Corporate Finance

Bonds, Stocks, and Capital Allocation

Overview

• The corporation– Ownership and Control– Limited Liability

• How does a corporation raise money?– Venture Capital– Stocks– Bonds

• Textbook topics– Weighted Average Cost of Capital, MARR and wealth of

the firm– Other capital allocation issues

(linear programming)

So you have this great idea…

• Computer matching service for ships and cargo

• Rocket Sled

• New gambling device

• (soon to be) Famous web site

• ?

Forms of Business• Sole proprietor 1 person business; assets and debts of the business are the debts of the

owner (proprietor). No protection from losses/liabilities.• Partnership

Several partners own the business and its cash flows. No protection from losses/liabilities.

• Limited PartnershipSeveral partners own a business and its cash flows. Losses are limited to the initial investment.

• Limited Company (or Corporation)Shareholders own the business in proportion to their shares. The shareholders elect a board of directors to manage the business. Losses are limited to the price of shares. The board of directors choose how much of the company profits to redistribute to shareholders, and how much to keep for future investment.

Example Corporation

ShareholdersTrade shares

Stock market

Vote to Appoint

Board of Directors

Officers

CEO (President), VP, Treasurer, Secretary

Appoint

Hire

Employees

Dividends

($$$)

Annual report

Issue more shares

Advantages of Corporations• Independent existence

– The corporation has an existence independent of its founder, shareholders, managers, or employees.

– It is treated like a person under the law, and can hold bank accounts, owe taxes, or be penalized for wrong doing.

• Tradable shares• Infinite life• Separation of ownership (shareholders) from

control (directors, officers, and employees)• Limited liability for owners (shareholders),

directors, and employees.– Can not lose more than they have invested.

Disadvantages of Corporations

• Paperwork and Regulatory costs• In some countries, the need to have annual

board of directors meetings in the country of registration

• Double taxation when profits are distributed as dividends to the share holders (in some countries)

• Added Bureaucracy in decision making

Profit of a Corporation

Taxable Profit = Revenues – Tax Deductible Costs

(Deductible Costs include labor, rent, lease of equipment, O&M for equipment, depreciation of purchased equipment, and interest on loans & bonds)

Net Profit = Taxable Profit * (1-t) t = tax rate (e.g. 15%; 40%)

Venture Capital 1011. Initial investors, called “Angels” are usually the

friends/family/associates of the entrepreneur.2. In high tech startups, the company may

participate in a “business incubator”. The entrepreneurs share facilities and advice with other startup companies.

3. Initial employees may work for stock options instead of cash. Stock options gives the right to buy the stock later at a low price. The employee takes a gamble to make a lot of money, or nothing. This practice saves the startup some costs when money is scarce. It can also allow them to lure top talent that they can not afford.

Venture Capital 1014. After proving the idea a bit, VC firms may be

interested in investing. This takes much begging and rejection. The VC firms will want to buy stock very cheap (a few cents/share), hoping to sell out at the IPO (Initial Public Offering of Shares)

5. After a few rounds of VC funding, and continued success, the startup may be “famous” and ready for an IPO.

6. At the IPO, the VCs often cash out first, while others (e.g., employees) may have to wait a while before being allowed to sell their options or shares.

7. After the IPO, success is still not assured. Over 80% of IPOs are bad investments and decline in value.

Venture Capital 1017. After the IPO, success is still not assured.

Over 80% of IPOs are bad investments and decline in value.

Equity (stock)

• Stock in a corporation is often called “equity”

• The term “equity” comes from the equation

Stockholders’ equity = Corp. Assets – Corp. Debts

• The book value of a share of stock =(stockholders’ equity / number of shares)

Valuing stock – PV of Dividends

• The stock price is usually determined in a market of voluntary buyers and sellers

• One early theory of stock valuation is that the price should equal the Present Worth (PW) of future dividends

• However, many famous companies (e.g. Microsoft) do not pay dividends.

Valuing stock – PW of future expected earnings

• Later theory assumed that except for tax issues, it should not affect stock price if a company distributes earnings as dividends or retains them for future investment.

