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Corporate Finance
Rutgers University, Newark School of Law
Gatti, Matteo


I. Valuation

Three Components to Valuation:

1) Money has time value

2) Valuation is based on expected returns

3) People are risk adverse

A. Elements of Fundamental Value:

1. Time Value of Money (p. 42)

Investing money today requires the guarantee of more money in the future.

Valuation requires discounting or capitalizing. (Translating expected future value into present value)

Discounting is used for a finite set of payments, such as interest on a loan that will be repaid.

Capitalizing is used for an infinite stream of payments such as dividends on stock.

Discounting and capitalizing allows us to compare the present value of money with the future value of money.

This is important because:

1) Money today can buy me stuff today and it can buy more stuff today than in the future

2) I can invest money today in a savings account and get the guarantee of something more in the future.

To get the Future Value of some amount from its Present Value: Table 11-2 (pg. 45)

FV = PV(1 + r)^t

r = rate (interest rate)

t = time (years, months etc.)

Ex: $100 one year from now with a discount rate of 6%

100(1 + .06)1 = $106

To get the Present Value of some amount from its Future Value: Table 11-1 (pg. 44)

PV = FV/(1+ r)^t

Ex: $100 one year from now with a discount rate of 6%

100/ (1 + .06)1 = $94.3

What about two years from now? Take the PV at year one and reduce its present value by the same proportion (the discounting factor)

$94.3 x .943 = $89. For year three, merely reduce by the same proportion again. 89 x .943 = $83.9.

To get the Present Value of a series of future payments. Table 11-3 (pg. 47)

Just add up the present value for each year or look at the table.

Ex. Value of receiving $1 every year for the next three years with a discount rate of 6%

PV of receiving $1 in one year 1/[(1 + .06)(1)] = $.943, + 1/[(1 + .06)^2] = $.89 + 1/[(1 + .06)^3] = $.839 = $2.67

Discounting in Bond Valuation (see pg. 48)

Formula for determining the PV of a bond


PV = ∑ A / (1 + r)^t

t = 1

However, if there is a chance of a default in payments that must be factored in. Therefore,

Expected value = future amount1 x (chance of this outcome) + future amount2 x (chance of this outcome). Then take the expected payment and discount that value. This is the expected value (or the price that should be paid)

Expected payment = $1,050 x 0.8 [chance of default] + $500 x 0.2 [chance of default] = $940. The expected payment would be the FV that would be used in the formula.

PV of notes = $940 / (1 + .05) = $895

That’s the value at which bond would trade

Investor purchasing at $895 would get a promised yield of 17.3% if company does not default and investor receives $1,050

($1,050 – $895) / $895 = 0.173. But the Expected Yield would still be 5% because you must also include the promised yield if there is a default which would be -44.1

Formula would be (chance of default) x (expected rate of return) + (chance of default) x (expected rate of return)

Ex. 0.8 x 17.3% [approx 13.84%] + 0.2 x -44.1% [approx -8.8%] = approx 5%

Therefore, Expected Yield would be 5%.

What if the investor demands a Risk Premium of 3%?

Bonds will sell for $940/1.08 = $870 with promised yield of 20.7%

Discounting and Capital Budgeting Decisions (pg. 49)

Discounting must also be used in assessing internal investment decisions (putting capital to work).

Net Present Value (NPV) Method (pg. 50): Discounts the sum of expected inflows minus costs.

Use with: purchase of security, whole firm, or machinery.

Internal Rate of Return (IRR) Method (pg 50): Under the IRR method we would first establish what rate of discount serves to equate the anticipated inflows of a the amount per year for the period of years with the required cash outlay. The result is compared to the required rate of return to determine whether the net yield on the investment is positive.

2. Expected returns.

a. The composition of returns:

Warren Buffet Reading: Owners earnings are a better indicated for valuing a company than GAAP.

GAAP is based on too many assumptions and best market situations.

Owners Earnings = accounting earnings (additional revenue) + depreciation, depletion, amortization, and other non-cash charges – average annual capitalized expenditures for plant and equipment.

