Investment choice: 7 Corrected exercises

Welcome to this article whose sole purpose is to help you progress in the chapter entitled choosing investments using corrected exercises from the Operational Management subject of the BTS MCO.

If you would like to first see or review the course on choosing investments, I invite you to read my article the choice of investments.

Lesson 7 corrected exercises on the choice of investments The main topics on this page are the Net Cash Flow (NCF) statement and the calculation of NPV (Net Present Value).

You will also find corrected exercises on the following concepts: the calculation of the profitability index (PI), the internal rate of return (IRR) (or the internal rate of return (IRR).

Here is the list of 7 corrected exercises on the choice of investment:

1. 1. Corrected exercises Investment choice: Establishment of the net cash flow table (NCF)
   2. Corrected exercises Investment choice: Calculation of discounted net flows
   3. Corrected exercises Investment choice: Calculation of the NPV
   4. Corrected exercises Investment choice: Calculation of the profitability index
   5. Corrected exercises Investment choice: Calculation of the internal rate of return (IRR)
   6. Corrected exercises Investment choice: Calculation of the payback period for invested capital (DRCI)

1. Corrected exercises Investment choice: Calculation of the payback period for invested capital (DRCI)

 

Corrected exercises Investment choice: Establishment of the net cash flow table (NCF)

States

The Café business unit, which specializes in the manufacture of machines for bars and restaurants, wants to invest in new machine tools.

The manager, Mr Lacaféine, gives you some points in appendix 1.

 

Annexe 1 : Investment project

• Acquisition: €55 excluding VAT at the start of the year
• Depreciation: linear mode over 5 years
• Additional turnover: €100 per year
• Annual charges: €60
• Residual value: zero
• Tax rate: 33,33%

 

Work to do

Using Annexes 1 and 2:

1. Complete the net cash flow table.

 

Correction of exercise 1 of the investment choice

1. Complete the net cash flow table.

 

Here are the explanations of the different references:

(1): The increase in turnover is given in the statement, you just have to copy it over the entire period.

(2): In the statement it is specified that the depreciation is linear. This means that the amount is identical for each year. To calculate the amount of depreciation, it is necessary to divide the amount of the investment by the number of periods.

So we have: 55 ÷ 000 = €5 per year.

(3): Current result before corporate tax is calculated by taking the difference between receipts (the increase in turnover) and disbursements (all expenses).

So we have: 100 – 000 – 60 = €000.

(4): Corporate tax is obtained by multiplying the amount of current profit before tax by the tax rate of 33,33% (see statement).

So we have: 29 × 000% = €33,33.

(5): The result after corporate tax is obtained by taking the difference between the current result before tax and the amount of tax.

So we have: 29 – 000 = €9.

(6): It is necessary to re-enter the depreciation amount in order to cancel it. In fact, it is only used for calculating the tax because it is not a disbursed expense.

(7): Net cash flow (NCF) corresponds to the sum of the depreciation amount and the result after tax.

So we have: 19 + 333,34 = €11.

 

Corrected exercises Investment choice: Calculation of discounted net flows

States

The Cafétéatre business unit, specializing in the manufacture and design of furniture for cafes, bars, restaurants and also for theaters, wishes to invest in a new production unit.

The manager, Mr. Latourné, gives you the net cash flow table.

Appendix 1: Net cash flow table

 

Work to do

1. Complete the net cash flow table by adding the discounted net cash flows, knowing that the discount rate is 11%.

Correction of exercise 2 of the investment choice

1. Complete the net cash flow table by adding the discounted net cash flows, knowing that the discount rate is 11%.

 

To answer the question, you need to apply the following updated FNT formula:

Discounted FNT = Annual FNT × (1 + Discount rate)^-n

With the following elements:

Annual FNT: you must take the annual FNT calculated just above.

The discount rate is given in the statement. Here the discount rate is 11%.

The exponent “n” corresponds to the calculation period.

Example of calculation of the updated FNT for period 2 therefore in N+1:

Updated FNT = 30 × (333,34 + 1)^-2

Updated FNT = €24

Corrected exercises Investment choice: Calculation of the NPV

States

The Cafouillage business unit specializes in industrial cleaning in the Lille region.

Its manager, Mr. Propre, wants to invest in a new, high-performance self-cleaning machine.

The cost of this investment is estimated at €55 excluding VAT. He gives you Appendix 000 to help you with your calculations.

 

Work to do

1. Calculate the NPV amount.

 

Correction of exercise 3 of the investment choice

To calculate the net present value, the following formula must be applied:

NPV = Sum of discounted FNT – Investment amount

So:

(27 + 327,33 + 24 + 619,22 + 22) – 179,47 = 57 108,89 €

The NPV amount is therefore €57.

