Businesseconomics costanalysis-110308030741-phpapp02

12/23/14
Sameer Gunjal – Business
Economics (MGBEN 10101)
Business Economics –
Cost Analysis
Sameer Gunjal

12/23/14
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

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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.

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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

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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

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Fixed and Variable Costs
• Fixed Costs:
• Variable Costs:

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Total Costs

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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)

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

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Changes in cost - Isocost Lines

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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.

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

12/23/14
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

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Illustration to compute, total,
average and marginal costs
• Plot the chart of the different costs.

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Variable and Marginal Cost charts

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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

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Short Run Average Cost Curve
SRAC

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Long Run Average Cost

Break-Even Analysis
Costs/Revenue
Output/Sales
FC
VC
TC
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
VC
TCTR (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
VC
TC
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

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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.

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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.

12/23/14
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

12/23/14
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.

12/23/14
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

12/23/14
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 Costs
Material Rs. 4.00 per unit
Direct Labour Rs. 0.60 per unit
Overhead Rs. 24,000 per year
Administrative Expenses Rs. 28,000 per year
Selling costs Rs. 1,590 per year

12/23/14
Solution
Sales Qty 24,000 units
Material 4.00 /units
Direct Labour 0.60 /units
Overhead 24,000 / year
Administrative Expenses 28,000 / year
Selling 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

12/23/14
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!

12/23/14
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

12/23/14
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?

12/23/14
Thank You

Businesseconomics costanalysis-110308030741-phpapp02

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