Answer:
- Present value is the value today of a future amount of money discounted at the rate of return expected.
- Present value = Future value / (1 + r)ⁿ.
Explanation:
What would you prefer to receive $1,000 today or the same amount in a year?
- You should prefer to receive the $1,000 today than in a year from now.
What would you prefer to receive $1,000 today or $1,200 in a year?
- If you do not have an urgent need today, most likely you would be willing to receive $1,200 in a year because $1,200 is much more money than $1,200.
What if I ask to choose between $,1000 today and $1,050 in a year?
- How would you tell what is, financially, better?
The <em>present value</em> is the amount of money today that is financially equal to an amount of in the future.
<u>How can you </u><em><u>mathematically</u></em><u> calculate the present value?</u>
Assume you are offered $1,000 in a year, how much money does it represent today?
That depends on the opportunities that you have to do with the money. Let's say that you can invest your money today in a business that gives you a 10% return in a year. This is, r = 10%.
To calculate the value in a year of an investment today, you would multiply your investment for 1 + 10% = 1 + 0.01 = 1.01. This is:
Value today Value in a year
$1,000 $1,000 × 1.10 = $1,100
That means that $1,100 in a year are equal to $1,000 in the present. Hence, the<em> present value</em> of $1,100 in a year is $1,000.
- $1,000 = $1,100 / (1 + 0.10) = $1,100 / (1.10)
In general, the<em> present value</em> is the value of a future amount of money discounted at the rate of return expected.
- Present value = Value in one year / (1 + r).
But it also depends on the number of years elapsed. If it is 2 years you have to discount it two times, this is divide the value in two years by (1+r) two times:
- Present value = Value in two year / (1 + r)².
For a number n of years, you obtain:
- Present value = Value in the futre / (1 + r)ⁿ.
