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Key Concepts and Skills 6 Calculators Discounted Cash Flow Valuation Be able to compute the future value of multiple cash flows Be able to compute the present value of multiple cash flows 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 0 1 Multiple Cash Flows Future Value Example 6 1 Chapter Outline Future and Present Values of Multiple Cash Flows Valuing Level Cash Flows Annuities and Perpetuities Comparing Rates The Effect of Compounding Loan Types and Loan Amortization Find the value at year 3 of each cash flow and add them together z z z z z Today Today s year 0 CF 3 N 8 I Y 7 000 PV CPT FV 8817 98 Year 1 CF 2 N 8 I Y 4 000 PV CPT FV 4 665 60 Year 2 CF 1 N 8 I Y 4 000 PV CPT FV 4 320 Year 3 CF value 4 000 Total value in 3 years 8 817 98 4 665 60 4 320 4 000 21 803 58 Value at year 4 1 N 8 I Y 21 803 58 PV CPT FV 23 547 87 2 Multiple Cash Flows Example 2 Continued Multiple Cash Flows FV Example 2 Suppose you invest 500 in a mutual fund today and 600 in one year If the fund pays 9 annually how much will you have in two years z z z 3 How much will you have in 5 years if you make no further deposits First way z Year 0 CF 2 N 500 PV 9 I Y CPT FV 594 05 Year 1 CF 1 N 600 PV 9 I Y CPT FV 654 00 Total FV 594 05 654 00 1 248 05 z z Second way use value at year 2 z 4 Year 0 CF 5 N 500 PV 9 I Y CPT FV 769 31 Year 1 CF 4 N 600 PV 9 I Y CPT FV 846 95 Total FV 769 31 846 95 1 616 26 3 N 1 248 05 PV 9 I Y CPT FV 1 616 26 5 1 Multiple Cash Flows Present Value Example 6 3 Multiple Cash Flows FV Example 3 Suppose you plan to deposit 100 into an 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 z z z Find the PV of each cash flows and add them Year 1 CF 4 N 100 PV 8 I Y CPT FV 136 05 Year 3 CF 2 N 300 PV 8 I Y CPT FV 349 92 Total FV 136 05 349 92 485 97 z Year 1 CF N 1 I Y 12 FV 200