3^rd PART – TOPIC 7

Break-even point.-

• Break-even point.-

  • Q = TFC : (P – UVC)

• Total revenues.-

  • TR = P x Q

• Costs.-

  • TC = TFC + TVC

  • TC = TFC + UVC x Q

  • UVC = TVC : Q

  • AvgC = TC : Q

• Profit.-

  • Profit = TR – TC => Profit = P x Q – TC

  • Profit = TR – TFC – TVC => Profit = P x Q – TFC – TVC

  • Profit = TR – TFC – UVC x Q => Profit = P x Q – TFC – UVC x Q

• Chart.-

  • Q_max = 2 x Break-even point (if the amount of sold units is higher than this quantity we must get to the amount of sold units if we need to represent it in the chart)

  • TR_max = P x Q_max

  • Calculate TR₀ and TR_bep

  • Calculate TC₀ and TC_bep

  • Calculate TVC₀ y TVC_bep (if the problem asks for it)

Acquisition cost and Production cost.- The formulas are similar to the formulas of break-even point but with these variations:

• Costs.-

  • ADQcost = P x Q (similar to TR = P x Q)

  • PROcost = TFC + TVC (similar to TC = TFC + TVC)

  • PROcost = TFC + UVC x Q (similar to TC = TFC + UVC x Q)

• Chart.-

  • Q_max = 2 x Break-even point (if the amount of produced units is higher than this quantity we must get to the amount of produced units if we need to represent it in the chart)

  • ADQcost_max = P x Q_max

  • Calculate ADQcost₀ and ADQcost_bep

  • Calculate PROcost₀ and PROcost_bep

Wilson Model.-

• Economic order quantity.- Q* = sqrt (2DS : H)

  • Q* = optimal order quantity

  • D = annual demand quantity of the product

  • S = fixed cost per order (not per unit, in addition to unit cost)

  • H = annual holding cost per unit (also known as carrying cost or storage cost) (warehouse space, refrigeration, insurance, etc. usually not related to the unit cost)

• How often do we need to realise the order?.-

  • Example.- The firm needs 1,000 kgs each year (D), works 300 days annually and its orders reach and amount of 100 kgs (Q)

1,000 kgs. --------------------- 300 days

100 kgs. --------------------- x days

• Which is the stock level to do a new order?.-

  • Example.- The firm needs 1,000 kgs. each year (D), works 300 days annually and the average time to receive the order is five days

1,000 kgs. --------------------- 300 days

x kgs. --------------------- 5 days

Productivity.-

• Factor productivity = Output quantity of a product : Input quantity of a factor (the outcome will be chairs – for example- per hour man or per hour machine)

• Global productivity of year zero.-

  • PG₀ = (P₁Q₁ + P₂Q₂ + … + P_nQ_n) : (f₁F₁ + f₂F₂ + … + f_nF_n)

• Global productivity of year one.-

  • PG₁ = (P₁Q'₁ + P₂Q'₂ + … + P_nQ'_n) : (f₁F'₁ + f₂F'₂ + … + f_nF'_n) (we must use the prices from year zero)

• Global productivity index 0-1.-

  • IPG_0-1 = PG₁ : PG₀

3^rd PART - TOPIC 8

Share market.-

• Share market = Firm's sales : Sector's sales

3^rd PARTE – TOPIC 9

Pay-back.-

• We must do a summary of the previous table by subtracting the payments from the collections:

• Calculate the years.-

  • 1^st year.- We have recovery only 40,000 € (so we haven't got still the 200,000 €)

  • 2^nd year.- We have recovery 40,000 + 84,000 = 124,000 € (so we haven't got still the 200,000 €)

  • 3^rd year.- We have recovery 40,000 + 84,000 + 90,000 = 214,000 (we have got more than 200,000 € so pay-back is two years and something more)

• Calculate the months.- We take the year where we have got more than 200,000 € and we do the following rule of three, being 76,000 = 200,000 – 40,000 – 84,000:

