Question

BACKGROUND

The company ABC, L.C. manufactures some products with an average sales price of € 25/unit, with fixed annual costs of € 110,000. The average unit variable costs are € 5.

DEVELOP

a) At what volume of production will the threshold of profitability be reached?

b) Assuming that annual sales are estimated at 20,000 units, being the distribution evenly over a year, on what date will the break-even point be reached?

c) What would be the sales value or turnover corresponding to the threshold of profitability?

2. The company Derabel, S.A. is considering buying a new machine for its production process. This project means an initial cost of € 200,000 and the machine is estimated to have a useful life of 5 years. The maximum productive capacity of the machine is 200,000 units per year. However, the first year it is expected that the activity will be 70% of the maximum installed capacity, reaching 100% from the second year.

During the first year, the unit sales price will be € 2.50, the unit variable cost € 1.50 and the fixed annual cost € 60,000, resulting in cumulative yearly increases of 4% in the price of the product sale, 3% on variable costs and 2% on fixed costs.

Also, it is assumed that:

• The company uses a linear depreciation system, and the residual value of the machine is € 25,000. Besides, the sale value of the machine at the end of its physical life will be € 30,000 that will be charged in cash.
• The nominal discount rate (kN) used by the company is 8% per year and constant for the planned period.
• The tax rate that taxes the benefits is 25%. Taxes are paid in the period following their accrual.
• All production is sold in the reference period.
• All income and expenses are charged and paid in cash.

With the above data, determine the Net Cash Flows after taxes of the project described above. Calculate the net absolute return.

3. The person in charge of the finances of the company MGT, S.A. wants to know the company's situation concerning the industrial sector to which it belongs. For this, it has the following information regarding the industry:

1. General liquidity ratio is 1.55; the acid test is 1.20, and the ratio between the available and the current liabilities is 0.95.
2. The debt ratio stands at 1.25. The margin on sales is 21%. The investment rotation is 1.45 times.
3. Economic profitability is around 23%, and financial profitability is 29%

The data referred to the company (in thousands of €) are the following:

Assets		Liability and Net Equity
Non-current asset (net)	170	Equity	125
Stocks of finished products	45	Reservations	25
Clients	65	External Resources	105
Banks	70	Loans	65
		Supplier	30
Total Assets	350	Total Net Equity	350

In addition, it is known that:

• Sales are € 250,000 and its direct cost of € 105,000.
• Amortization of € 70,000.
• Long-term debt generates interest at 5%, short-term bank loans at 7%, and the departure of suppliers does not accrue any interest.
• The Corporation Tax is 25%.

Calculate the liquidity, acid test and debt ratios, and compare them with the sector data. It also calculates the economic and financial returns, and the margin on sales and investment rotation, even making a comparison between the company and sector.

4. An investment requires an initial disbursement of € 2,500,000 and the duration of the project is 3 years, in the first of which it generates a cash flow of € 1,500,000, in the second € 3,700,000 and the third € 4,100,000.

1. Calculate the Net Present Value of the investment, knowing that inflation is 3% cumulative annually and that the required profitability in the absence of inflation is 8%.
2. Calculate the actual internal rate of return of the previous investment.

5. We know the following data of the company Perfilados, S.A:

1. It bought and consumed € 105,000 in raw materials for the manufacture of its product and, on average, maintained a stock level of them in the stock of € 9,250. Calculate the average storage period.

Calculate the average storage period.

2. The cost of its annual production is € 198,000, and the average value of the products under development is € 11,000. Calculate the average manufacturing period.
3. Taking into account that the company exclusively sold all its annual production and that the average value of its stock in finished goods warehouse was € 18,500, it calculates its average sales period.
4. Assuming that the company sold its products for an amount of € 290,000 and that the customers had on average a debt with the company of € 17,000, it calculates the average collection period.
5. With the data obtained in the previous points, it calculates the average period of economic maturity of Perfilados, S.A.

