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Unformatted text preview: 6 Formulas Discounted Cash Flow Valuation 1 Key Concepts and Skills Be able to compute the future value of multiple Be cash flows cash Be able to compute the present value of multiple Be cash flows cash Be able to compute loan payments Be able to find the interest rate on a loan Understand how interest rates are quoted Understand how loans are amortized or paid off 2 Chapter Outline Future and Present Values of Multiple Future Cash Flows Cash Valuing Level Cash Flows: Annuities and Valuing Perpetuities Perpetuities Comparing Rates: The Effect of Comparing Compounding Compounding Loan Types and Loan Amortization 3 Multiple Cash Flows –Future Multiple Value Example 6.1 Value Find the value at year 3 of each cash Find flow and add them together. flow Today (year 0): FV = 7000(1.08)3 = 8,817.98 Year 1: FV = 4,000(1.08)2 = 4,665.60 Year 2: FV = 4,000(1.08) = 4,320 Year 3: value = 4,000 Total value in 3 years = 8,817.98 + 4,665.60 + 4,320 Total + 4,000 = 21,803.58 4,000 Value at year 4 = 21,803.58(1.08) = 23,547.87 4 Multiple Cash Flows – FV Multiple Example 2 Example Suppose you invest $500 in a mutual Suppose fund today and $600 in one year. If the fund pays 9% annually, how much will you have in two years? you FV = 500(1.09)2 + 600(1.09) = 1,248.05 5 Multiple Cash Flows – Example 2 Multiple Continued Continued How much will you have in 5 years if you How make no further deposits? make First way: FV = 500(1.09)5 + 600(1.09)4 = 1,616.26 Second way – use value at year 2: FV = 1,248.05(1.09)3 = 1,616.26 6 Multiple Cash Flows – FV Multiple Example 3 Example Suppose you plan to deposit $100 into an Suppose account in one year and $300 into the account in three years. How much will be in the account in five years if the interest rate is 8%? interest FV = 100(1.08)4 + 300(1.08)2 = 136.05 + 349.92 = 485.97 349.92 7 Multiple Cash Flows – Present Multiple Value Example 6.3 Value Find the PV of each cash flows and add Find them them Year 1 CF: 200 / (1.12)1 = 178.57 Year 2 CF: 400 / (1.12)2 = 318....
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