90,000 € ------------------------ 12 months

76,000 € ------------------------ x months x = 10.13 months

• Calculate the days.- We only take the decimal numbers

1.00 months --------------------- 30 days

0.13 months --------------------- x days x = 3.9 = 4 days

• Total calculation.- Pay-back is 2 years, 10 months and 4 days

3^rd year cash-flow calculation.-

• Example.- Initial outlay = 170,000 €; 1^st year cash-flow = 50,000 €; 2^nd year cash-flow = 90,000 €; Pay-back = 2 years and 5 months

• 3^rd year cash-flow.- We recover 30,000 in five months (170.000 – 50.000 – 90.000 = 30.000). So:

30,000 € ------------------------- 5 months

x € ------------------------ 12 months x = 72,000 €

Cash Conversion Cycle.-

• Cash Conversion Cycle = Raw Material Conversion Period (Warehouse Conversion Period) + Goods in Process Conversion Period (Production Conversion Period) + Finished goods Conversion Period (Sales Conversion Period) + Receivables Conversion Period = RMp + GPp + FGp + Rp

  • Raw material Conversion Period (Warehouse Conversion Period).-

    • Raw material rotation = n1 = Annual raw material purchases : Average raw material stock

    • Raw Material Conversion Period = RMp = 365 : n1

  • Goods in Process Conversion Period (Production Conversion Period).-

    • Goods in Process rotation = n2 = Annual cost of production : Average goods in process stock

    • Goods in Process Conversion Period = GPp = 365 : n2

  • Finished goods Conversion Period (Sales Conversion Period).-

    • Finished goods rotation = n3 = Annual sales at factor cost : Average finished goods stock

    • Finished goods Conversion Period = FGp = 365 : n3

  • Receivables Conversion Period.-

    • Payment from customers rotation = n4 = Annual sales at market prices : Average receivables stock

    • Receivables Conversion Period = Rp = 365 : n4

Shares values and dividend.-

• Nominal value.-

  • NV = Share capital : Number of shares

• Market value.-

  • MV = Nominal value x Quotation

  • MV = The problem gives you the value (example: the firm quotes in the Stock Market at 27 €/share)

• Theoretical value.-

  • TV = (Share capital + Reserves) : Number of shares

  • TV = Average dividend : Interest rate (in amount per one unit – e.g. 10% = 0,1)

• Dividend per share.-

  • D = Distributable profit : Number of shares

• Net worth.-

  • Net worth = Share capital + Reserves

Net Present Value.-

• NPV = - R₀ + [R₁ : (1 + i)] + [R₂ : (1 + i)²] +... + [R_t : (1 + k)^t] (we must add the salvage value, as a revenue, last year)

4^th PART – TOPIC 10

Working capital.-

• Working capital = Current assets – Current liabilities

Equity.-

• Equity percentage = Net worth / (Net worth + Liabilities)

Liabilities.-

• Liabilities percentage = (Current liabilities + Non-current liabilities) / (Net worth + Liabilities)

Aportación.-

• Contribution = Share capital : Number of shareholders (or number of shares according to the problem)

Economic-financial balance.-

• Balance.- Non-current assets + Working capital = Long term resources or Non-current assets + Working capital = Net worth + Non-current liabilities

Annual depreciation expense.-

• Annual depreciation expense = (Countable value – Salvage value) : Number of years

Economic and financial profitability.-

• Economic profitability = Profit before interests and taxes : Assets

• Liabilities = Assets x Liabilitites percentage

• Interests = Liabilities x Interest rate

• Countable profit = Profit before interests and taxes - interests

• Financial profitability = (Profit before interest and taxes – Interests - Taxes) : Net wort

• Taxes = (Profit before interests and taxes - Interests) x Tax rate

Stock market value.-

• Stock market value = Quotation x Number of shares

Price Earnings rate.-

• PER = Quotation : Dividend

Cash-flow.-

• Cash-flow = Countable profit + Amortization – Taxes

• Countable profit = Profit before interests ans taxes - Interests

Equity.-

• Equity = Long term capitals – Non-current liabilities