Business economics cost analysis

04/11/23Sameer Gunjal – Business

Economics (MGBEN 10101)

Business Economics – Cost Analysis

Sameer Gunjal



Cost Function

•Cost function is defined using the budget constraint by the following equation:▫C = wL + rK

Where, C = Cost involved w = wage rate L = labor input r = Rate of capital K = Capital



Opportunity Cost?

•Opportunity cost is the value of the next best alternative forgone as the result of making a decision.

• Implies the choice between desirable, yet mutually exclusive results.



Types of Costs

• Implicit and Explicit costs▫Implicit costs – Opportunity cost▫Explicit costs – Out of pocket expenses

•Direct and Indirect Costs▫Direct Costs – Raw Materials, etc.▫Indirect Costs – Admin expenses



Types of costs

•Fixed Cost: These are costs that the firm has to pay independently of whether it is operating or not, e.g. rent on a building.

•Variable Cost: These costs come from the inputs the firm uses in its production process, e.g. the wages paid to laborers.

•Total Cost: These are the sum of fixed and variable costs.▫TC = TFC + TVC



Fixed and Variable Costs

•Fixed Costs:

•Variable Costs:



Total Costs



Isocost Lines

• Isocost is derived from the greek word iso meaning equal.

• Isocost lines represent a combination of inputs which all cost the same amount. The typical isocost line represents the ratio of costs of labour and capital.

•The cost function for the same is given by :▫C = (w*L) + (r*K)



Application of Isocost Lines

• Isoquants are used in combination with isocost lines to arrive at the solution to the cost minimization – optimization solution.



Changes in cost - Isocost Lines



Expansion Path

•The points of tangency between isoquants and isocost lines each show the least expensive way of producing a particular level of output. Connecting these tangency points gives the firm’s expansion path.



Optimization ProblemThe level of output varies with the change in the input combinations.Q = 100KL2,w =Rs.25r = Rs.50

• Find the quantity of labour the firm should use to produce 1600 units of output▫ L=1▫ L=2▫ L=3▫ L=4

• Find the quantity of labour the firm should use to produce 1600 units of output▫ K=1▫ K=2▫ K=3▫ K=4

• Find the minimum cost for the same level of output▫ 100▫ 125▫ 150▫ 175



Total, Average and Marginal Costs•TC = TFC + TVC•Average Cost = AFC + AVC

▫Ratio of the cost component and the average productivity of the input factor

▫AFC = TFC / Q and AVC = TVC / Q•Marginal Cost is the cost incurred for every one

additional input t production.▫MC = d(TVC)/dQ



Illustration to compute, total, average and marginal costs

•Plot the chart of the different costs.



Variable and Marginal Cost charts



Example

•Suppose a cost function is given as ▫TC = 100 + 5Q + Q2

•Find:▫Equation for AC and MC▫AC and MC for 5 units of output▫The value of Q at which AC = MC

Solution

Sol - 1• TC = 100 + 5Q + Q2

• AC = TC / Q▫AC = 100 / Q + 5 + Q

• MC = d(TC)/dQ▫MC = 5 + 2Q

Sol - 2• AC Q=5 = 100 / 5 + 5 + 5

= 30• MC Q=5 = 5 + 2*5 = 15

Sol - 3• The value of Q for AC =

MC▫100 / Q + 5 + Q = 5

+ 2Q▫100 / Q = Q▫Q2 = 100▫Q = 10



Short Run Average Cost Curve

SRAC



Long Run Average Cost

Break-Even Analysis

Costs/Revenue

Output/Sales

FC

VCTC

TR

Q1

The Break-even point occurs where total revenue equals total costs – the firm, in this example would have to sell Q1 to generate sufficient revenue to cover its costs.

Break-Even Analysis

Costs/Revenue

Output/Sales

FC

VCTCTR (p = Rs.20)

Q1

If the firm chose to set price higher than Rs.20 (say Rs.30) the TR curve would be steeper – they would not have to sell as many units to break even

TR (p = Rs30)

Q2

Break-Even Analysis

Costs/Revenue

Output/Sales

FC

VCTC

TR (p = Rs.20)

Q1

If the firm chose to set prices lower (say Rs.10) it would need to sell more units before covering its costs

TR (p = Rs.10)

Q3

Break-Even Analysis

Costs/Revenue

Output/Sales

FC

VC

TCTR (p = Rs.20)

Q1

Loss

Profit



Break Even Analysis

Contribution • Contribution is the difference between sales and

marginal or variable costs. It contributes toward fixed cost and profit. The concept of contribution helps in deciding breakeven point, profitability of products, departments etc. to perform the following activities: ▫Selecting product mix or sales mix for profit

maximization ▫Fixing selling prices under different circumstances such

as trade depression, export sales, price discrimination etc.



