The following information is available for Donald Corporation: If total fixed costs increased to $394,850,then the break-even volume in dollars would increase by ________.
A)10.0%
B)12.3%
C)18.4%
D)34.3%

Question

The following information is available for Donald Corporation:  If total fixed costs increased to $394,850,then the break-even volume in dollars would increase by ________.
A)10.0% 
B)12.3% 
C)18.4% 
D)34.3%

Quizplus · Accepted Answer

To calculate the increase in the break-even volume in dollars, we need to use the formula: Break-even volume = Fixed costs / (1 - Variable cost percentage). Let's assume that the current break-even volume in dollars is BEV1. Then, we can write:

BEV1 = 394,850 / (1 - Variable cost percentage)

We don't know the variable cost percentage, but we don't need it to find the increase in the break-even volume in dollars. Instead, we can use the fact that the only thing that changed is the fixed costs. Let's call the new break-even volume in dollars BEV2. We have:

BEV2 = (394,850 + ΔFC) / (1 - Variable cost percentage)

where ΔFC is the increase in fixed costs. Now, we can divide BEV2 by BEV1 and simplify:

BEV2 / BEV1 = (394,850 + ΔFC) / 394,850
BEV2 / BEV1 = 1 + ΔFC / 394,850
ΔBEV / BEV1 = ΔFC / 394,850

Therefore, the percentage increase in the break-even volume in dollars is equal to the percentage increase in fixed costs divided by 394,850. In this case, ΔFC = 394,850 - original fixed costs, and we don't know the original fixed costs. However, we can still find the percentage increase in fixed costs based on the given information. Let's assume that the original fixed costs were FC1. We have:

FC1 / BEV1 = P/V
where P/V is the contribution margin ratio, which we don't know. However, we also have:

BEV1 = FC1 / (1 - P/V)

Combining these two equations, we can solve for P/V:

P/V = 1 - BEV1 / FC1

We don't know FC1 or P/V, but we can assume that they were constant before the increase in fixed costs. Therefore, we can write:

FC1 / BEV1 = FC2 / BEV2

where FC2 is the new fixed costs ($394,850). We can simplify this equation as follows:

BEV2 / BEV1 = FC1 / FC2
BEV2 = BEV1 * FC1 / FC2

Now, we can use the fact that BEV2 = BEV1 + ΔBEV:

BEV1 + ΔBEV = BEV1 * FC1 / FC2

Dividing both sides by BEV1, we get:

1 + ΔBEV / BEV1 = FC1 / FC2

Therefore, we can find the percentage increase in the break-even volume in dollars based on the ratio of the original and new fixed costs:

ΔBEV / BEV1 = (FC1 - FC2) / FC2

ΔBEV / BEV1 = (FC1 / FC2) - 1

ΔBEV / BEV1 = (BEV1 / FC1) * (FC1 / FC2) - 1

ΔBEV / BEV1 = (1 - P/V) * (FC1 / FC2) - 1

Using the information given in the problem, we can calculate that if the fixed costs were originally $350,000, then the break-even volume in dollars was:

BEV1 = 350,000 / (1 - P/V)

We don't need to know P/V to find the percentage increase in the break-even volume in dollars. We can simply substitute FC1 = $350,000 and FC2 = $394,850 in the above equation:

ΔBEV / BEV1 = (1 - P/V) * (350,000 / 394,850) - 1

ΔBEV / BEV1 = (1 - P/V) * 0.885 - 1

Now, we can use the answer choices to see which one gives us a percentage increase close to this value. Checking choice C, we have:

ΔBEV / BEV1 = 0.184

Plugging in the numbers, we get:

0.184 = (1 - P/V) * 0.885 - 1

Solving for 1 - P/V, we get:

1 - P/V = (0.184 + 1) / 0.885 = 1.208

This means that P/V = -0.208 or -20.8%, which doesn't make sense. Therefore, choice C is incorrect. Checking the other choices, we get:

A) ΔBEV / BEV1 = 0.100
1 - P/V = 1.100 / 0.885 = 1.242
P/V = -0.242 or -24.2%

B) ΔBEV / BEV1 = 0.123
1 - P/V = 1.123 / 0.885 = 1.268
P/V = -0.268 or -26.8%

D) ΔBEV / BEV1 = 0.343
1 - P/V = 1.343 / 0.885 = 1.517
P/V = -0.517 or -51.7%

Therefore, the best choice is B, which implies a 12.3% increase in the break-even volume in dollars.

The Following Information Is Available for Donald Corporation: If