Accounting Earnings = additional revenues – direct costs, depreciation – income tax.

Machine purchase example.

• 5-year life

• Cost = $18,000

• Additional revenues per year = $12,600

• Annual direct costs to operate = $6,000

• Straight-line depreciation = $3,600 (cost / 5-year life)

• Income taxes at 33 1/3 percent

$12,600 additional revenues

• minus 6,000 direct costs of operating machine

• 6,600 earnings before depreciation and taxes

• minus 3,600 depreciation

• 3,000 net earnings

• minus 1,000 income tax [Why do we deduct? Duh…]

• 2,000 net earnings after tax

• $2,000 net earnings after tax

• plus 3,600 depreciation

• $5,600 net cash flow

If we capitalize at 10% for 5 years…

$5,600 x 3.79 [remember Table 11-3? That’s the PV of getting one dollar a year for five years at 10% capitalization rate] = $21,224

NPV = $21,224 – $18,000 = $3,224

Scrap Value:

• $18K minus $3K of scrap value means $3K of depreciation per year ($15K / 5)

• Net earnings are $3,600 [$12,600 – $6K of direct costs – $3K of depreciation]

• Net earnings after tax = $3,600 minus 1/3 of $3,600 = $2,400

• If you add back depreciation, you get to net cash flow of $5,400 – capitalized at 10% for 5 years… $5,400 times 3.79 = $20,466

• Add back scrap value discounted at capitalization rate.

• Plus $3,000? Not really. It’s $1,860 discounted at 10% at year 5

• NPV = $20,466 + $1,860 – $18,000 = $4,326


What if I need to spend $3,000 at year three for special maintenance?

That’s something I will have to deduct as a (c) capital expenditure per Buffet.

Remember I will have to discount $3,000!

In 3 years at 10%… $3,000 times 0.751 = $2,253, which cost will reduce NPV by a corresponding amount (that is, the cost o

H proponents:

(a) They cancel each other out or (b) rational analysts eliminate their influence on prices.

Shleifer & Summers

-A) Irrational, noisy traders don’t follow fundamentals, B) Arbitrage is risky [b/c fundamentals can change and future resale prices are unpredictable] and can’t fully correct A)

-Risk of arbitrage is exacerbated by short-time horizon in which traders have to operate [First, borrowing costs for both cash and securities; second, money managers performance is evaluated in short horizons]

-Investor sentiment: Some demand changes not driven by fundamentals / investor rationality. For example following financial gurus or trend chasing.

-Although noise traders lose money and get pushed out of the markets, new ones always enter to replace them.

-S&S agree that what matters is not just predicting future fundamentals.

-Also, predicting what other investors will do. Market pros actually track trends, indexes all the time.

-Here’s what’s worse: some money managers actually take advantages of irrational trading by creating more of what irrational investors want (mutual funds, new share issues, junk bonds).

The Limits of Arbitrage:

-Some unexpected good news might come up in noisy bullish market and can confirm noisy trend in the middle of arb’s “correcting” trade

-Same for the opposite: unexpected bad news come up in noisy bearish market

-Any shock in noisy markets can make cash / securities lenders (cash; securities) nervous.

Bubbles and Crashes:

-Growth in stock indexes of late 90s not in line with main economic indicators (personal income, GDP) and corporate profits

-Shiller: P/E ratio of S&P composite index in Jan 2000 was 44.3 v. 32.6 in Sept 1929.

Shiller: Stock prices have ceased to signal fundamental value.

-Markets experiencing a bubble

-Bubble factors:

– Demographics

– Internet

– Changes in pension plans

– Rise of mutual funds

– Low inflation

– Low taxes (especially expectations for capital gains cuts)

– Reverence for business success and financial gurus

– Trading on-line

– Gambling acceptance

– Low quality of professional investment advice

-Result: feedback loop – naturally occurring Ponzi process

-Investor confidence buoyed up by past prices drove up markets

-New investors showed up; mom & pop traders drove up prices even more

-News media obsessed market records

-Bandwagon effect

Shleifer & Summers:

-Positive feedback trading

-Chasing the trend

-Rise and fall – fast and violent