Break Even Analysis

Profit Volume Ratio (P/V Ratio), its Improvement and Application

• The ratio of contribution to sales is P/V ratio or C/S ratio. It is the contribution per rupee of sales and since the fixed cost remains constant in short term period, P/V ratio will also measure the rate of change of profit due to change in volume of sales. The P/V ratio may be expressed as follows: P/V ratio = Sales – Marginal cost of sales = Contribution

Sales Sales • A fundamental property of marginal costing system is

that P/V ratio remains constant at different levels of activity.



P/V Analysis• A change in fixed cost does not affect P/V ratio. The concept of P/V ratio

helps in determining the following: • Breakeven point • Profit at any volume of sales • Sales volume required to earn a desired quantum of profit • Profitability of products • Processes or departments

• The contribution can be increased by increasing the sales price or by reduction of variable costs. Thus, P/V ratio can be improved by the following: • Increasing selling price • Reducing marginal costs by effectively utilizing men, machines, materials and

other services • Selling more profitable products, thereby increasing the overall P/V ratio



Breakeven Point

•Breakeven point is the volume of sales or production where there is neither profit nor loss. Thus, we can say that:

Contribution = Fixed cost •Now, breakeven point can be easily calculated with

the help of fundamental marginal cost equation, P/V ratio or contribution per unit.



Margin of Safety

•Margin of safety represents the difference between the sales at break-even point and the total actual sales.

•Three measures of the margin of safety are given below:▫Margin of Safety = Profit * Sales / (PV ratio)▫Margin of Safety = Profit / (PV ratio)▫Margin of Safety = Sa – Sb / Sa * 100

Break-Even Analysis

Costs/Revenue

Output/Sales

FC

VC

TCTR (p = Rs.20)

Q1 Q2

Margin of Safety

Margin of safety shows how far sales can fall before losses made. If Q1 = 1000 and Q2 = 1800, sales could fall by 800 units before a loss would be made

TR (p = Rs.30)

Q3

A higher price would lower the break even point and the margin of safety would widen



Example

•A firm has purchased a plant to manufacture a new product. Cost data for the plant is given below:

•Calculate selling price if profit per unit = Rs. 1.02•Find break even output level

Estimated Annual Sales 24000 units

Estimated CostsMaterial Rs. 4.00 per unitDirect Labour Rs. 0.60 per unitOverhead Rs. 24,000 per yearAdministrative Expenses Rs. 28,000 per yearSelling costs Rs. 1,590 per year



SolutionSales Qty 24,000 units

Material 4.00 /unitsDirect Labour 0.60 /unitsOverhead 24,000 / yearAdministrative Expenses 28,000 / yearSelling costs 1,590 / year

Fixed Costs = Overhead + Admin + Selling 53,590

Variable Costs per unit 4.60 Variable Costs = VC/unit * units 110,400

Total Costs = FC + VC 163,995

Total Profit = Qty * Profit/unit 24,480 Total Revenues = TC + Profit 188,475

Selling Price per unit 7.85 Brealk Even Sales = FC / Contribution 16,473



Break-Even Analysis

Remember:

•A higher price or lower price does not mean that

break even will never be reached!

•The BE point depends on the number of sales

needed to generate revenue to cover costs – the BE

chart is NOT time related!



Break-Even Analysis

Importance of Price Elasticity of Demand:

•Higher prices might mean fewer sales to break-even

but those sales may take a longer time to achieve.

• Lower prices might encourage more customers but

higher volume needed before sufficient revenue

generated to break-even



Break-Even Analysis

Links of BE to pricing strategies and elasticity

•Penetration pricing – ‘high’ volume, ‘low’ price – more

sales to break even

•Market Skimming – ‘high’ price ‘low’ volumes – fewer

sales to break even

•Elasticity – what is likely to happen to sales when

prices are increased or decreased?



Thank You

Business economics cost analysis

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