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Unformatted text preview: ceive $500 12 years from now 4 Example: Simple Present Value PVA = PVB = • Even though under plan B we receive more money, it is worth less than the $229 under plan A, because it is obtained further in the future. Present Value of $1 for Different Periods and Rates Intuition
The further away the cash flow, the more sensitive the PV to the discount rate
C 100 100 100 T 2 5 10 PV(5%) 90.70 78.35 61.39 PV(10%) 82.64 62.09 38.55 Diff. 8.06 16.26 22.84 % Diff. 8.9% 20.8% 37.2% 5 A Stream of Cash Flows
Everything else is just a combination of these formulas using the fact the PVs and FVs are additive. Example: Present Value Addition • Assume an interest rate of r = 7% and calculate the PV of the following cash flows:
Year 0 Cash Flow $1000 Years to Discount: n 0 1 2 3 Present Value $200 1 $1500 2 $2000 3 Present Value Equals Special Case #1: Annuities • A special case of this addition is the case of annuities.
– An annuity is simply a set of identical cash flows, one each year (or period). 6 Future Value of Annuities • It is important to get the timing straight. Consider a three year annuity that pays $C for each payment. Future Value Calculation
Year
1 2 3 Cash Flow
C C C Years to Future Value End: n
2 1 0 C×(1+r)2 C×(1+r) C Future Value of Annuities • Using the addition principle, the future value of this 3year regular annuity is FV = C × (1 + r ) 2 + C × (1 + r ) + C = C (1 + r ) 2 + (1 + r ) + 1 [ Future Valu...
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