of October and cash flows
were assumed to come in the middle of the measured period (mid-November), the
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first period’s power would be .126 (46/365). In the following year the FCF would
come in the June/July period and the power would be .126 + .5 or .6126. The next
year would be 1.6126, the following year .6126, and so on. It is not possible to use
IRR in these cases because the intervals between periods are not the same and IRR
assumes equal periods. In these cases, use the XNPV and XIRR features of Excel
that are explained at Excel Help.
Since debt is tax deductible and cheaper than equity, financial theory
following Modigliani and Miller (M&M) maintains that the overall cost of capital
tends to drop as tax-deductible debt is added up to the point where bankruptcy risk
becomes an important factor due to overreliance on debt. In the case of debt, interest
and return of capital must occur when due, even when cash is hard to come by. The
alternatives are debt restructuring or default. On the other hand, dividends to
common stockholders may never be paid; dividends to preferred stockholders may
be delayed.
For various kinds of investments made by the firm, many modify their cost of
capital by adding or subtracting percentage points to account for differentials in risk.
This is done subjectively (risking an anchoring and adjustment bias). Alternatively,
financial managers may compare the investment to the cost of capital associated with
pure play companies—companies where 75% or more of the products or services are
comparable to the investment being contemplated. For example, a highly diversified
company that includes a restaurant chain might value the chain using the median or
average cost of capital for companies in the restaurant industry only. Modified costs
of capital derived subjectively or by use of pure play firms are referred to as hurdle
rates or risk adjusted discount rates (RADRs).
There are numerous other methods for evaluating risk. The 5 C’s of Credit
are popular, especially with lenders. Lenders evaluate: Commitment (willingness to
pay interest and principle when due); Capacity (future cash flow available to pay
debts); Collateral (assets available to provide security to the creditor); Conditions
(state of the economy); and Covenants (conditions on the credit such as the
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minimum level of debt / equity and working capital maintained by the company, and
limits on certain spending without creditor authorization).
Forecasting an optimistic and pessimistic level of sales to test the effects on
profitability is another way to test risk. Scenario analysis, where profits and NPV
are examined assuming different key events and conditions occur or fail to occur, is
related to optimistic/pessimistic forecasting and provides insights into risk.
Evaluating financing risk, market risk, and operating risk is common.
Financing risk (the extent of leverage, or gearing as it is called in the UK) may be
evaluated by the use of debt / equity, debt / total assets, EBIT / interest, and similar
ratios.
Market risk can be examined by estimating the sales level required to reach
profit breakeven (where profit just equals 0). To get that breakeven you divide total
fixed cost (FC) by 1 minus the ratio of variable cost (VC) per unit of output to price
(P) per unit. The denominator (1 – VC per unit / P per unit) equates to the fraction
FC per unit / Price per unit, but is used instead because it is generally easier to
determine the variable costs on a per unit basis. Alternatively, you can divide the FC
by 1 – Variable Costs / Sales. Variable Costs / Sales is defined as the contribution
margin.
The greater the fixed cost (operating risk), the greater the sales must be to
reach profit breakeven. The degree of operating leverage (DOL) is found by the
equations: DOL = % Change in Profits / % Change in Sales. Studies have shown
that companies with high fixed costs (high operating leverage) show relatively large
DOLs, so that a relatively small change in profits requires a relatively large change
in sales.
Firms may also adjust for risk by using certainty equivalents (CEs).
Managers forecast lower but practically certain returns in place of higher but
uncertain best estimate returns. These returns are discounted by the riskless rate of
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interest to take into account inflation and liquidity preference. Thus, risk is treated
in the numerator instead of the denominator in estimating PV.
A simple mathematical formula may be used to translate a CE free cash flow
into a best estimate, demonstrating that one is directly related to the other. Thus, PV
= CE / (1+i) = BE / (1+k), where PV = present value, CE = certainty equivalent cash
flow, BE equals expected or best estimate cash flow, i = risk free rate, and k =
RADR or cost of capital including risk. If they are not equal in a practical
application, it means that the person who forecasts CE has a different risk propensity
or inflation forecast than the market.
The cost of capital or hurdle rate may be thought of as a way to estimate the
“real” cost of capital (not the same as the “real” rate of interest). However, the real
cost of capital is actually its opportunity cost, the return available from a financial
security such as a stock with a similar risk. You forego the return on that financial
investment if you invest in a project, plant, equipment, or working capital. If your
next best investment opportunity in the financial markets (an opportunity with
similar risks) would earn you 10%, your discount rate should be 10%. You need to
be careful making this comparison because a stock with similar risk traded on an
exchange has almost immediate liquidity, whereas the investment may not be able to
be sold rapidly. As a result, you must apply a discount for lack of liquidity to the
non-financial asset investment.