• This theory would suggest that stock price is related to the PW of future expected earnings

Valuing stock – PW of future expected earnings

• EPS = corporate profit / number of shares

• P/E ratio = Stock price / EPS

Example via Yahoo Finance

P/E ratio is higher for high-tech growth companies than for established industrial companies. Why is this?

Valuing Stock – PW of future expected earnings

Exponential growth formula

Growth Rate=g = (Ak- Ak-1)/ Ak-1

“Convenience rate” icr=[(1+i)/(1+g)]-1=(1+i-1-g)/(1+g)=(i-g)/(1+g)

Special formula PV = A1(P/A, icr%,N)/(1+g)

Earnings/Share

2002 2003 2004 2005

Price of Stock = PRESENT VALUE

For an infinite time horizon, we’ll need (P/A, icr%,)=1/ icr%

PV= A1*(P/A, icr%,)/(1+f)

PV of earnings = EPS*( (1+g)/(i-g) )/(1+g) = EPS/(i-g)

Valuing Stock – PW of future expected earnings

If price of stock is related to present value of future expected earnings

and we see thatPV = EPS/(i-g)

Thenthe P/E ratio should be P/E = PV/EPS = 1/(i-g)

Where i = industry MARRg = earnings growth rate

THIS EXPLAINS WHY COMPANYS with an EXPECTATION of GROWING EARNINGS have a HIGHER P/E ratio

Valuing Stock – Risk, Diversification, and

Industry MARRRisk – individual stocks may go up or down due to individual

company results. Price = Expected PV no reward or penalty for “gambling”Diversification – “Do not put all your eggs in one basket.”

Imagine holding small shares of many different companies: some of the individual risks will cancel each other.

Systematic risk – Risks that do not cancel. National and global risks (unemployment, inflation). Disaster. War.

Capital Asset Pricing Model (CAPM) => Rates of return seems to be correlated with Systematic risk – NOT risk that can be diversified.

Bonds• Are a way for companies to borrow large amounts of money

– more than they could borrow from a single source• Allow the company to borrow at a fixed interest rate• Are traded in a market, called the bond market.• Can vary in value with the market’s attitude about the

company’s credit rating or ability to repay the debt.• Usually give the bondholders rights to control the company

if the debts are not repaid• Do not otherwise give the bondholder any rights to manage

the company or any additional profit beyond the terms of the bond

• (In the USA) interest is a tax deductible cost for the company. In contrast, dividends paid on stock do not generate any tax deductions.

Coupon rate vs. Yield

• The coupon rate is the interest rate payment set by the company. It is fixed. Usually the interest payment consists of 2 payments per year.

• The yield of a bond is the IRR of buying the bond at a price P determined by willing traders on the bond market. The price P varies with market forces.

Bond pricing formula

Relationship between bond market prices (P),Face value (F), coupon rate per period (r%),

number of periods until repayment (N), and bond yield per period (y%).

Bond market price P is the PW of future bond paymentsP = F * (P/F,y%,N) + (r% * F) * (P/A,y%,N)

Example: Kmart, Inc. Bond

This is the cash flow from buying a $1000 KMART 7.75% bond that matures in 12 years.

Repayment of

Face amount us$1000

The bond entitles the owner to payments of

7.75%*$1000/2 = $38.75 every 6 months

The 7.75% is known as the “coupon rate”.

23 interest payments of us$38.75

Bond Pricing: Kmart ExampleWe know that the bond market price for buying or

selling this bond today can be obtained from a Present Worth analysis.

P = F * (P/F,y%,N) + (r% * F) * (P/A,y%,N) In the case of the KMART bond,P= $1000 *(P/F,y%(/6mo),23)+

$38.75 * (P/A,y%(/6mo),23)Note: the yield is not the same as the coupon rate.

The yield and market price are linked by the formula above.

