RWJ chapter 4

# RWJ chapter 4 - Chapter 4 Discounted cash flow valuation...

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Chapter 4: Discounted cash flow valuation Corporate Finance Ross, Westerfield, and Jaffe

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Outline 4.1 Future value 4.2 Present value 4.3 Other parameters 4.4 Multiple cash flows 4.5 Comparing rates 4.6 Loan types
Definitions Present value (PV): earlier money on a time line. Future value (FV): later money on a time line. Interest rate ( i ) , e.g., discount rate, required rate, cost of capital: exchange rate between earlier money and later money. The number of time periods on a time line ( N ). PV FV: “time value of money” via the exchange rate, i.e., interest rate, i .

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End-of-period cash flows By default, in this class cash flows occur at the end of each period. If cash flows occur at the beginning of each period, it will be explicitly specified.
One equation; one solution In general, we have one equation: 0 = f (PV, FV, i , N ). Since we have only one equation, we can only allow for one unknown parameter (variable). That is, if we’d like to calculate the value of a parameter, say FV, the values of the remaining parameters, i.e., PV, i , and N , need to be known.

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FV example I Suppose that we buy a 12-month CD at 12% annual interest rate for \$10,000. FV = PV × (1 + i ) N = \$10,000 × (1 + 12%) 1 = \$11,200.
Do not compare apples with oranges Why N = 1 while the CD matures in 12 months? The key is that: The time frequency of i and N must be the same. If we use annual interest rate, then we need to measure the investment period using the unit of year. In this case, 12 months equal a year; so N = 1. What is the value of N if the example provided us monthly interest rate, say 0.96% per month? Any volunteer?

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Compounding Of course, the previous formula, FV = PV × (1 + i ) N , is based on the notion of compounding. Compounding: the process of accumulating interest on an investment over time to earn more interest. Earn interest on interest. Reinvest the interest. A popular method.
FV example II Deposit \$50,000 in a bank account paying 5%. How much will you have in 6 years? Formula: FV = PV × (1 + i ) N = \$50,000 × (1 + 5%) 6 = \$67,000. Financial table (Table A.3): FV = \$50,000 × 1.3401 = \$67,000. Financial calculator: 6 N; 5 I/Y; 50000 PV; CPT FV. The answer is FV = -67,004.7820. Ignore the negative sign.

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Texas Instruments BAII Plus (keys) FV: future value. PV: present value. I/Y: period interest rate. - Interest is entered as a percent. N = number of time periods. Clear the registers (CLR TVM, i.e., 2nd FV) after each calculation; otherwise, your next calculation may come up with a wrong answer.
FV example, III Jacob invested \$1,000 in the stock of IBM. IBM pays a current dividend of \$2 per share, which is expected to grow by 20% per year for the next 2 years. What will the dividend of IBM be after 2 years? Formula: FV = PV

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RWJ chapter 4 - Chapter 4 Discounted cash flow valuation...

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