Useful Formulas for Cost-Volume / Breakeven Point Analysis

These are the formulas for use in the Breakeven Analysis in Week #4. They are cross referenced to those shown in the Stevenson OM text (13 ed.) pgs. 206-07.

DATA TERMS: (terms in parenthesis are those used in OM Table 5.4, p.206)

R = Revenue per unit (price)	Q = quantity
FC = total fixed cost for all quantities	TR = total revenue (R * Q)
VC (v) = variable cost per unit	TC = total cost (FC + VC * Q)
P = profit per unit	TP (P) = total profit (P * Q)
M = margin per unit (R - VC)	TVC (VC) = Total variable cost (VC * Q)

Everything is derived from this formula: TP = TR - TC

Component formulas: TR = (R * Q); TC = (FC + VC * Q)

Substituting formulas leads to: TP = (R * Q) - [FC + (VC * Q)]

Combining terms leads to: TP = [Q * (R - VC)] - FC

Substituting M leads to: TP = (Q * M) - FC

1. TOTAL PROFIT MADE BY A GIVEN QUANTITY, PRICE, AND COSTS:

TP = (Q * M) - FC(OM text formula 5-7)

1. QUANTITY NEEDED TO EARN A GIVEN TOTAL PROFIT: (derived from #1 - OM text formulas 5-8 & 5-9)

Q = (TP + FC) / M

If TP = $0, then this quantity is the breakeven volume.

1. QUANTITY NEEDED TO EARN A GIVEN PROFIT PER UNIT AT A GIVEN PRICE: (OM text does not have this formula)

Q = FC / (M - P)

If P = $0, then this quantity will also be the breakeven volume.

1. QUANTITY NEEDED TO MAKE A GIVEN TOTAL REVENUE AT A GIVEN PRICE: (derived from OM text formula 5-6)

Q = TR / R

1. PRICE NEEDED TO MAKE A GIVEN TOTAL PROFIT AT A GIVEN QUANTITY: (OM text does not have this formula)

R = VC + (TP + FC) / Q

1. PRICE NEEDED TO MAKE A GIVEN PROFIT PER UNIT AT A GIVEN QUANTITY: (OM text does not have this formula)

R = P + VC + (FC / Q)

1. PRICE NEEDED TO MAKE A GIVEN TOTAL REVENUE AT A GIVEN QUANTITY: (derived from OM text formula 5-6)

R = TR / Q

1. TOTAL REVENUE MADE FROM A GIVEN QUANTITY AT A GIVEN PRICE

TR = Q * R(derived from OM text formula 5-6

1. PROFIT PER UNIT MADE FROM A GIVEN PRICE AT A GIVEN VOLUME

P = (TR -TC) / Q => [(Q * M) - FC] / Q

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1) identify the formula used for the calculation either from the textbook pgs 208-09 or from the list provided in the 'Content' Resources folder and attached here =Wk-04 Cost-Volume Formulas.8a.doc

2) set-up the calculation by inserting data into the formula chosen

3) solve the calculations for the result

4) answer the management analysis question for each result

Problem questions:

a. What is the monthly breakeven in units if the price is $1.00 each? In revenue? Will the forecast sales be profitable?

b. What price must be charged to earn a monthly profit of $5,000 if the forecast is correct? Is this likely to be happen?

c. What volume is needed at a price of $1.00 to earn a monthly profit of $5,000? Is this likely to happen?

d. What volume is needed at a price of $1.00 to obtain a monthly profit of $.10 per unit? Is this likely to happen?

e. What volume is needed at a price of $1.00 to obtain a monthly revenue of $20,000? Is this likely to happen?

. A producer of felt-tip pens has received a forecast of demand of 30,000 pens for the coming month from its marketing department. Fixed costs of $25,000 per month are allocated to the felt-tip opera- tion. and variable costs are 37 cents per pen