Economics

Many business decision calls for business managers to employ mathematical analysis so to come up with a prudent decision. In this sense various analyses can be undertaken in the whole process of decision making so as to forecast the outcomes and design good business plan. Break even analysis has proved to be an important tool in helping business managers to make prudent decisions.

Break even analysis involves determining the point at which a business costs will be equal to revenue i.e. neither loss is incurred nor profit gained. Linda (2008 p.98l) describe the break even point as the point where companies cost match the sale volume where neither profit is made nor loss is incurred.

Answer to question 1
Given the information about the Healthy Spring Water Company
Sales revenue 60000
Incremental variable cost 15000
Non incremental Fixed cost 20000
Then the following explanation need to be clear a
At break even point total revenue (TR)  total Cost (TC)
On the other hand TRPQ, where P is the price of a unit sold and Q is unit sold
Also, TCFCVQ, where FC is fixed cost and VC is the variable cost
Finding VC per unit sold (V)
V total variable costunits sold 1500030005
The break even point (BEP) condition is that TRTC. This is equivalent of PQFCVQ
Given PQFCVQ
PQ-VQFC
Factoring out Q then Q (P-V) FC from this equation
 QFCP-V Where P-V represent contribution of unit sold, Q represent the quantity sold at BEP.

Maximum sale loss to be tolerated
 New price is 12510020 25
Current units sold is 3000 and the sales is 60000
Beak even quantity after increase in price is
FCP-V2000025-51000 units the break even sales will be 10002525000
Fall in sales to tolerate is current sale - break even sales after price increase 60000- 2500035000
Fall in units sold will be 3000-10002000 units
Percentage sales loss is  change in sales up to break even sales current sale100
350006000010058.33

Answer to question 2
Current sales60000
Sales after 20 decrease is (100-20)100 6000048000
Sales TRPQ
Then 4800025Q
Q48000251920
Contribution before price increase is P-V
20-515
Total contribution is (P-V) Q 152000030000
Total contribution with price increase
(P-V)Q (25-5)192038400
Contribution increase is therefore 38400-300008400

Answer to question 3
  The additional variable cost is 2
Then, the new variable cost is 527
The break even quantity after increase in price and variable cost will be
QFCP-V2000025-71111.111 approximately 1111 units
Sales will then be PQ 25111127775
  Current sales is 60000
Then the sales loss Healthy Spring company can tolerate is 60000-2777532225
Percentage sale change to be tolerated is sales changecurrent sale100322256000010053.71
 Answer to question 4
Sales before increase in fixed cost is 60000
Break even sales after change in price and fixed cost can be calculated as follows
QFCP-V. The new FC is 20000135021350
Then break even quantity is
Q2135025-71186.111 approximately 1186 units
Break even sales after increase in price and fixed cost is 29650
  The sales fall that will be tolerated is 60000-2965030350
The percentage change is
Sales changecurrent sales100303506000010050.58