Weighted Cost of Capital
September 25, 2013
Sources of Funds
You have a brilliant idea for
a money-making project.
Where do you get the
start-up funds?
Bonds
These are promises to pay a specified amount – the `par value’ –
at a specified date in the future.
They may or may not bear interest.
Often used to fund public-sector projects, or by large corporations.
(why not by small corporations?)
There is trading in partially matured bonds.
Selling Stock
Common Stock
Preferred Stock
No dividend
Dividend
Lowest Priority
Higher Priority
Vote
No Vote
Stock may be publically traded, e.g. on the TSE or VSE.
Preferred Stock may be callable
-- company can buy it back at a fixed price
and convertible
-- can be turned to common stock at a fixed
ratio
Why would anyone want common stock?
-- to get a vote
-- to get income as capital gains
Cost of Capital Raised by Selling Equity:
1. If a share of stock costs $P, and pays an average annual
dividend $D, the effective interest rate on this capital is
k = D/P
2. This estimate errs on the low side, since people may
choose to invest in a company that doesn’t pay dividends.
A better estimate might be:
k = D/P + growth rate
The Wonders of Leverage
The Wonders of Leverage
Scenario 1: I sell $1 000 000’s worth of shares in my company
and buy $100 000 worth of these shares myself.
In one year’s time, the company is worth
$2 000 000. How much do I have?
Scenario 2: I borrow $900 000 at 10% interest and put
up $100 000 of my own to start a company.
In one year’s time, the company is worth
$2 000 000. How much do I have?
Compound Leverage
Value of shares in the Goldman Sachs Trading
Corporation:
1928
1932
$104/share
$1.75/share
Capital Structure
Industry
Debt
Equity
Other
Oil
17.6
79.0
3.4
Steel
27.2
67.2
5.6
Utility
44.2
52.6
3.2
Chemicals
5.2
82.9
11.9
Manufacturing
2.7
93.0
4.3
Mortgages
These are fixed-term loans, secured by a lien
or title on some tangible property.
Usually used by larger companies (though the
principals of small start-up companies may
raise money by mortgaging their personal
property.)
Small-Business Loans
Some governments set aside funds to finance
small start-up companies.
(e.g.,Western Economic Development, SBIR’s,…)
Weighted Cost of Capital
If a company obtains funds Xi at an interest rate
Ai, the weighted cost of capital for the company is
Σi XiAi
Σi Xi
This sets a lower bound on the MARR.
Capital rationing
Limit of cash
i
Project 1
Project 2
Project 3
MARR
$
Capital Inventory
i
Project 1
MARR
Project 2
Project 3
Project 4
(Don’t
fund)
$
Capital Budgetting: Other Factors
•Are the chosen projects the best fit to available capital?
•How do the projects interact?
•Are they equally risky?
•Are there intangibles to consider?
•Are some projects mandatory? (E.g. pollution controls)
•Are there relevant political factors?
Business Organization
The Three Kinds of Organization
Single Proprietorship
Partnership
Corporation
Most businesses are small.
But most business is done by big businesses.
Most small businesses fail within their first
five years.
John Kenneth Galbraith claimed that North
American business is characterised by oligopoly
rather than competition.
Time Warner, Disney, Murdoch, Bertlemann and Viacom
(formerly CBS)
Detecting Oligopoly: the `four-firm concentration’:
UK supermarkets:
UK brewers:
US music:
US breakfast cereals:
US auto top three:
US computers:
74.4%
85%
80%
80-90%
60%
65%
Counterexample: Internet porn
The Single Proprietorship
Advantages:
Simple
Total Control
Can use money as you like
Disadvantages:
Can lose all you own
Limited capital
Limited expertise
The Single Proprietorship
Advantages:
Simple
Total Control
Can use money as you like
Disadvantages:
Can lose all you own
Limited capital
Limited expertise
Cash Flow Problems
You have an idea that can make $150 000 in the first
year, for an investment of $80 000.
But you have to get the $80 000 first. How?
i)Buy on credit
Can do this explicitly, or just pay bills late.
Either way costs about 25% plus loss of good
will. Many suppliers offer a 2% discount for
prompt payment.
Cash Flow Problems
You have an idea that can make $150 000 in the first
year, for an investment of $80 000.
But you have to get the $80 000 first. How?
i)Buy on credit
ii)Talk to the bank
Bank will ask, ``What’s the collateral?’’
Mortgageable property? Track record?
If not, they charge a risk premium.
Cash Flow Problems
You have an idea that can make $150 000 in the first
year, for an investment of $80 000.
But you have to get the $80 000 first. How?
i)Buy on credit
ii)Talk to the bank
iii)Government help
Bureaucratic overhead, may not be worth it.
Partnership
Advantages
Disadvantages
More capital
Liable for debts
Easier Credit
Limited Credit
More Talent
Arguments
Retain Valuable
Employees
Frozen Investment
Liability for Debts
The general partners are jointly and severally liable
for the debts of the partnership.
The only way to get out of this is to be a limited partner.
