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Exam: Dec. 2015 Level 1 > Study Session 2. Quantitative Methods: Basic Concepts > Reading 5. The Time Value of Money
Learning Outcome Statements
Subject 6. The cash flow additivity principle
The additivity principle: Dollar amounts indexed at the same point in time are additive. Suppose we are considering two series of cash flows (A and B). The annual interest rate is 5%. We want to know the future value of combined cash flows at t = 3.
- We can calculate the future value of each series and add them up. The future value of series A is 100 x 1.052 + 100 x 1.05 + 100 = 315.25, and the future value of series B is 150 x 1.052 + 150 x 1.05 + 150 = 472.875. The future value of A + B is 788.125.
- Alternatively, we can add the cash flows of each series first, and then find the future value of the combined cash flows: 250 x 1.052 + 250 x 1.05 + 250 = 315.25 = 788.125.
We can use this principle to solve many uneven cash flow problems if we add dollars indexed at the same point in time. Consider a cash flow series, A, with $100 indexed at t = 1, 2, 3 and 5, and $0 at t = 4. This series is an almost-even cash flow, flawed only by the missing $100 at t = 4. How do we find the present value of this series?
- We can create an annuity B with $100 indexed at t = 1, 2, 3, 4, 5. It's easy to find the present value of this series.
- Then we isolate an easily evaluated cash flow B - A: it has a single cash flow of $100 at t = 4. It's also easy to find the present value of this single cash flow.
- We then subtract the present value of B - A from the present value of B.
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