On this criterion, the NPV being positive, the business unit can consider investing in the acquisition of a new self-cleaning machine.

 

Corrected exercises Investment choice: Calculation of the profitability index

States

The Cafouillis business unit specializes in space optimization coaching.

In fact, she advises companies on the storage and optimization of office space, storage areas, and furniture.

Cafouillis wishes to invest in new, innovative and high-performance professional software.

The amount is €55 excluding VAT.

Its manager, Ms. Carré, gives you Appendix 1 to help her evaluate an assessment criterion: the profitability index.

Appendix 1: Discounted net cash flow table

 

Work to do

1. Calculate the profitability index.

 

Correction of exercise 4 of the investment choice

To calculate the profitability index, the following formula must be applied:

Profitability index = Sum of discounted FNT ÷ Investment amount

So:

Sum of updated FNTs :

(27 + 327,33 + 24 + 619,22 + 22) = €179,47

IP : 112 ÷ 108,89 = 2,03

The profitability index is greater than 1.

Based on this criterion, the business unit may consider investing in the acquisition of a new self-cleaning machine.

 

Corrected exercises Investment choice: Calculation of the internal rate of return (IRR)

States

The Cahot business unit specializes in the manufacture of industrial machines for the construction industry.

She wants to make an investment and asks you to help her choose based on an assessment criterion: the internal rate of return (IRR).

 

Appendix 1: Calculation elements

NPV at 11% rate: €57

NPV at 18% rate: – €45

 

Work to do

1. Determine the internal rate of return (IRR).

 

Correction of exercise 5 of the investment choice

To calculate the internal rate of return (IRR), two NPVs and two discount rates are required.

 

NPV at 11% rate: €57 (this is usually the first NPV to be calculated)

NPV at 18% rate: – €45 (this element is generally provided subsequently)

 

To calculate the TIR we must pose the following equality:

(0 – 57) ÷ (-108,89 – 45) = (TIR – 896,93) ÷ (57 – 108,89)

 

Then by solving the equation we find the TIR:

– 57 ÷ (- 108,89) = (TIR – 103) ÷ 005,82

0,55442392 = (TIR – 0,11) ÷ 0,07

0,55442392 × 0,07 = TIR – 0,11

0,03880967 = TIR – 0,11

TIR = 0,03880967 + 0,11

TIR = 0,14880967 or 14,88%

The internal rate of return is 14,88%.

 

Corrected exercises Investment choice: Calculation of the payback period for invested capital (DRCI)

States

The Cajo business unit specializes in the manufacture and sale of crates for professional market gardeners.

The UC wishes to invest in a new, high-performance machine tool (€76 excluding VAT) which is five times more productive than the machine it currently has.

The manager, Ms. Lemarchet, gives you Appendix 1 to help her evaluate an assessment criterion: the payback period for invested capital (PRIP).

Appendix 1: Discounted net cash flow table

 

Work to do

1. Determine the payback period for invested capital.

 

Correction of exercise 6 of the investment choice

To calculate the payback period for invested capital, the following table can be drawn up:

To complete the “Cumulative” column, you must gradually add the amount of the updated FNT on the left.

Of course, this does not apply to the first line.

For period N, simply copy the amount of the updated FNT.

So for N+1 we have: 27 + 327,33 = 24.

By simple reading, we see that the investment will be recovered from year N+3 because the cumulative discounted FNT becomes greater than the amount invested (€76).

Based on this criterion, the Cajo business unit can decide to invest since the payback period for the invested capital is less than the duration of the project.

 

Corrected exercises Investment choice: Calculation of the payback period for invested capital (DRCI)

States

The Cajolé business unit specializes in the manufacture and sale of small crates for professional market gardeners.

The UC wishes to invest in a new, high-performance machine tool (€76 excluding VAT) which is five times more productive than the machine it currently has.

The manager, Mr Lagrande, gives you Appendix 1 to help him evaluate an assessment criterion: the payback period for invested capital (PRIP).

 

Work to do :

1. Determine the payback period for invested capital (PRIP).

 

Correction of exercise 7 of the investment choice

 

By simple reading, we see that the investment will be recovered from year N+3.

Based on this criterion, the Cajo business unit can decide to invest since the payback period for the invested capital is less than the duration of the project.

We can be more precise in calculating the DRCI by calculating the exact date.

The initial capital (investment) will be recovered within a period of 3 to 4 years. The date is calculated as follows:

3 + [(76 – 000) ÷ (74 – 126,02) × 94]

That is: 3 years + 1,12… months is 1 month and (0,12… × 30) days or 3,76 rounded to 4 days.

The exact date is therefore February 4, N+3.