(Extract from the
stock valuation and behavioral finance site)
What does an investor's return include?
Milking the cow but feeding it also.
An investor return includes all the "cash flows" (*) he/she gets from
its investment (whether an asset, a business project, even a professional
- Positive cash
differences between resale values (**) and buying / subscription
- and Negative cash flows: expenses (fees, taxes...), capital loss (*).
* its recuperation at the end as a positive one.
(*) Past cash flows when calculating historical returns, or expected
cash flows when addressing a present investment.
(**) Based on the past, actual or expected resale transaction.
If there is a market for the asset, its current price shows a possible
* the more risky the investment is
* (and the more risk averse investors are),
* the higher should the rate of return be,
so as to convince investors to put money in the
In other words, the rate of return used in the calculation should include
a risk premium adapted to the type of investment
A similar calculation can be applied to the financial
weight of a loan on the borrower.
(the loan received itself is a positive cash flow; refunds, interests
and other costs are negative ones).
"Snowball arithmetic" under "geometric progression".
* the past or future return of assets / projects / investments over
* and the present financial value of those assets / projects / investments.
Compound rate calculations are used notably
- in finance, investing / borrowing (rates of return, interest rates)
- and by extension in economics (growth rates, inflation effects).
For savers, investors, entrepreneurs, borrowers, compound rates are
- Find out:
- the rate of return (*) of an investment, a business project
- or the real financial cost ("actuarial interest rate) of a debt
- Or find the future value FV.
debt) will be worth after several years .
- Or give the present value PV, aka discounted value
(*) to compute an expected future return (and a present value),
to make cash flow previsions is needed.
Definition / calculation
The compound annual rate of return of an asset (or of a project) is:
- An annual return (*) R
- which, compounded (**) year after year,
- brings a total return TR at the end of the period.
(**) Compounded = cumulated by using the hypothesis that:
Every year the asset value is increased ("capitalized") by the annual
In the next year the return rate is applied to that increased
For example if the rate is 6%, an asset which
value is today 1 Euro will be worth:
- 1.06 Euro after 1 year,
- 1.06 x 1.06 after 2 years, and so on...
(the table below shows that "snowballing effect / hyperbolic
Future value FV
R = the annual "compounded" rate of return
Y = the number of years
FV = the future value at the end of the period
TR = the total return of that period
|1 Euro x 1.06 x 1.06 x 1.06 x 1.06 = 1.262 Euro |
(this is the future value FV)
The total return TR (relative increase in value)
is therefore 26,2 %
Present value PVSuch asset valuation is done by "discounting" the future expected
asset worth (or its expected cash flows) with a return rate that is
considered necessary when investing money.
If we use the data above, 10,000 Euros that we will receive in 4 years
aretheoretically worth now (PV / present value, aka discounted
10,000 / 1.262 = 7,924 Euros (present value)
and use of probabilities
Getting fresh eggs day after day,
and the hen for your soup at the end
Most financial assets bring not only a final worth at the end of a
period (for example at maturity) but also a chain of cash flows
year after year.
=> The calculations must take that into account, for example to
determine the PV of the asset
In that case, every cash flow is discounted according to the
number of years in which it will take place to obtain its
=> Then all those PV are added together to give the asset PV.
Also, we can have several scenarios, each one with its probability.
of every scenario multiplied by its
To mention what the extreme scenarios would bring is useful also
to make decisions
| ||Y|| |
Annex: calculation of real (*) rates
- The inflation rate is 4%
- The return rate is 10%
Back to collection : Finance articles migrated from Knols
1.10 / 1.04 = 1.058, therefore 5.8 %
Pageviews for this article before migration from Knol: 4.9 k