## The Debt Equity Ratio and Liabilities Equity Ratio come in many variations Financial debt

Is usually defined as the sum of long-term debt ( 2,651) and debt in current liabilities ( 354). Total Liabilities ( 21,695- 8,648 13,047) includes such obligations as current liabilities, pension liabilities, etc. Equity is best measured in terms of market value. Quoting all dollar figures in millions, Other ratios can be used to judge health and profitability. Long Term Debt + Debt in Current Liabilities Market Value (MV) of Equity 2,651 + 354 87,407 Market Value (MV) of Equity 87,407 Some...

## The Discount Factor on Tax Obligations and Tax Shelters

We know the future tax-related cash flows. How do you discount them Let's work a simple example with risky payoffs. The tax payment is as risky as the firm, and thus warrants a higher cost of capital. For our 1-year, non-growing firm, the tax shelter is safer than the firm, and thus warrants a lower cost of capital. Alas, you can often use the firm's cost of capital also on the tax shelter. Why Worry more about the correct discount factor on big amounts. On Page 480,1 stated that it is common...

## Some Other Corporate Tax Avoidance Schemes

Wall Street and Main Street employ armies of tax experts to help their clients avoid taxes, but this is really an arms race between the IRS (Congress) and investors. Investors keep looking for new tax avoidance schemes and the IRS tries to close these new loopholes. There are a large number of both past (now closed) and current tax avoidance schemes. Some of the more noteworthy remaining tax reduction schemes are as follows Sometimes, high-tax firms may be able to purchase low-tax firms, and...

## Put Options

A put option gives the owner the right (but not the obligation) to sell (put) shares for a given price at or by a given point in time. For example, a put might be the right to sell 300 shares of the firm for 50 share on or before January 15, 2050. Say you sell me such a put for 5 put today. If shares will then trade for 35 share, I can buy the shares on the open market for 35 share, and exercise my right to sell them to you for 50 share, i.e., at a profit of 15 share. If shares will then trade...

## End of Chapter Problems

Q 6.42 What is the difference between a perfect market and a competitive market Q6.43 What are the perfect market assumptions Q 6.44 What is the difference between a perfect market and an efficient market Q6.45 Your borrowing rate is 15 year. Your lending rate is 10 year. The project costs 5,000 and returns a rate of return of 12 . Should you take the project a if you have 2,000 to invest b if you have 3,000 to invest c if you have 4,000 to invest If you have 3,000 to invest, should you take...

## Reverse Engineering Accounting into Finance

Discounting the Net If you did not know about the details of this machine but saw only the financials, could you heuue o'ect NPV compute the correct firm value by discounting the net income Discounting net income with a t e true project . cost of capital of 12 would yield which is definitely not the correct answer of 73.16. Neither would it be correct to discount the net income with a cost of capital of 10 , Cash flows can be How can you reverse-engineer the correct cash flows for the NPV...

## You need to memorize the CAPM formula

If you believe that the risk-free rate is 3 and the expected rate of return Plugging into the on the stock market is 7 , then the CAPM states that formula. E fi 3 7 - 3 piM 3 4 piM Therefore, a project with a beta of 0.5 should have a cost of capital of 3 4 -0.5 5 , and a project with a beta of 2.0 should have a cost of capital of 3 4 -2.0 11.0 . The CAPM gives an opportunity cost for your investors' capital if the project with the beta of 2.0 cannot earn a rate of return...

## How Bad Are Mistakes Averaging PE Ratios and the 1X Problem

A P E ratio in which E Unfortunately, averaging P E ratios is not only formally wrong, it can also create huge problems is smaN is bad, bad, by itself. The main problem is that ratios are not sensible if their denominator can be zero or negative. This is the case for the P E ratio. Earnings can be temporarily zero or negative. This can totally mess up any P E ratio analysis. The function 1 E is both discontinuous and very steep when earnings are close to zero. We shall call this the 1 X...

## B A Common Misuse of the CAPM Using Badly Blended Costof Capitals

Common misuse of CAPM a uniform cost of capital. Section 7 1.B dropped a cryptic hint that practitioners sometimes forget that NPVs are additive. You may have wondered what was meant. You are now ready to see why this is such a common mistake. The most common abuse of the CAPM arises from the use of the firm's overall cost of capital for individual projects. Let me explain how this can happen. What happens if the firm uses its overall cost of capital for all projects, rather than project...

