Future value: Difference between revisions
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'''Example''' | <span style="color:#4B0082">'''Example 1: One year at 10% per year'''</span> | ||
$100m | We hold $100m today. | ||
The rate of return on capital (r) is 10% per year. | The rate of return on capital (r) is 10% per year. | ||
The Future value is: | The Future value in one year's time is: | ||
= $100m x 1.1<sup>1</sup> | = $100m x 1.1<sup>1</sup> | ||
= $110m | = '''$110m'''. | ||
| Line 25: | Line 25: | ||
Where: | Where: | ||
CF = ( 1 + r )<sup>n</sup> | CF = (1 + r)<sup>n</sup> | ||
r = return on capital or cost of capital per period | r = return on capital or cost of capital per period | ||
n = number of periods | n = number of periods | ||
<span style="color:#4B0082">'''Example 2: One year at 6%'''</span> | |||
If we hold $10m today, and the return on capital (r) is 6% per year, | |||
the Future value in one year's time is: | |||
FV = $10m x 1.06<sup>1</sup> | |||
= '''$10.6m'''. | |||
<span style="color:#4B0082">'''Example 3: One year at 6%, starting with $9.43m'''</span> | |||
If we hold $9.43m today, and the return on capital (r) is still 6% per year, | |||
the Future value in one year's time is: | |||
FV = $9.43m x 1.06<sup>1</sup> | |||
= '''$10m'''. | |||
<span style="color:#4B0082">'''Example 4: Two years at 6%, starting with $8.90m'''</span> | |||
Now we hold $8.90m today, and the return on capital (r) is still 6% per year, | |||
the Future value in two years time is: | |||
FV = $8.90m x 1.06<sup>2</sup> | |||
= '''$10m'''. | |||
<span style="color:#4B0082">'''Example 5: Two years at 6%, starting with $10m'''</span> | |||
Now we hold $10m today, and the return on capital (r) is still 6% per year, | |||
the Future value in two years time is: | |||
FV = $10m x 1.06<sup>2</sup> | |||
= '''$11.24m'''. | |||
== See also == | == See also == | ||
* [[Compounding factor]] | * [[Compounding factor]] | ||
* [[Discounted cash flow]] | |||
* [[Internal rate of return]] | |||
* [[Net present value]] | |||
* [[Present value]] | * [[Present value]] | ||
* [[Terminal value]] | * [[Terminal value]] | ||
* [[Time value of money]] | * [[Time value of money]] | ||
[[Category:The_business_context]] | |||
[[Category:Cash_management]] | |||
[[Category:Financial_products_and_markets]] | |||
[[Category:Liquidity_management]] | |||
[[Category:Trade_finance]] | |||
Latest revision as of 14:48, 27 October 2022
(FV).
If we invest money today (and roll up all the expected income) the future value receivable is the expected total value of our investment at its maturity.
If we borrow money today (and roll up all the interest payable) the future value payable is the total principal and interest repayable to the lender at the final maturity of the borrowing.
Example 1: One year at 10% per year
We hold $100m today.
The rate of return on capital (r) is 10% per year.
The Future value in one year's time is:
= $100m x 1.11
= $110m.
More generally
FV = Present value x Compounding Factor (CF)
Where:
CF = (1 + r)n
r = return on capital or cost of capital per period
n = number of periods
Example 2: One year at 6%
If we hold $10m today, and the return on capital (r) is 6% per year,
the Future value in one year's time is:
FV = $10m x 1.061
= $10.6m.
Example 3: One year at 6%, starting with $9.43m
If we hold $9.43m today, and the return on capital (r) is still 6% per year,
the Future value in one year's time is:
FV = $9.43m x 1.061
= $10m.
Example 4: Two years at 6%, starting with $8.90m
Now we hold $8.90m today, and the return on capital (r) is still 6% per year,
the Future value in two years time is:
FV = $8.90m x 1.062
= $10m.
Example 5: Two years at 6%, starting with $10m
Now we hold $10m today, and the return on capital (r) is still 6% per year,
the Future value in two years time is:
FV = $10m x 1.062
= $11.24m.