6. We know the following data of an investment that the company has made:

• An initial disbursement of € 2,000,000 and generates the collections and payments in the successive years of its duration that are shown in the following table:

Years	Collection (€)	Payments (€)
1 Year 2 Year 3 Year 4 Year	4.500.000 5.500.000 6.000.000 4.000.000	3.800.000 4.500.000 5.000.000 3.200.000

Calculate the IRR of the previous project. Justify for what type of discount this investment will be made.

Answer 1

Answer :

Answer 1) a) Threshold is 5500 units

                  b) 100 days

                  c) €137,500 is the sales value

                 

Answer 2) Net absolute return is 113.07%

Answer 3) liquidity and margin of sales of the company is better than the sector. Debt ratio of the sector is higher.

Answer 4)NPV is €4,817,018 and IRR is 87%

Answer 5) a) 32.2 days

                 b) 18 days

                 c) 34.1 days

                 d) 21.4 days

                 e) 50.2 days

Answer 6) IRR is 26.08%

Explanation :

Answer 1)

a) Threshold of profitability is where we reach the breakeven quantity and it is where,

Revenue = Fixed cost + variable cost

Let the quantity be X

€25*X = €11,000 + €5*X

€25X = €11,000 + €5X

€20X = €11,000

   X = 5500

b)

Annual sales are given as €20,000

Sales per day would be (€20,000/365) = 54.79 or 55

Breakeven points in units is 5,500

No. of days taken to achieve the breakeven = Break even units / Per day sale

                                                                              = 5,500/55

                                                                              = 100 days

c) Sales value = Break even units * Sales per unit

                        = 5,500* €25

                        = €137,500

Answer 2)

Calculation of Net cash flow using excel:

Formula sheet:

Calculation of net absolute return:

Profit after tax = €33,750 + €86,100 + €93,829.5 + €101,956 + €110,498

                          = €426,133.50

Net absolute return = [(Profit after tax - Original cost)/Original cost]*100

                                    = [(€426,133.50 -€200,000) / €200,000]*100

                                   = 113.07%

Answer 3)

Liquid ratio = liquid assets/liquid liabilities

                       = €70,000 / €30,000

                      = 2.33

Industry has 1.55 current ratio. Company has higher current ratio which means liquidity of the corporation is better than industry.

Acid test is also equal to the current ratio.

Debt ratio = total debt / total assets

                  = €130,000/ €350,000

                  = 0.3714

Debt ratio of the industry is 1.25 which is more than the company's debt ratio.

Margin of Sales = (profit / revenue)*100

Profit = sales - direct cost

           = €250,000 - €105,000

           = €145,000

Margin of sales = (€145,000/2 €50,000)*100

                            = 58%

Company has a higher margin of sales than industry.

ROI = profit / Investment

        = €145,000 / €350,000

         = 41.42%

Financial profitability of the company is more than the sector.

Answer 4)

Calculation of NPV and IRR using Excel:

Formula sheet:

Answer 5)

a) Average storage period = (Average inventory/ cost of annual purchases)*360 days

                                              = (€9,250 / €105,000)*360

                                             = 32.2 days

b) Average manufacturing period = annual production cost/average value of products

                                                          = €198,000/ €11,000

                                                          = 18 Days

c) Annual sales would be €198,000 as it is given that complete annual production is sold

Average accounts receivable would be average value of stocks in finished goods which is €18,500

Therefore, average sales period = Average accounts receivables/ (annual sales/365 days)

                                                         = €18,500/( €198,000/365)

                                                         = 34.1 days

d) Receivable turnover = Sales revenue / average accounts receivable

                                          = €290,000/€17,000

                                     = 17.05

Collection period = 365 / Receivable turnover

                               = 365 / 17.05

                               = 21.4 days

e) Average period of economic maturity = storage period + period of manufacturing

                                                                       = 32.2 + 18

                                                                       = 50.2 days

Answer 6) calculation of IRR using excel:

Formula sheet: