1. Basics of Valuation
Corporate Finance
Peking University HSBC UK Campus
1
Outline
• Intro to corporate finance.
• Basics of valuation:
– Review of financial tools.
– Discounted cash flow analysis:
• Perpetuities.
• Annuities.
2
Corporate Finance
• Every decision that a business makes has financial
implications, and any decision which affects the
finances of a business is a corporate finance decision.
• Defined broadly, everything that a business does fits
under the rubric of corporate finance.
3
Traditional Accounting Balance Sheet
• The figure above shows a traditional accounting
balance sheet.
4
Financial View of the Firm
• The figure above shows the financial view.
5
Forms of Organization
•
•
•
Sole proprietorship:
– A business owned by a single individual that keeps all the profits and has
unlimited liability for business debts.
Partnership:
– Two or more owners (partners).
– The advantages and disadvantages of a partnership are basically the same as
those of a proprietorship, unless there are some limited partners.
Corporations:
– Ownership represented by shares of stock that can be readily transferred, and
the life of the corporation is therefore not limited.
– The corporation borrows money in its own name so that the stockholders
have limited liability for corporate debts:
• The most they can lose is what they have invested.
– The corporate form has a significant disadvantage, i.e. double taxation:
• Profits are taxed both at the corporate level when they are earned and at
the personal level when they are paid out.
6
Financial Decisions
• We focus on corporations and the three decisions:
– Capital budgeting, i.e., the process of planning and managing a firm’s
long-term investments.
– Capital structure, i.e., the mixture of debt and equity maintained by a
firm.
– Dividend decision, i.e., the amount of cash should be returned to the
owners.
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Who Decides?
• Agency theory:
– One person or entity (the agent) is able to make
decisions and/or take actions on behalf of, or that
impact, another person or entity (the principal).
• What about corporations?
– Corporate management is the agent.
– Shareholders are the principal.
Managers decide
8
Goal of a Financial Manager
• The primary goal of a financial manager of a corporation is
to maximize the shareholder value, i.e., to maximize the
price of the stock of the corporation (public companies) or
the market value of the owners’ equity (private
companies).
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How to Maximize the Value?
• How should the financial manager maximize shareholders’ value?
– Choose projects with positive and greatest net present value
(NPV) (investment decisions):
• Which real assets should the firm acquire?
– Choose capital structure that minimizes the cost of capital
(financing decisions):
• How should the firm finance the investments?
Both decisions impact firm value
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Agency Problems
• Do financial managers always maximize shareholders’
value?
– No, agency problems and information asymmetry.
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Valuation
• General Dynamics, a large defense contractor,
took 43 years to obtain a stock value of
$2.7𝐵𝑁.
• Netscape took a few minutes to do the same,
when it announced an IPO.
• Netscape had no profits and paid no dividend.
• How is it possible for these two very different
firms to have the same value?
12
How to Value an Invesment?
• Use of the discount cash flow approach (DCF).
• Key factors in the DCF analysis:
– Current and expected future cash flow (CF).
– Discount rate, i.e., 𝑟𝑡 , of expected future cash flow.
– Timing of cash flow, i.e., 𝑡.
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Expected?
•
•
•
In finance, a key ingredient in each decision problem is choosing uncertainty about
future conditions.
Implications of uncertainty:
– Outcomes (or states of the world).
– Probabilities associated to the possible outcomes.
Since it is impossible to know the exact event in the future, expectation could help
one to make decisions.
Expected value as decision criterion
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Uncertainty in Corporate Finance
• Estimate expected future cash flows:
– Analyze historical accounting statement.
– Predictions for the future.
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Discount Rate in Corporate Finance
•
For capital budgeting decisions, the discount rate is the cost of capital, i.e., the
firm’s expected required rate of return:
– The cost of company’s fund, i.e., both debt and equity.
– Other names include cost of capital, weighted average cost of capital (WACC),
hurdle rate, etc.
Analyze the capital structure and how it impacts the cost of capital
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Discounting
•
Why discounting?
– A dollar received in one year is less than a dollar today (time value of money).
• If you have a dollar today, you can invest it in the bank and receive more
than a dollar by some future date.
– Thus, we discount future cash flows using the appropriate discount rate:
𝑇
𝐸[𝐶𝐹1 ]
𝐸[𝐶𝐹2]
𝐸[𝐶𝐹𝑇 ]
1
𝑃𝑉 =
+
+
⋯
+
=
෍
𝐸[𝐶𝐹
]
.
𝑡
1 + 𝑟1 1
1 + 𝑟2 2
1 + 𝑟𝑇 𝑇
1 + 𝑟𝑡 𝑡
𝑡=1
17
Simplifying the DCF Analysis
• Let’s assume the following:
– Cash flow and discount rates are given (no expected cash
flows at the moment):
• As starting point, we assume that 𝐸[𝐶𝐹𝑡 ] = 𝐶𝐹𝑡 .
• As time goes on, we will learn how to compute these
two key inputs when facing corporate finance
decisions!!!
– Cash flow occurs at the end of each period.
– Discount rate is the same for all the future periods, i.e.,
𝑟𝑡 = 𝑟.
18
Patterns
• If future cash flows have certain patterns, then
the DCF formula can be simplified into various
forms.
• Examples:
– All future cash flows are constant.
– Future cash flows are growing at a constant rate.
– Future cash flows grow at different rate over
different period.
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Example
• We just bought a vacation house.
• The vacation house can be rented for $30,000 a
year, and you expect the first payment to be
made in a year.
• The maintenance and upkeep will cost $5,000 a
year.
• You plan to rent out the house forever.
• The appropriate discount rate is 20%.
• What is the vacation house worth?
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Perpetuity
• If the cash flows are constant forever, they are
called a perpetuity.
• Compute the present value of a perpetuity:
𝐶𝐹1
𝑃𝑉𝑃0 = .
𝑟
• Note that the value is as of one period before the
first payment.
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Value of the House
•
•
30000
𝑃𝑉𝑃0 𝐶𝐹1 = 0.2 = $150,000.
−5000
𝑃𝑉𝑃0 𝐶𝐹2 = 0.2 = −$25,000.
• 𝑃𝑉 𝐻𝑜𝑢𝑠𝑒 = $150,000 − $25,000 = $125,000.
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Preferred Stock
• Preferred stock (or preference stock) is an
important example of a perpetuity:
– When a corporation sells preferred stock, the
buyer is promised a fixed cash dividend every
period (usually every quarter) forever.
– This dividend must be paid before any dividend
can be paid to regular stockholders–hence the
term preferred.
23
Selling the House
• Now we are not going to hold the house forever,
but sell it some time in the future.
• We plan to rent it out for $30,000 a year, and we
expect the first payment to be made in one year.
• On the other hand, the maintenance and upkeep
will cost us $5,000 a year.
• We will hold the property for 4 years, after which
we will sell for $130,000.
• The appropriate discount rate is 20%.
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Annuity
• If the cash flows are constant for a set number of years,
i.e., 𝑛, then you have an annuity.
• Compute the present value of an annuity:
– DCF formula is simplified as:
𝐶𝐹1
1
1
1
𝑃𝑉𝐴0 =
∙ 1−
= 𝐶𝐹1 ∙ −
.
𝑛
𝑛
𝑟
1+𝑟
𝑟 𝑟 1+𝑟
• Note that the value is as of one period before the first
payment.
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The Value Becomes
• 𝑃𝑉𝐴0 𝐶𝐹1 =
• 𝑃𝑉𝐴0 𝐶𝐹2 =
• 𝑃𝑉0 𝐶𝐹3 =
30000
0.2
−5000
0.2
130,000
1+0.2 4
[1 −
[1 −
1
1+0.2 4
1
] = $77,662.04.
1+0.2 4
] = −$12,943.63.
= $62,692.90.
• 𝑃𝑉 𝐻𝑜𝑢𝑠𝑒 = 𝑃𝑉𝐴0 𝐶𝐹𝑆1 + 𝑃𝑉𝐴0 𝐶𝐹𝑆2 + 𝑃𝑉0 𝐶𝐹3
= $77,662.04 − 12,943,63 + 62,692.90 = $127,411.27.
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Growth and Perpetual Cash Flows
• Now instead of charging $30,000 each year,
assume that you charge the first year’s rent
$15,000 and will grow each year at the rate of
5%.
• Again, the maintenance will cost you $5,000 a
year.
• Now you intend to hold the property indefinitely.
The appropriate discount rate is 20%.
• What about cash flows?
27
Growing Perpetuity
• If perpetual cash flows are growing at a
constant rate, then we call it a growing
perpetuity.
• Compute the present value of a growing
perpetuity.
• The 𝐷𝐶𝐹 formula is simplified as:
𝐶𝐹1
𝑃𝑉𝑃0 =
.
𝑟−𝑔
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Growth
• Now, instead of charging $30,000 each year,
assume that you charge the first year’s rent
$15,000, and will grow it at the rate of 10%
for 3 years after that.
• The maintenance will cost you $5,000 a year.
• You will hold the property for 4 years, and sell
it for $130,000.
• The appropriate discount rate is 20%.
• What about cash flows?
29
Growing Annuity
• If the cash flows occur for a set of period and
grow at a constant rate, then they are called a
growing annuity.