Annual Yield 6-mo Yield (P/A,y6%,23) (P/F,y6%,23) Bond Pricey12% y6% P/A*interest payments of $38.75 every 6 months

"+ P/F* $1000 repaymentsqrt(1+y12%)-1

5% 2.47% 17.38854453 0.570588561 $1,244.395.50% 2.71% 16.9448912 0.540252412 $1,196.876.00% 2.96% 16.51857021 0.511661276 $1,151.766.50% 3.20% 16.10875212 0.484707244 $1,108.927.00% 3.44% 15.71465293 0.459289542 $1,068.237.50% 3.68% 15.33553136 0.435314027 $1,029.578.00% 3.92% 14.97068627 0.412692724 $992.818.50% 4.16% 14.61945421 0.391343397 $957.859.00% 4.40% 14.28120722 0.37118915 $924.599.50% 4.64% 13.95535066 0.352158057 $892.93

10.00% 4.88% 13.64132128 0.334182821 $862.7810.50% 5.12% 13.33858535 0.317200456 $834.0711.00% 5.36% 13.04663697 0.301151995 $806.7111.50% 5.59% 12.76499641 0.285982215 $780.63

From yahoo on 1/May/2001 the bond is priced at $896.875 per bond plus $7.75 accrued interest (interest from 1/4 to 1/5)for a total price in the market of $904.63

The YIELD-TO-MATURITY is the IRR of purchasing this bond.we can see from the above chart that the IRR would be between 9 and 9.5% in terms of annual yield

Yahoo gave the yield as 9.229%

Kmart Bond Price as function of yield

Weighted Average Capital CostWhat?

A Measure of overall capital costs.Includes effect of taxation.

Why? WACC can be a guide for setting MARR.When a firm chooses a project with IRR>WACC, the

project will earn a profit after paying the interest and returns expected by shareholders. The firm will become wealthier.

If a firm sets MARR=WACC, then it will tend to choose profitable projects that reflect the firm’s access to capital.

How? See next slides for an example.

WACC Example: Part 1Lucky Holdings Limited, Hong Kong

Capital Rate of return

Bank Loans $5 000 000 6% (interest)

Bonds $10 000 000 8% (interest)

Stock $30 000 000 12% (historical returns on stock)

Retained Earnings $ 5 000 000 Same as stock 12%

TOTAL CAPITAL $50 000 000

What is the WACC? It is the average cost of capital, weighted by the amounts of capital, and adjusted for taxes.

WACC Example: Part 2Lucky Holdings Limited, Hong KongInterest is a tax deduction, the HK tax rate is 15%

=> HK government pays 15% of our interest!

Capital Rate of return After-tax Adjusted Cost

Bank Loans $5 000 000 6% (interest) 6%*0.85 = 5.1%

Bonds $10 000 000 8% (interest) 8%*0.85= 6.8%

Stock $30 000 000 12% (historical returns on stock)

12%

Retained Earnings $ 5 000 000 Same as stock 12% 12%

TOTAL CAPITAL $50 000 000 WACC(next slide)

WACC Example: Part 3Lucky Holdings Limited, Hong KongWACC is the weighted average of the after-tax adjusted cost

of capital. The weights are the capital amounts.

Capital After-tax Adjusted Cost

Bank Loans $5 000 000 6%*0.85 = 5.1%

Bonds $10 000 000 8%*0.85= 6.8%

Stock $30 000 000 12%

Retained Earnings $ 5 000 000 12%

TOTAL CAPITAL $50 000 000 10.27%

WACC=

{(5.1%)(5)+

(6.8%)(10)+

(12%)(30)+

(12%)(5)

}/50

=513.5%/50=

10.27%

Linear Programming and Capital Allocation

Let x[j]=1 if project j is selected, 0 if project j is not selected

PW of project j is PW[j]

Initial capital requirements for project j are K[j]

Max PW = j PW[j]*x[j]

With respect to constraints

j K[j]*x[j] <= Starting Capital

(and other constraints, which can be added here)Example of additional constraint: projects 3 and 4 need the same land, can not choose both…. => This constraint can be written as x[3]+x[4]<=1

Review• The corporation

– Separation of Ownership and Control and Limited Liability are needed to help convince others to invest

• How does a corporation raise money?– Venture Capital – Stocks– Bonds

• Textbook topics– Weighted Average Cost of Capital, MARR and wealth

of the firm– Other capital allocation issues

(linear programming)