The partnership may include the names of the general
partners in the firm’s name, but not the word `Limited’
A partnership must be registered according to the law
in the province.
Incorporating
Advantages
Disadvantages
Limited liability
Costs money
More capital
Corporate Tax
Professional
management
Lack of privacy
Loss of Control
Registration
In BC, you have to submit a Memorandum of Association
to the Registrar of Joint Stock Companies. This specifies
who is applying, the amount of share capital, and the
responsibility for debt. (If the shareholders’ liability is
limited, the word `Limited’ must be the last word in the
company name.
Some provinces have a slightly different system, the
letters patent.
The Corporation
A corporation is a business which is legally distinct from
its shareholders; that is, a corporation can owe money
without its shareholders being responsible for the debt.
Corporations are of two kinds, public and private.
A private corporation has between 3 and 50 shareholders,
and shares can be transferred only with the approval of
the Board of Directors. The public must not be invited
to buy shares.
A public corporation can have as many shareholders
as it likes and can sell shares to anyone.
Tax Advantages and Disadvantages
Once you are incorporated, that part of the firm’s
income that comes to you gets taxed twice – once
at the corporate rate, once as it goes from the
corporation to your pocket.
Nevertheless, you can use incorporation to reduce
the tax you pay….
Tax Advantages and Disadvantages
Company
(Pre-tax)
Company
(After-tax)
You
25%
25%
Tax Advantages and Disadvantages
Company
(pays wages)
60%
You
Tax Advantages and Disadvantages
Company
You
Selling Shares
Once you’re a corporation, how do you actually go about
selling stock?
For a small company, you usually have an investment
banking firm act as an intermediary. They will market
your shares and take a cut – perhaps 25% -- to pay for
their efforts.
If you’re a big company, the investment banker may
underwrite the stock, that is, guarantee to buy all you
want to sell.
How much stock can you reserve for yourself?
Accounting
A company needs to monitor its internal cash flows so it
can diagnose its state of health.
The two most important monitoring documents are the
Income Statement and the Balance Sheet.
These must be available to be checked by independent
auditors, and made available to potential investors.
Several diagnostic instruments can be applied to the
accounting data.
Current Assets
Fixed Assets
Current Liability
Owed this year
Long-Term Liability
Owed in the more distant future
Diagnostics
Current ratio
=
Total Current Assets
Total Current Liabilities
Working capital = Current Assets – Current Liabilities
Diagnostics
Acid-test ratio
=
Cash & Accounts Receivable
Total Current Liabilities
(After-Tax) MARR =
After-Tax Profits
Total Assets
A Paradox?
The Fundamental Equation of Accounting is:
Equity = Assets – Debts
so the value of one share should be
Share Value = Equity/Number of Shares
So how can the stock market crash?
After a long period of unemployment, Jamal signs a contract to work in the
distant nation of Placidia. The job requires him to be away from home for two
years, and the majority of his pay is held back until he has completed the contract.
If he leaves before this, he gets nothing. He receives an immediate signing
bonus of Rs 70 000, but he has to spend Rs 30 000 of this on an air ticket to
Placidia. The rest he gives to his family. Once in Placidia, he is provided with
food and board, but after working for a year, there are unexpected difficulties in
renewing his work permit. Eventually he has to pay Rs 150 000 in fees and
bribes, for which he has to re-mortgage his house back home. At the end of
his second year he is paid Rs 170 000. Air fares have gone up in the meantime,
so he spends another Rs 35 000 on an air ticket and flies home.
Regarding the entire trip as a business investment, what was Jamal’s IRR?
If there are multiple solutions, you should also calculate his approximate
and his exact ERR. You should assume that he can invest his funds at 12.5%.
Finding the IRR
8.0000
6.0000
PW (r)
4.0000
2.0000
Series1
0.0000
0.00
0.50
1.00
1.50
- 2.0000
- 4.0000
- 6.0000
Nominal Interest Rate
2.00
2.50
Yan invests $10 000 000 to build a casino in Macao. In the
first year he makes a profit of $20 000 000. But in the
second year, a syndicate of card-counters infiltrate his
casino, and he loses $15 000 000. In the third year he is
able to eliminate the card-counters, and makes a profit
of $50 000 000. Assume that his income and his losses
occur continuously throughout each year, and that they
are all continuously compounded. What is his IRR?
Any money he does not invest in the casino, he can
put in his cousin’s banking business, where he can
earn 15%. What is his approximate ERR?
The heating system in Jacob’s building has worn out and
he has to get a new one. All the alternatives are gas-fired
furnaces, but they vary in efficiency. Model A is leased
at $500/year. It has installation charges of $500, and
saves $200 a year compared with his previous system.
Model B is purchased for $3600, including installation.
After 10 years it will have a salvage value of $1000.
It saves $500 a year compared with the old system.
Model C is purchased at a total cost of $8000, half paid
now, half paid in two years time. It has a salvage value
of $1000 after ten years, and saves $1000/year compared
with the current system. Assuming an MARR of 12%
and using the IRR method, which furnace should Jacob get?