• Compute the present value of a growing annuity:
– The 𝐷𝐶𝐹 formula is simplified as:
𝑛
𝐶𝐹1
1+𝑔
𝑃𝑉𝐴0 =
∙ 1−
𝑟−𝑔
1+𝑟
1
1+𝑔 𝑛
= 𝐶𝐹1 ∙
−
.
𝑛
𝑟−𝑔
𝑟−𝑔 1+𝑟
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Adjusting the Discount Rate
• The discount rate used to find the present
value of cash flows is comprised of 3 things:
– Time value of money.
– Risk.
– Inflation (if the rate is nominal).
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Risk-Adjusted Discount Rates
• Most real-world cash flows in the future are risky.
• The discount rate should be adjusted to incorporate for risk:
– Capital Asset Pricing Model (CAPM).
– Arbitrage Pricing Theory (APT).
• We will be more specific when studying the cost of capital (lecture VII).
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Inflation
• Inflation is a general increase in prices across the
economy over a period of time.
• Example:
– In 1997, movie “Titanic’’ made $600.80𝑀𝑀:
• It is worth $639.83𝑀𝑀 in year 2000.
– In 1939, movie “Gone with the wind’’ made
$198.60𝑀𝑀:
• It is worth $1,001.69𝑀𝑀 in 2000.
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Real Discount Rates
• The nominal discount rate, 𝑖, is the actual rate
of return without removing the impact of
inflation.
• The real discount rate, 𝑟, is the rate adjusted
for inflation, i.e., with inflation removed from
the rate.
• Fisher equation:
1+𝑖 = 1+𝑟 1+𝜋 ,
where 𝜋 is inflation rate.
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Be Consistent!!!!
• Nominal cash flow (actual dollars):
– Dollars as of the year in which they occur.
• Real cash flow (constant dollars):
– Dollars as of a particular base year.
• Consistency treatment:
– When discounting nominal dollars, use the
nominal discount rate.
– When discounting real dollars, use the real
discount rate.
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Example
• If you earn 8% return on an investment (or
your discount rate is 8%) and inflation over
this period is 3%, then a portion of your
return is due to inflation.
• What is your real rate of return?
1 + 8% = 1 + 𝑟 1 + 3% .
𝑟 = 4.854%
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Inflation Rate
• How do you calculate inflation rates?
– Consumer price index 𝐶𝑃𝐼 :
𝐶𝑃𝐼1990
1 + 𝜋1990 =
.
𝐶𝑃𝐼1989
• If the CPI for 1990 is 104, and it is 100 for
1989, then over this period:
𝐶𝑃𝐼1990
104
𝜋1990 = 𝐶𝑃𝐼
− 1 = 100 − 1 = 4%.
1989
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Constant Dollar Adjustment
• To restate cash flows in constant dollars, you
need to CPI-adjust the cash flows.
• In-class exercise:
– A firm’s sales were $100,000 in 1980, and $200,000
in 1990.
– You want to compare the dollar amounts excluding
the impact of inflation.
– If the 1990 CPI is 104 and the 1980 CPI is 80, then:
• What is the 𝟏𝟗𝟗𝟎 sales in terms of 𝟏𝟗𝟖𝟎 dollars?
• What is the average annual inflation rate between 𝟏𝟗𝟖𝟎
and 𝟏𝟗𝟗𝟎?
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Then
• The 1990 sales in terms of 1980 dollars are:
𝑆𝐴𝐿𝐸𝑆1980𝑠$ 1 + 𝜋1980−1990 = 𝑆𝐴𝐿𝐸𝑆1990𝑠$ ,
𝐶𝑃𝐼1990 104
1 + 𝜋1980−1990 =
=
= 1.3.
𝐶𝑃𝐼1980
80
𝑆𝐴𝐿𝐸𝑆1990𝑠$
$200,000
𝑆𝐴𝐿𝐸𝑆1980𝑠$ =
=
= $153,846.15.
1 + 𝜋1980−1990
1.3
• The average annual inflation rate between 1980 and 1990 is:
1 + 𝜋𝑎𝑛𝑛𝑢𝑎𝑙 10 = 1 + 𝜋1980−1990 = 1.3.
𝜋𝑎𝑛𝑛𝑢𝑎𝑙 = 2.658%
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Main References
• Ross, S.A., Westerfield, R. and B.D. Jaffe,
“Corporate Finance”, McGraw-Hill,
2015, Chapter 1.
• Ross, S.A., Westerfield, R. and B.D. Jaffe,
“Corporate Finance”, McGraw-Hill,
2015, Chapter 2.
• Ross, S.A., Westerfield, R. and B.D. Jaffe,
“Corporate Finance”, McGraw-Hill,
2015, Chapter 4.
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