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Therefore, E is equal to the sum of the En s This is a fundamental rule in series dc circuits It also holds for 60-Hz utility ac circuits almost all the time..

J3-1 J3-2 J3-3 J3-4

How do you find the voltage across any particular resistor Rn in a circuit like the one in Fig. 5-2 Remember Ohm s Law for finding voltage: E IR. The voltage is equal to the product of the current and the resistance. Remember, too, that you must use volts, ohms, and amperes when making calculations. In order to find the current in the circuit, I, you need to know the total resistance and the supply voltage. Then I E/R. First find the current in the whole circuit; then find the voltage across any particular resistor.

Problem 5-1

J1-4

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its free cash flow to shareholders through dividends or share repurchases. When return on investment equals a company s WACC, investors are just compensated for the risk that they are taking in owning the company s stock and no additional value is created from new business investments. The stock price is still growing in value, but its growth does not exceed its risk-adjusted market expectation (or match investors hopes). At that point in time, the after-tax earnings of the company can be treated and valued as what is known as a cash flow perpetuity equal to the company s net operating profit after tax divided by its WACC (NOPAT/WACC). This number is discounted to the present also at the company s WACC. This discounted value is called the company s residual value a very important number, and generally represents 60 percent to 90 percent of the total value of the company. The residual value is very sensitive to projections of the company s NOPAT and its WACC, as described in the section that follows.

In Fig. 5-2, there are 10 resistors. Five of them have values of 10 , and the other five have values of 20 . The power source is 15 Vdc. What is the voltage across one of the 10 resistors Across one of the 20 resistors First, find the total resistance: R (10 5) (20 5) 50 100 150 . Then find the current: I E/R 15/150 0.10 A 100 mA. This is the current through each of the resistors in the circuit. If Rn If Rn 10 , then En 20 , then En I(Rn) I(Rn) 0.1 0.1 10 20 1.0 V. 2.0 V.

3 2 1

You can check to see whether all of these voltages add up to the supply voltage. There are five resistors with 1.0 V across each, for a total of 5.0 V; there are also five resistors with 2.0 V across each, for a total of 10 V. So the sum of the voltages across the resistors is 5.0 V 10 V 15 V.

What is our preferred excess return period This is a judgment call. We use the 1-5-7-10 Rule and suggest that you do likewise. We group companies into one of four general categories and excess return periods. We then value them using a 10-year excess return period to calculate what we consider to be their maximum value, and a more conservative 1-year, 5-year, or 7-year return period to calculate a reasonable or minimum value. Here are the criteria we use to determine the lower, more conservative excess return period: 1. Boring companies that operate in a highly competitive, low-margin industry in which they have nothing particular going for them a 1-year excess return period; 2. Decent companies that have a recognizable name and decent reputation and perhaps a regulatory benefit (e.g., a utility like Consolidated Edison), but don t control pricing or growth in their industry a 5-year excess return period; 3. Good companies with good brand names, large economies of scale, good marketing channels, and consumer identification (e.g., McDonald s) a 7-year excess return period; and

Problem 5-2

Rear view female DB-9

In the circuit of Fig. 5-2, what will happen to the voltages across the resistors if one of the 20- resistors is shorted out In this case the total resistance becomes R (10 5) (20 4) 50 80 130 . The current is therefore I E/R 15/130 0.12 A. This is the current at any point in the circuit. This is rounded off to two significant figures. The voltage En across Rn 10 is equal to En I(Rn) 0.12 10 1.2 V.

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