Before we proceed further, you need be aware of simple interest and compound interest which we discussed under a separate article. If you don't remember, please go through the below link.
https://osmi-edu.wixsite.com/osmi-edu/post/simple-interest-compound-interestOkay!! Now we are all set to move forward..
Let's take a scenario where you deposit some amount of money in the bank for a period of 5 years. The value of the investment at the time of its maturity (after 5 years) is called the Terminal Value.
Definitely this value will depend on the deposited amount, interest rate & stable growth rate.
Calculation is not that complex if you can build a general formula for the concept.
Assume you deposit $100 at an interest rate of 8% per annum in a bank. Taking compound interest where interest is added back to the capital at end of every year, let us try to build a formula.
Did you figure out a pattern???
Consider the final formula under each year.
$100 is the initial investment - we would call this the present value
8% is the annual interest rate
The power is the number of periods from the date of investment (In this case its no:of years)
All variables remain constant except for the number of periods. By any chance if you are to find the Future Value after 10 years, FV = 100 * (1 + 8%)^10
Hence, a common formula can be introduced as below......
Above formula will be the future lifesaver for you in investment appraisal.
DISCOUNTED CASH FLOW
Discounting is a way to compute the present value of future money. This may be better understood if explained as below.
You need to have $1,500 with you in 5 years time. Then what is the amount you need to have today which will assist you to reach $1,500 in 5 years. Assume a scenario where you want to know how much you should deposit in a bank today which pays 10% interest per annum to reach the target of $1,500 in 5 years.
Isn't this the opposite of compounding????
$1,500 is the Future Value
10% is the Interest Rate
5 years is the Time Period
Then what you don't know is the Present Value.
Take your lifesaving equvation and make the present value the subject.
Hope you remember Grade 6 Mathematics :)
If you deposit $931.38 today, you can have $1,500 in 5 years without any further investment.
Okay!!! Now let's see how this concept can be adopted in Investment Appraisal.
Before going into this section, you need to know the concept of Time Value of Money. Do you remember how value of money depreciate when time goes on???? If not, refer below link prior to reading the rest.
https://osmi-edu.wixsite.com/osmi-edu/post/time-value-of-money
To buy the same product you pay a higher amount of money due to value depreciation. This means $5, 5 years back had the same value as $15 now. So, value wise it is equal.
Same way if a potential project has estimated a gain of $150 profit in the third year of operation, it will not give you the same value as $150 gained today. Probably this may give a value equivalent to somewhere around $90 or $100 today. This is simply because of the concept of Time Value of Money.
You can also say, $90 today is the equivalent value of $150 in 3 years.
We will now go through an investment opportunity and see how the above concept works............
If a potential investment opportunity which requires an initial investment of $500 and has a life of four years would generate Net Cash Flows of $150, $175, $220 & $250 in year 1, 2, 3 & 4 respectively to be evaluated,
One adds all potential cash flows and say that the investment opportunity has a net worth of $295, hence it seems to be viable opportunity, it is WRONG.
But Why?? You perfectly know that the cash flows recorded from year 1 to 4 are future cash flow estimations (amount of money) but all these are in different value terms. Even if all 4 years to have $150 each, those four $150 cash flows will have different values. So, if you are to do a proper analysis all recorded cash flows should be brought to one base platform. Easiest is to bring all to today's value but to do so, you need to know the Cost of Capital (CoC is a rate) which will be given in any question you get in any level of study.
In other words, show the present values of all the future values given in the table.
How on earth are you going to do that??? Simple....... Just use the adjusted magical formula you learned before,
This formula should be used for all four future cash flows separately.
Look!! There is a small modification that can be done to the above formula.....
Why did we modify the formula??? Your life should be simplified. If modified, you can use a table called present value table which gives the Discount Factors for any known CoC & period.
Since you know the requirement to discount cash flows and how to discount, shall we discount the above four cash flows and calculate the present valus???????????
Assume the Cost of Capital for the considered investment is 10%.
The present values calculated above are the discounted cash flows for respective future cash flows.
That is enough for today. Let's discuss on Investment Appraisal Techniques in a different article.
Purindu B Jayatilake
MSc Eng (Reading), MBA, BSc (Hons) Eng, ACMA (UK), CGMA
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