Management Accounting for a Firm Operations Order Instructions: To explain the calculations
Management Accounting for a Firm Operations Sample Answer
For a firm operating with the following costs and revenues:p=20, VC=18q, FC=1000; calculations are as follows:
(a) The contribution per unit
Contribution margin per unit = $20 – $18 = $2
Contribution margin ratio = (Contribution margin)/Sales
= $2/$20 = 0.1
(b) The quantity required before the firm breaks even
Let X = the number of units sold to break even
Sales revenue – Costs = Income
(Price × Quantity) – Variable costs – Fixed costs = Income
$20X – $2X – $1,000 = $0
$2X – $1,000 = 0
X = 500 units
(c) What should be done by the firm considering that the maximum quantity they can sell is just 400 units?
The company should determine its desired revenue necessary to earn a pretax income of a certain preset percentage of revenue. This helps to ensure that the costs are adjusted. For example, let X = the number of units sold to generate the desired revenue necessary to earn pretax income of 20% of revenue at 400 units production level.
(d) Calculate profits for each of the following quantities:
(i) q=600
Profit = sales revenue – total costs (fixed costs + variable costs)
Profit = ($20 x 600) – ($1000 + $18×600)
Profit = ($12,000 – ($1000+$10,800)
Profit = $12,000-$11,800 = $200
(ii) q=700
Profit = sales revenue – total costs (fixed costs + variable costs)
Profit = ($20 x 700) – ($1000 + $18×700)
Profit = ($14,000 – ($1000+$12,600)
Profit = $14,000-$13,600 = $400
(iii) q=800
Profit = sales revenue – total costs (fixed costs + variable costs)
Profit = ($20 x 800) – ($1000 + $18×800)
Profit = ($16,000 – ($1000+$14,400)
Profit = $16,000-$15,400 = $600
(e) Is it reasonable to assume that the firm can sell any quantity at the given price?
Yes. The company can sell any quantity at the given price mainly because an increase in the produced quantity is directly proportional to the costs of production and then profits which means the product can be effectively sustained.
Question 2
Calculate the optimum quantity and price, along with maximum possible profits for the firm described below:
qd= 10000 – 25p
FC = 50000
VC = 200q
Marginal cost (MC) = 100 + 2Q
Total cost (TC) = FC + VC
TC = 50,000 + 200Q
To obtain optimum quantity and price MC is equated to TC to get:
100 + 2Q = 50,000 + 200Q
-198Q = 49,900
Q = 252 (the negative sign is ignored)
To get the optimal price quantity demanded is equated to TC, since the optimal quantity is already known as follows:
qd= 10000 – 25p
TC = 50,000 + 200Q
10,000 – 25p = 50,000 + 200Q
Q = 252 units
10,000 – 25p = 50,000 + 200 x 252
10,000 – 25p = 100,400
-25P = 100,400 – 10,000
-25P = 90,400
P = $3616 (ignore the negative sign)
Maximum profit for the company obtained from:
Maximum profit = Total revenue (TR) – TC
TR = Price (P) x Quantity (Q)
TR = $3616 x 252 = $911,232
TC = $100,400
Maximum profit = $911,232 – $100,400 = $810,832
Question 3
(a) Calculate equilibrium price and quantity for the following market model (price is in pence here):
qd = 2500 – 0.5p
qs = -200 + 4p
At optimal price and quantity the demand is equal to supply
Thus, the two equations are substituted to get the price (p)
2500-0.5p =-200 + 4p
2500+200 = 0.5p+4p
2700 =4.5p
P = $600
Substituting p for the demand quantity and supplied quantity we can get the optimal quantities:
Optimal quantity demanded = 2500 – 0.5 x 600 = 2200 units
Optimal quantity supplied = -200 + 4 x 600 = 2200 units
(b) Now include a 10 pence tax per unit (remember to modify the supply equation for this). Calculate the new equilibrium price and quantity and comment on the effect on price charged – who absorbs the majority of the tax? Why?
