More Shortcuts – Growing Perpetuities and Annuities

1. Growing Perpetuities You now know how to value level streams of cash flows, but you often need to value a stream of cash flows that grows at a constant rate. For example, think back to your plans to donate $10 billion to fight malaria and other infectious diseases. Unfortunately, you made no allowance

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How Interest Is Paid and Quoted

In our examples we have assumed that cash flows occur only at the end of each year. This is sometimes the case. For example, in France and Germany, the government pays interest on its bonds annually. However, in the United States and Britain, government bonds pay interest semiannually. So if a U.S. government bond

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Using the Present Value Formula to Value Bonds

If you own a bond, you are entitled to a fixed set of cash payoffs. Every year until the bond matures, you collect regular interest payments. At maturity, when you get the final interest payment, you also get back the face value of the bond, which is called the bond’s principal. 1. A Short

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How Bond Prices Vary with Interest Rates

Figure 3.1 plots the yield to maturity on 10-year U.S. Treasury bonds[1] from 1900 to 2017. Notice how much the rate fluctuates. For example, interest rates climbed sharply after 1979 when Paul Volcker, the new chairman of the Fed, instituted a policy of tight money to rein in inflation. Within two years the interest

The Term Structure of Interest Rates

When we explained in Chapter 2 how to calculate present values, we used the same discount rate to calculate the value of each period’s cash flow. This discount rate was the bond’s yield to maturity y. For many purposes, using a single discount rate is a perfectly acceptable approximation, but there are also occasions

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Explaining the Term Structure of Interest Rates

The term structure that we showed in Figure 3.4 was upward-sloping. Long-term rates of interest in December 2017 were more than 2.5%; short-term rates were about 1.8%. Why then didn’t everyone rush to buy long-term bonds? Who were the (foolish?) investors who put their money into the short end of the term structure? Suppose

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Real and Nominal Rates of Interest

It is now time to review more carefully the relation between inflation and interest rates. Suppose you invest $1,000 in a one-year bond that makes a single payment of $1,100 at the end of the year. Your cash flow is certain, but the government makes no promises about what that money will buy. If

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The Risk of Default

1. Corporate Bonds and Default Risk Look at Table 3.7, which shows the yields to maturity on a sample of corporate bonds. Notice that the bonds all mature in 2023, but their yields to maturity differ dramatically. With a yield of 13.0%, the bonds of Quorum Health appeared to offer a mouth-watering rate of

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How Common Stocks Are Traded

Boeing has 596 million shares outstanding. Shareholders include large pension funds and insurance companies that each own millions of shares, as well as individuals who own a handful. If you owned one Boeing share, you would own .0000002% of the company and have a claim on the same tiny fraction of its profits. Of

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How Common Stocks Are Valued

Finding the value of the stock of Boeing or GE may sound like a simple problem. Public com­panies publish quarterly and annual balance sheets, which list the value of the company’s assets and liabilities. For example, at the end of September 2017, the book value of all GE’s assets—plant and machinery, inventories of materials,

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Estimating the Cost of Equity Capital

In Chapter 2, we encountered some simplified versions of the basic present value formula. Let us see whether they offer any insights into stock values. Suppose, for example, that we forecast a constant growth rate for a company’s dividends. This does not preclude year-to-year deviations from the forecast: It means only that expected dividends

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The Link between Stock Price and Earnings per Share

Investors separate growth stocks from income stocks. They buy growth stocks primarily for the expectation of capital gains, and they are interested in the future growth of earnings rather than in next year’s dividends. They buy income stocks primarily for the cash dividends. Let us see whether these distinctions make sense. Imagine first the

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Valuing a Business by Discounted Cash Flow

Investors buy or sell shares of common stock. Companies often buy or sell entire businesses or major stakes in businesses. For example, we have noted BHP Billiton’s plans to sell its U.S. shale business. Both BHP and potential bidders were doing their best to value that business by discounted cash flow. DCF models work

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A Review of the Basics of Net Present Value

Vegetron’s chief financial officer (CFO) is wondering how to analyze a proposed $1 million investment in a new venture code-named project X. He asks what you think. Your response should be as follows: “First, forecast the cash flows generated by project X over its economic life. Second, determine the appropriate opportunity cost of capital

Book Rate of Return and Payback

1. Book Rate of Return Net present value depends only on the project’s cash flows and the opportunity cost of capital. But when companies report to shareholders, they do not simply show the cash flows. They also report book—that is, accounting—income and book assets. Financial managers sometimes use these numbers to calculate a book

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Internal (or Discounted Cash Flow) Rate of Return

Whereas payback and return on book are ad hoc measures, internal rate of return has a much more respectable ancestry and is recommended in many finance texts. If we dwell more on its deficiencies, it is not because they are more numerous but because they are less obvious. In Chapter 2, we noted that

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Choosing Capital Investments When Resources Are Limited

Our entire discussion of methods of capital budgeting has rested on the proposition that the wealth of a firm’s shareholders is highest if the firm accepts every project that has a positive net present value. Suppose, however, that there are limitations on the investment program that 9In Chapter 22, we discuss when it may

Applying the Net Present Value Rule

Many projects require a heavy initial outlay on new production facilities. But often the largest investments involve the acquisition of intangible assets. For example, U.S. banks invest huge sums annually in new information technology (IT) projects. Much of this expenditure goes to intangibles such as system design, programming, testing, and training. Think also of

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Corporate Income Taxes

Look at Table 6.1, which shows corporate income tax rates in 11 countries. These are the tax rates imposed by the national governments, but corporations may also need to pay tax to a regional government. For example, in Canada, the provincial governments levy an additional tax of between 11% and 16%. In the United

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Example – IM&C’s Fertilizer Project

1. The Three Elements of Project Cash Flows You can think of an investment project’s cash flow as composed of three elements: Total cash flow = cash flow from capital investment + operating cash flow                                    + cash

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