Consider a project with the following data: accounting break-even quantity = 5,4
ID: 2726633 • Letter: C
Question
Consider a project with the following data: accounting break-even quantity = 5,440 units; cash break-even quantity = 5,000 units; life = three years; fixed costs = $200,000; variable costs = $46 per unit; required return = 12 percent. Ignoring the effect of taxes, find the financial break-even quantity. (Do not round intermediate calculations and round your final answer to 2 decimal places, e.g., 32.16.)
Consider a project with the following data: accounting break-even quantity = 5,440 units; cash break-even quantity = 5,000 units; life = three years; fixed costs = $200,000; variable costs = $46 per unit; required return = 12 percent. Ignoring the effect of taxes, find the financial break-even quantity. (Do not round intermediate calculations and round your final answer to 2 decimal places, e.g., 32.16.)
Explanation / Answer
Answer
Accounting Break even Quantity = Fixed costs / Sales price per unit – Variable cost per unit
5,440 units = $200,000 / Sales price per unit – $ 46
Sales price per unit – $ 46 = $200,000 / 5,440
Sales price per unit – $ 46 = 36.76
Sales price per unit = $ 36.76 + $ 46
Sales price per unit = $ 82.76
Cash breakeven Quantity = Fixed costs – Non Cash expenses / Sales price per unit – Variable cost per unit
5,000 = Fixed costs – Non Cash expenses / $ 82.76 - $ 46
5,000 = Fixed costs – Non Cash expenses / $ 36.76
Fixed costs – Non Cash expenses = 5,000 * $ 36.76
Fixed costs – Non Cash expenses = 183800
Contribution per unit = Selling price per unit – Variable cost per unit
= $ 82.76 - $ 46
= $ 36.76
Suppose quantity at financial breakeven point is X.
Year
Total Contribution
Fixed cost less non-cash expense
Cash flow
Disc Rate : 12%
Present value
A
B
C
D
A-B
C*D
1
36.76X
183800
36.76X - 183800
0.89
(36.76X - 183800)*0.89
2
36.76X
183800
36.76X - 183800
0.80
(36.76X - 183800)*0.80
3
36.76X
183800
36.76X - 183800
0.71
(36.76X - 183800)*0.71
NPV
0
Solving above Equation,
Net Present Value = Present value of Cash flows
0 = (36.76X - 183800)*0.89 + (36.76X - 183800)*0.80 + (36.76X - 183800)*0.71
0 = (36.76X - 183800)*(0.89 + 0.80 + 0.71)
0 = (36.76X - 183800)* 2.40
0 =88.29X - 441456.6
88.29X = 441456.6
X = 5000
Answer : Break Even quantity is 5000
Year
Total Contribution
Fixed cost less non-cash expense
Cash flow
Disc Rate : 12%
Present value
A
B
C
D
A-B
C*D
1
36.76X
183800
36.76X - 183800
0.89
(36.76X - 183800)*0.89
2
36.76X
183800
36.76X - 183800
0.80
(36.76X - 183800)*0.80
3
36.76X
183800
36.76X - 183800
0.71
(36.76X - 183800)*0.71
NPV
0