Tax increases production costs and the supply equation Is modified as follows:
qs = -200 + 4p + 10
At equilibrium price and quantity the demand is equal to supply
Thus, the two equations are substituted to get the price (p)
2500-0.5p =-200 + 4p + 10
2500+200 -10 = 0.5p+4p
2690 =4.5p
P ~ $598
Substituting p for the demand quantity and supplied quantity we can get the optimal quantities:
Optimal quantity demanded = 2500 – 0.5 x 598 = 2201 units
Optimal quantity supplied = -200 + 4 x 598 +10 = 2201 units
The tax decreases the price charged and the increased charge is absorbed by the manufacturer because a decrease in the market price without effect of tax.
Question 4
(a) Calculate equilibrium price and quantity for the following market model (price is in pence here):
qd = 2500-20p
qs = -200+4p
At optimal price and quantity the demand is equal to supply
Thus, the two equations are substituted to get the price (p)
2500-20p = -200 + 4p
2500+200 = 20p+4p
2700 =24p
P = $112.5
Substituting p for the demand quantity and supplied quantity we can get the optimal quantities:
Optimal quantity demanded = 2500 – 20 x 112.5 = 250 units
Optimal quantity supplied = -200 + 4 x 112.5 = 250 units
(b) Now include a 10 pence tax per unit (remember to modify the supply equation for this). Calculate the new equilibrium price and quantity and comment on the effect on price charged – who absorbs the majority of the tax? Why?
Tax increases production costs and the supply equation Is modified as follows:
qs = -200 + 4p + 10
At equilibrium price and quantity the demand is equal to supply
Thus, the two equations are substituted to get the price (p)
2500-20p =-200 + 4p + 10
2500+200 -10 = 20p+4p
2690 =24p
P ~ $112.5
Substituting p for the demand quantity and supplied quantity we can get the optimal quantities:
Optimal quantity supplied = -200 + 4 x 112.5 +10 = 260 units
The tax decreases the price charged and the increased charge is absorbed by the manufacturer because a decrease in the market price without effect of tax.
Question 5
(a) Calculate equilibrium price and quantity for the following market model (price is in pence here):
qd = 23000 – 50p
qs = -1000 + 10p
At optimal price and quantity the demand is equal to supply
Thus, the two equations are substituted to get the price (p)
23000-50p = -1000 + 10p
23000+1000 = 50p+10p
24000 =60p
Equilibrium price = $400
Substituting p for the demand quantity and supplied quantity we can get the optimal quantities:
Optimal quantity demanded = 23000 – 50 x 400 = 3000 units
Optimal quantity supplied = -1000 + 10 x 400 = 3000 units
- Now calculate the new equilibrium assuming 40 pence per unit subsidy is applied. Comment on your result.
Subsidy reduces production costs and the supply equation is modified as follows:
qs = -1000 + 10p – 40
At equilibrium price and quantity the demand is equal to supply
Thus, the two equations are substituted to get the price (p)
23000-50p = -1000 + 10p – 40
23000+1000 +40 = 50p+10p
24040 =60p
P ~ $401 (rounded)
Substituting p for the demand quantity and supplied quantity we can get the optimal quantities:
Optimal quantity demanded = 23000 – 50 x 400 = 2960 units (rounded)
Optimal quantity supplied = -1000 + 10 x 401 – 40 = 2960 units
The tax decreases the price charged and the increased charge is absorbed by the manufacturer because a decrease in the market price without effect of tax.
Question 6
Calculate the elasticity of demand (Ped) for:
Qd = 3000-10p at:
- p=100
Qd = 3000-10p
Qd = 3000-10 x 100
Qd = 3000-1000 = 2000
- p=150
Qd = 3000-10p
Qd = 3000-10 x 150
Qd = 3000-1500 = 1500
p=200
Qd = 3000-10p
Qd = 3000-10 x 200
Qd = 3000-2000 = 1000
Question 7
Calculate the elasticity of supply (Pes) for:
Qs = -1000+12p at:
- p=100
Qs = -1000+12p
Qs = -1000+12 x 100
Qs = -1000+1200 = 200
- p=150
Qs = -1000+12p
Qs = -1000+12 x 150
Qs = -1000+1800 = 800
p=200
Qs = -1000+12p
Qs = -1000+12 x 200
Qs = -1000+2400 = 1400
Management Accounting for a Firm Operations References
Atkinson, A., Kaplan, R. S., Matsumura, E. M. & Young, S. M. (2011). Management Accounting: Information for Decision Making and Strategy Execution, (6th ed.). New York, NY: Prentice-Hall.