## NonCAPM Worlds and Non Linear SMLs

What happens if a stock offers too much or too little expected rate of return No CAPM would not mean arbitrage, but it could imply good deals. The Security Market Line if the CAPM is the wrong model with respect to its own functional form . The Security Market Line if the CAPM is the wrong model with respect to a specific better alternative . What would happen from the CAPM's perspective if a stock offered more than its due expected rate of return Investors in the economy would want to buy more...

## Anecdote Trading Places and Citrus Futures

The 1983 hit comedy Trading Places, starring Dan Akroyd and Eddie Murphy, centers around the trading of Orange Juice Frozen Concentrate Futures Contracts securities that promise delivery of oranges on the New York Futures Exchange. If it is going to rain or there is a frost, oranges will be scarcer and the futures price will rise. You can learn more about futures contracts at the website of the New York Mercantile Exchange at www.nyce.com. In a 1984 paper in the American Economic Review,...

## Application Stock Valuation with A Gordon Growth Model

Perpetuities are With their fixed interest and growth rates and eternal payment requirements, perpetuities are a roximationerfeijt rarely exactly correct. But they can be very helpful for quick back-of-the-envelope estimates. apopfteximveanuseful For example, consider a stable business with profits of 1 million next year. Because it is stable, upper bound. its profits are likely to grow at the inflation rate of, say, 2 per annum. This means it will earn 1,020,000 in two years, 1,040,400 in...

## Important The Yield to Maturity is the quantity YTM which given a complete set of bond cash flows solves the NPV

0 CF0 ITyTM 17 TTYTMP ''' 425 An example of solving In this case, you want to solve the YTM equation. ffmnnnn 5,000 10,000 120,000 0 - 100'000 1 1 YTM 2 1 YTM 3 426 In general, you solve this equation by trial and error. Start with two values, say 5 and 10 . nnnnnn 5,000 10,000 120,000 - 100'000 1 5 U W O W M 17,493 100 000 . 5,000 , 10,000 . 120,000 2 968 - 100, 000 1 10 1 10 2 1 10 3 2, 968 To reach zero, you need to slide above 10 . Try 11 and 12 , - 100,000 1 11 1 11 2 1 11 3 M 363 100 000...

## Returns Net Returns and Rates of Return

The most basic financial concept is that of a return. The payoff or dollar return of an invest- Defining return, net ment is simply the amount of cash CF for cash flow it returns. The net payoff or net return is the difference between the return and the initial investment, which is positive if the project is profitable and negative if it is unprofitable. The rate of return is the net return expressed as a percentage of the initial investment. Yield is a synonym for rate of return. For example,...

## The Annuity Formula

An Annuity pays the The second type of cash flow stream that lends itself to a quick formula is an annuity, which is a stream of cash flows for a given number of periods. Unlike a perpetuity, payments stop after T periods. For example, if the interest rate is 10 per period, what is the value of an annuity that pays 5 per period for 3 periods Let us first do this the slow way. You can hand-compute the net present value to be PV0 1 10 ur1W Ot1W m 12.4343 3 20 What is the shortcut to compute the...

## The Goal of Finance Relative Valuation

Finance is such an important part of modern life that almost everyone can benefit from understanding it better. What you may find surprising is that the financial problems facing PepsiCo or Microsoft are not really different from those facing an average investor, small business owner, entrepreneur, or family. On the most basic level, these problems are about how to allocate money. The choices are many money can be borrowed or saved money can be invested into projects, undertaken with partners...

## Ivo Welch

Professor of Finance and Economics Brown University Far and away, the most important contributor to this book was Mary-Clare McEwing. As editor, she helped me improve the substance of the book tremendously. There are also a large number of other individuals who have helped me with this book. Among them were Rick Antle, Donna Battista, Randolph Beatty, Wolfgang Buhler, Kangbin Chua, Diego Garcia, Stan Garstka, Roger Ibbotson, Ludovic Phalippou, Matthew Spiegel, John Strong, Julie Yufe, and many...