Welcome to this course on investment choice!
Here is what you will learn in this article on the investment choice of the BTS MCO in Operational Management:
- What is an investment?
- What are the different types of investments?
- How to calculate an investment?
- Basic Financial Calculations
- The net cash flow statement (NCF)
- How to calculate net present value (NPV)?
- How to calculate the profitability index (PI)?
- How to calculate the payback period for invested capital (PRIP)?
- How to calculate the internal rate of return IRR?
- Conclusion
What is an investment?
An investment is an amount of money that the business unit spends on an operation from which it hopes to profit.
This action allows the company to improve its production capacities and increase its profitability.
Very often, these are acquisitions of new, more efficient fixed assets.
What are the different types of investments?
There are different types of investments depending on the objectives of the business unit.
We distinguish the investments by nature such as:
- investments intangible which are fixed assets that cannot be touched. These are lease rights or research and development.
- investments bodily which are fixed assets that can be touched such as machinery or equipment.
- investments financial which are fixed assets that correspond to acquisitions of financial securities.
We also distinguish the investments according to their objective :
- The investment of replacement or renewal
- The investment of capacity
- The investment of productivity
How to calculate an investment?
The cost of an investment is the total expenses incurred by the business unit to implement its project.
In addition to the investment amount, additional costs and/or discounts may be added.
The whole forms the cost of investment.
To this cost, we must add the variation in working capital requirement (WCR) which will necessarily be incurred. This is the amount of money that the company will have to advance to cover the gap between its receipts and its disbursements.
Do not hesitate to consult this article on the BFR if you want to know more about the subject.
This amount will be increasingly important because it is proportional to the activity of the company.
Investment Choices and Fundamental Financial Calculations
Before moving on to the FNT table, you must master essential notions of financial calculations. They will help you better understand the calculations of the project assessment criteria.
The acquired value
An amount placed in a remunerated account yields a sum called acquired value (capital + interest).
We distinguish :
- The simple interest : they are calculated over a maximum period of twelve months
- The compound interest : they are calculated over a period of more than twelve months.
The interest is said to be capitalized.
Here is the formula for earned value:
With:
- Vn: acquired value
- V0: Initial amount
- i: the interest rate
- n: the number of placement periods
Here is an example of calculating earned value:
Investment of €2 for two years at a rate of 000% per year.
Simple interest :
Year 1: 2 x 000% = €1,5
Year 2: (2000 + 30) x 1,5% = €30,45
Acquired value :
2 + 000 + 30 = €30,45
Acquired value (compound interest) :
2 x (000 + 1)2 £2
Current value
This is the amount of capital initially invested at the time p0.
With:
Vn: acquired value
V0: Initial amount
i: the interest rate
n: the number of placement periods
Here is an example of calculating the present value
Calculation of the amount invested at time 0 knowing that the amount of the acquired value is €2 and that it was remunerated at the annual rate of 500%.
Calculating the present value
V0 = 2 x (500 + 1)-2
V0 = 2 379,53 €
Interpretation & translation services : By investing €2 today for 379,53 years at a rate of 2% per year, the sum obtained will be €2,5.
Earned value: investment of a series of constant annuities
In a regular investment over the same period, the sum of these investments increased by interest over n periods corresponds to the value acquired by the investment of a series of constant annuities.
With:
a: the amount of the constant annuity.
i: the interest rate
n: the number of payments
Example :
Regular investments for 3 years of €1 at an annual rate of 000%
Calculation of earned value
Present value: investment of a series of constant annuities
In a regular investment at the same period, the amount of the initial investment, i.e. the current value, corresponds to the following formula:
With:
a: the amount of the constant annuity.
i: the interest rate
n: the number of payments
Here is an example of calculating the present value with a series of constant annuities
A company can only repay €5 per year if it had to borrow to invest. The interest rate is 500% per year. The company wants to borrow over 2,5 years.
Calculating the present value
The net cash flow statement (NCF)
Net cash flows (NCF) represent the potential gains from the investment project if the company decided to invest in this project.
To determine the FNT, it is necessary to establish a table in which the revenues generated by the project as well as the costs related to the investment are grouped.
Here's how to calculate FNT:
FNT = Total Receipts – Total Disbursements
FNT = Project-related revenues – Project-related expenses
Here is an example of a FNT table:
| Element | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 |
|---|---|---|---|---|---|
| Turnover excluding tax | |||||
| - Operating costs | |||||
| - Depreciation | |||||
| - Interest charges | |||||
| = Profit before tax | |||||
| - Tax | |||||
| = Result after tax | |||||
| + Depreciation | |||||
| - Repayment of capital | |||||
| = Operating CAF | |||||
The calculation of the CAF (self-financing capacity) only takes into account the operating elements of the business unit.
A second table is necessary to determine the net cash flows taking into account the residual value and the change in WCR.
The residual value corresponds to the value that the company could recover at the end of the period if it decided to resell the asset attached to the investment.
The BFR corresponds to the amount of cash advanced by the company which can be recovered at the end of the project.