MORE ON TERMINAL VALUE
PV should include the value of the fixed tangible and intangible assets and
working capital (if any) at the end of the horizon period. That value may be its salvage
value or other market value determined by an estimate of the future selling price of
similar assets (see Market Value above). If there is no depreciation left on the asset—a
piece of equipment or building, for example—the full salvage value is taxed. The tax is
subtracted from the salvage value to determine the TV. If there is depreciation remaining
and it exceeds the selling price, the firm can claim the difference as a capital loss and
deduct the tax rate times the capital loss from the selling price to obtain the TV. If
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depreciation is less than the selling price, there is a capital gain. The tax rate times the
capital gain is subtracted from the selling price to determine the TV. The capital gains
tax rate is the same as the corporate rate. The lower capital gains rate enjoyed by
individuals is not available to corporations.
Alternatively, the TV may be found by using the perpetuity model: FCF divided
by the discount rate (i). If the FCFs beyond the horizon period are expected to grow at
some constant percentage rate (g), the formula becomes FCF * (1+g) divided by (i – g).
FCF * (1+g) is the FCF that is expected in the next period. The next period is used
because the NPV formula already accounts for the FCF at the end of the horizon period.
As alluded to earlier, his growth formula is sometimes referred to as the Gordon Growth
Model after the person who came up with it. Always remember to discount the TV to the
PV after it is calculated.
OTHER WAYS TO EVALUATE INVESTMENT OPPORTUNITIES
USING
PRESENT VALUE ANALYSIS
Alternatives to PV and NPV include the internal rate of return (IRR), the
modified internal rate of return (MIRR), the profitability index (PI), and the payback
period. It is important to note that different countries exhibit different risk premiums
requiring adjustments in the cost of capital
The most popular alternative to NPV is the internal rate of return (IRR),
discussed earlier. IRR is that percentage discount rate that equates cash outflows with
cash inflows. IRR will always be greater than the discount rate if NPV is positive and
smaller if NPV is negative. IRR will equal the discount rate when NPV = 0. It provides
what many executives see as an estimate of the return on investment in percentage
form—a subjectively preferable way to evaluate return on investment.
There are several downsides to the use of IRR. If the free cash flows are
reinvested at a rate different from the IRR (as is probable), the actual return will be
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different from the calculated IRR. Also, if there are two or more changes in the cash
flows from plus to minus, there may be two or more IRRs. Selecting the “real” IRR
becomes problematic. Finally, IRR cannot distinguish among the sizes of investment
alternatives. An investment with a high IRR may have a low NPV compared with a
second investment because the first investment and returns involved are very low relative
to the second.
Modified internal rate of return (MIRR) overcomes the first two of the problems
with IRR. MIRR compounds positive cash flows forward to the terminal value at a
reinvestment rate and discounts the total back at the hurdle rate. It is necessary to
forecast a reinvestment rate for the positive cash flows to use this method. Both IRR and
MIRR are available on Excel.
The profitability index (PI) is found by dividing the NPV by the investment
required; alternatively, by dividing the PV by the investment required. If the former is
positive, the investment is financially attractive; if the latter is greater than one, the
investment is financially attractive. The PI indicates which of several projects will give
the highest NPV per dollar spent. As an index, however, it cannot assure that the projects
it compares have equal costs or equal benefits as discussed on page 13 above.
The payback period measures how long in days, months or years it takes to return
the initial investment. The returns may or may not be discounted. The obvious limitation
to this method is that what happens beyond the payback period is not included. Two
opportunities may have a three-year payback (seen to be equal) with one earning $1
million in year four and the other being closed down in year four.
COUNTRY ANALYSIS
Evaluating investment opportunities in different countries requires special
attention to exchange rates, inflation, and country productivity growth—the value over
time of your currency compared with other currencies. Laying aside changes in
productivity, the easiest way to estimate NPV from an investment in another country is to
forecast FCFs in that country’s currency using Country B’s inflation rate. You then
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discount by a rate that takes into account Country B’s inflation rate compared with
Country A. The formula for this adjustment is:
{[1 + Country A’s discount rate) * (1 + B’s inflation rate)] / (1 + A’s inflation rate)} –
1.00.
You apply this discount rate to cash flows denominated in Country B’s currency to get
PV in Country B’s currency. You then divide Country B’s PV by the exchange rate
(Country B currency / Country A currency) to get PV in Country A’s currency.
THE MARKET METHOD
Fair market value (FMV) as defined by the Internal Revenue Service is:
“The price that property would sell for on the open market. It is the price that would
be agreed on between a hypothetical willing buyer and a hypothetical willing seller,
with neither being required to act, and both having reasonable knowledge of the
relevant facts.”
Usually, the value is the recent price of the item, the current price of
comparable products/services/real estate, the replacement cost, the price determined
by experts, or a current arms-length offer.
Analysts commonly use financial ratios of similar businesses (thus,
businesses with comparable risks) to value the business or company division or other
unit under consideration. These companies are termed “pure play” companies—
ones with 75% or more of their sales in the same industry as the company being
valued. This is valuation by Comparables (“Comps”).
