Discounting
The time value of money: present value of a future sum, discount rate and factor, streams of cash flows and constant annuities, comparing sums at different dates.
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Time value of money: what is it?
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The principle that a sum available now is worth more than an equal sum available later, because the first can be invested in the meantime.
It is not just inflation: even with no price rise, €1,000 today invested at 5% is worth €1,050 in a year. Comparing euros of different dates without bringing them to one date is a mistake.
What is the present value of €2,000 to be received in 2 years, at 10%?
- €1,653
- €1,600
- €2,420
- €1,818
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€1,653
2,000 ÷ 1.10² = €1,652.89. Subtracting 20% (€1,600) forgets that discounting compounds; €1,818 discounts only one year; €2,420 compounds instead of discounting.
The present value of a sum S payable in n periods at rate i is S ÷ ….
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The present value of a sum S payable in n periods at rate i is S ÷ (1 + i)^n.
You divide, not multiply: future money is worth less today. Dividing by (1 + i)^n is the inverse of compounding.
Discounting: what is it?
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The operation that brings a sum to be received or paid later back to its value today; it is the reverse of compounding.
Compounding multiplies by (1 + i)^n to move forward in time; discounting divides by (1 + i)^n to move back. The two cancel each other.