If you would like to know more about the BFR I invite you to read this article entitled Balance Sheet Analysis: 4 Essential Points to Know.
| Element | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 |
|---|---|---|---|---|---|
| JOBS | |||||
| Investments | |||||
| + Variation of BFR | |||||
| = Total Jobs | |||||
| FREE | |||||
| Operating CAF | |||||
| Residual value | |||||
| + Recovery of BFR | |||||
| = Total Resources | |||||
| Net Cash Flow (NCF) |
The Net Cash Flow (NCF) line corresponds to the following calculation:
Total Resources – Total Jobs
At the end of the period, the company may take into account the residual value and the recovery of the WCR.
Here is a great video on an exercise on investment choice:
How to calculate net present value (NPV)?
Net present value (NPV) is a decision criterion for investment choice.
Net present value is the difference between discounted cash flows and the amount of capital invested.
You should know that we can use different terms to express the operating CAF, we also speak of operating cash flow or elseEBE net of IS.
NPV = ? Discounted FNT – Amount Invested
Net present value allows us to take into account the impact of time on net annual cash flows (CAF from operations).
Indeed, the FNT acquired in Year 3 does not have the same value as the FNT acquired in Year 1.
The update makes it possible to correct this difference by relating all the numerical elements to the same period, that is to say year 0 (zero).
You must use the formula seen above on the current value.
To calculate the NPV, you can use this very practical type of table:
Here are the detailed explanations:
(1): these are the amounts calculated in the FNT table. Simply copy them over the entire period.
(2): The discount formula must be applied (1 + Discount rate)-n depending on the year considered.
For year 1 you must put (1 + discount rate)-1 .
For year 2 you must indicate (1 + discount rate)-2. And so on throughout the period.
(3): To calculate the updated FNT for a year, you need to take the year's update and multiply it by the FNT.
For year 1 we therefore have: FNT Year 1 x (1 + Discount rate)-1
For year 2 we therefore have: FNT Year 2 x (1 + Discount rate)-2
And so on…
Of course, before applying the FNT formula, you will need to add up the updated FNTs thus calculated.
When the NPV is positive, the business unit considers the project to be profitable.
How to calculate the profitability index (PI)?
The profitability index is another criterion for assessing a project.
The formula for the profitability index is as follows:
IP = ? Updated FNT / Amount Invested
The profitability index corresponds to the amount earned by the business unit for 1 euro invested.
This is the reason why when the profitability index is greater than 1, we consider that the project under consideration is profitable. Conversely, if the IP is less than 1, then it is advisable not to embark on the said project.
How to calculate the payback period for invested capital (PRIP)?
The payback period answers the question: From what date does the project become profitable?
To determine the DRCI, you must gradually accumulate the annual FNTs until you reach the investment amount.
From the moment when the cumulative discounted FNT becomes greater than the amount of the initial investment, then the project becomes profitable..
From the DRCI, the company begins to recover its funds. It is therefore preferable that the recovery period of the invested capital is as short as possible.
Here is an example of a table that can be used to determine the DRCI:
(1): In the Updated FNT column you copy the updated FNTs, logically already calculated.
(2): In the first cell of the Cumul column, you copy the amount of the updated FNT for year 1 located on the left.
(3): In the second cell of the Cumul column, you indicate the result of the sum: (2) + (4).
You then gradually add the cumulative amount found to the updated FNT for the following year.
How to calculate the internal rate of return IRR?
The internal rate of return or internal rate of return is the rate at which the discounted net cash flows equal the amount of the investment. It is also the rate at which the NPV is zero.
The IRR formula is an equality between discount rates on one side and the amounts of the corresponding NPVs on the other.
So here is the IRR formula:
The IRR is the unknown you need to find.
Rates 1 and 2 correspond to discount rates that are given to you in the statement in an obvious way or not.
NPVs are amounts that you have probably calculated beforehand.
You need to solve this equation with one unknown and find TRI.
Here's a very example of calculating IRR
The elements of the statement:
Rate 1: 7,5%
Rate 2: 15%
NPV at rate 1:140
NPV at rate 2: – 12
First I replace all the elements of the formula with the numerical elements except TRI which is the unknown:
Then I calculate the right part because it is a simple division to perform:
I also calculated the denominator of the left division (0,15 – 0,075 = 0,075).
Then I do what is called the cross product (equality of the multiplication of the ends):
IRR – 0,075 = 0,075 x 0,921052632
TRI – 0,075 = 0,0609078947
IRR = 0,069078947 + 0,075
IRR = 0,144078947
The rate is therefore 14,40%, it is from this that the project is considered profitable.
Conclusion on the investment choice
For the business unit, the investment decision is subject to several assessment criteria: NPV, PI, IRR and DRCI. In the case where the company must choose between several projects, it must compare the results among these different criteria to make the final decision.
If you want to apply what you have just read, I strongly invite you to consult my article on corrected management exercises entitled Investment choice: 7 Corrected exercises.
There you have it, now you know all the elements of investment choice. You no longer have any excuses for not reaching your goal: Get an excellent grade in the Operational Management test!
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