Ratios used for comparison among like companies include:
1. Enterprise value (EV) or market value of invested capital (MVIC), the
sum of all interest bearing debt plus equity either divided by or divided
into:
a.
Net Sales
b. Gross Profit
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c. EBITDA (Earnings Before Interest, Taxes, Depreciation, and
Amortization) or EBITA (without Depreciation)
d. EBIT (Earnings Before Interest and Taxes
e. Discretionary Earnings (EBIT + Owner’s Compensation +
Depreciation and Amortization)
f. EBIAT (Earnings Before Interest After Taxes)
2. Common stock price divided by net income per share or price times
number of shares outstanding divided by net income.
3. Common stock value (price * number of shares outstanding) divided by
the book value of the common shares).
4. The above as forecast one or two years out by analysts.
For example, if the enterprise value to EBITDA of the median company in the
industry were 10 and the EBITDA of the business being valued were $500 million,
the business would be valued at $5 billion before relevant adjustments (discussed
below). The stock price to earnings (net income) and market to book ratios may be
used in a similar way to value the equity. Using enterprise value to estimate the
value of equity requires subtracting interest-bearing debt.
[Note: there is lingering controversy over how to find enterprise value since
opinion differs on what current assets and current liabilities to include and exclude.
Do current assets include just inventory? or accounts receivable + inventory but not
cash? or operating cash + accounts receivable + inventory? Do current liabilities
include all current liabilities or just non-interest bearing current liabilities for the
purpose of calculating working capital? We calculate working capital as all
operating current assets (operating—but not excess—cash + accounts receivable +
inventory + other operating current assets if any, minus non-interest bearing current
liabilities. Other assets and liabilities are valued separately.]
A second market method of valuation compares the prices of recent sales
transactions in the industry with the asset to be valued. This is referred to as the
Transaction Method. Ratios are used with this method as well. Also, the assets and
liabilities of recently sold companies are directly compared with the asset being
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valued. If the assets and liabilities are comparable in a percentage sense, but larger
or smaller in an actual sense, the value of the asset being valued is decreased or
increased proportionately.
When combining comparative data on similar assets, should you use the
mean or the median? The mean is appropriate if there are two or three data points.
For more than three data points, it usually makes sense to use the median if there are
outliers that could bias the result. When ratios are involved, the harmonic mean is
sometimes used so that one large ratio will not unduly influence the outcome. As
mentioned earlier, size affects value—as company size increases, value increases
faster. This calls for adjustment factors. A discussion of these factors is beyond the
scope of this paper.
ADJUSTMENT FACTORS
The price of an asset found by using the asset, market, and income methods
described above should be adjusted by several factors when relevant. Income
statement data should be adjusted to remove or add factors that the buyer finds
reasonable. For example, the CEOs salary may be unrealistically high or low
reflecting the CEO’s best interest. Some new capital expenditures may be required
to keep the company competitive.
In general, the larger the percentage of ownership to be purchased, the lower
is the price per percentage. This corresponds to the idea in economics that the
greater the supply, the lower the price, other things being equal. More than a half
interest in an asset, however, confers the option of control that adds to the price (the
control premium). In the case of companies, larger amounts may confer other
options of value. For example, an 80% interest in a company allows the corporate
holder to transfer profits from the company without paying the relevant federal
corporate income tax. In valuing companies, the percent of the ownership is usually
more relevant than the number of shares owned. A firm may issue as many shares as
it deems appropriate.
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Ease of resale also adds to the value of an asset. Shares of a public company
can be sold almost immediately and therefore have greater value than the shares of a
privately held firm. Private companies are generally sold at a discount—discount for
lack of marketability (DLOM) or the smaller discount for lack of liquidity (DLOL) if
a controlling interest is to be sold. The smaller the firm, other things equal, the
greater the discount.
Economic theory demonstrates how demand and supply will affect price.
The greater the demand (the “hotter” the firm or industry), the higher is the price.
Speculation will sometimes distort the true value. The state of the economy will also
influence ratios and other data used to value assets. Sometimes these data need to be
normalized to reflect the value of the asset being considered.
In acquiring an interest in a joint venture, division, or company, the new
owners may find themselves with assets such as excess cash, land, plant, and
equipment not directly associated with the purchased asset. They should expect to
pay more for the asset if that is the case. The new owners can sell the unneeded
assets for cash. Alternatively, the new owners may have to add inventory or fixed
assets to support the level of sales used in the valuation. The price should be
reduced in those cases.
Pending lawsuits, potential synergies and other costs and benefits will also
affect the price of some assets. Recent studies have shown that most of the value of
expected synergies in corporate acquisitions goes to the seller.
Finally, the terms of purchase may influence the price. The opportunity to
buy over time may make the asset more valuable to the buyer depending upon the
interest rate charged.