How to Evaluate the Profitability of an Investment - Pt. 2
In the first part we evaluated the convenience of making a certain type of investment compared to another, using the Payback Period method.
Let's now look at a slightly more complex method, the calculation of the Net Present Value .
In practice, this involves discounting the future cash flows associated with the investment project.
Beyond the calculations, the idea behind NPV is very simple: time is money!
Having 1,000 euros today, or coming into possession of them in 5 years, makes a big difference.
Well, updating the value of sums of money (both incoming and outgoing) referring to future times means calculating the value of those same sums at a valuation date prior to those dates on which they will be realised in time.
To better understand the concept of present value, it is best to start from the concept of future value , with which the former is closely linked.
So for example, the future value of 100 in one year, at the rate of 20%, will be
Value at year 1 = 100.00 × (1 + 20%) = 120.00
And if we wanted to know the value in two years, at the rate of 20% we would have that:
Value at year 2 = Value at year 1 × (1 + 20%) = 144.00
In three years, always at the same rate of 20%, the value will be:
Value at year 3 = Value at year 2 × (1 + 20%) = 172.80
More generally, the future value VF of a sum S at rate r after n years will therefore be:
Future Value FV = S × (1 + r) n
But let's now come to the current value.
If I want to know how much I have to invest today, always at 20%, to have 120 in a year, I will have to do:
Current Value = 120.00 / (1 + 20%) = 100.00
If instead I want to know how much I have to invest today to have 144 in two years, I will have to do two steps:
Value at year 1 = 144.00 / (1 + 20%) = 120.00
And then again (second step):
Current Value = 120.00 / (1 + 20%) = 100.00
Finally, if I want to know how much I have to invest today to have 172.80 in three years, I will have to do three steps:
Value at year 2 = 172.80 / (1 + 20%) = 144.00
And then again (second step):
Value at year 1 = 144.00 / (1 + 20%) = 120.00
So finally (third step):
Current Value = 120.00 / (1 + 20%) = 100.00
More generally, with a single step, the present value VA of a sum S at the rate r that will be available in n years will therefore be:
Present Value VA = S / (1 + r) n
As we have seen, discounting a value necessarily implies defining a discount rate that allows us to transform, for example, the value of a certain sum that we expect to obtain in n years, into its equivalent value on today's valuation date.
The choice of a certain rate requires defining a standard of profitability expected by shareholders and financiers, which can also be understood as an opportunity cost, i.e. as a return offered by alternative investments with a similar level of risk .
Calculating Net Present Value means calculating the present value of future benefits (i.e. in our usual example the present value of inflows in years 1 to 5), net of the initial investment at time 0.
Assuming a discount rate r equal to 10%, with the NPV method we must report the cash flows expected in the various years to their current value, after which we will subtract the initial investment.
In case A (system repair) the following situation will occur:
To update the 50,000 of year 1, we will have:
Present Value Flow Year 1 = 50,000 / (1 + 10%) = 45,455
Wanting to update the 50,000 of year 2, we will have:
Present Value Flow Year 2 = 50,000 / (1 + 10%) 2 = 41,322
And so on, obtaining the amounts indicated in the “Year 0” column.
The sum of the current values will be subtracted from the 100,000 of the initial investment, to arrive at a total NPV of 29,186.
In case B (purchase of new system), however, the situation will be as follows:
Leaving aside the calculations – similar to the previous case –, the sum of the current values of the flows of years 1 to 5, indicated in the “Year 0” column, will be subtracted from the 200,000 of the initial investment, thus arriving at a total NPV of 53,785.
Both solutions A and B are advantageous, since at that specific discount rate the NPV is greater than zero , which means that both solutions create value for the company.
A negative NPV, on the contrary, would have meant destruction of value for the Company, therefore the investment associated with it would certainly have had to be abandoned.
The adoption of the NPV method in our case shows that the careful entrepreneur should opt for solution B, i.e. the purchase, since it is reasonably estimated that this type of investment will lead – in the five-year period of reference – to the creation of greater value.
Graphically, with the help of a waterfall chart, you will have:
We have just seen how the NPV method, overcoming the significant limitations of the Payback Period, leads to a different conclusion: taking into account the financial value of time, solution B is the preferable one.
In the third part of the article we will analyze the IRR method, a method that has some analogies with the NPV, as it also considers the financial value of time, but from a different perspective.