Managerial Accounting Practice Exam — Free

CVP analysis works in pre-tax dollars, so the first step is to convert the after-tax target into the operating income needed before tax:

$$\text{Pre-tax income} = \frac{\text{After-tax income}}{1 - t} = \frac{30{,}000}{1 - 0.25} = 40{,}000$$

Next find the contribution margin per unit, the amount each sale contributes toward covering fixed costs and then profit: $50 − $30 = $20 per unit.

Units needed to cover fixed costs and earn the pre-tax target:

$$Q = \frac{\text{Fixed costs} + \text{Target pre-tax income}}{\text{CM per unit}} = \frac{120{,}000 + 40{,}000}{20} = 8{,}000$$

Check: 8,000 units give a contribution margin of $160,000; less fixed costs of $120,000 leaves operating income of $40,000; tax at 25% is $10,000, leaving $30,000 after tax, which matches the target.

Option B (7,500) is the most tempting error: it plugs the $30,000 after-tax figure straight into the formula without grossing it up for tax. Option C (7,875) grosses up the wrong way, multiplying by 1.25 instead of dividing by 0.75. Option A (6,000) is the break-even point, which ignores the profit target entirely.

Answer: D — 8,000 units.

The high-low method fits a straight line through the observations at the highest and lowest activity levels (not the highest and lowest costs, although here they coincide). Those are February (9,000 hours, $61,000) and March (5,000 hours, $41,000).

(a) Variable cost per hour is the slope between the two points:

$$\text{Variable rate} = \frac{61{,}000 - 41{,}000}{9{,}000 - 5{,}000} = \frac{20{,}000}{4{,}000} = 5$$

so $5 per machine-hour.

Fixed cost is whatever remains after removing the variable portion at either point. Using February: $61,000 − ($5 × 9,000) = $61,000 − $45,000 = $16,000. Using March gives the same figure, $41,000 − $25,000 = $16,000, which confirms the arithmetic.

(b) Cost formula and prediction. The maintenance cost line is

$$Y = 16{,}000 + 5X$$

where $X$ is machine-hours and $Y$ is total maintenance cost in dollars. For 7,200 hours: $16,000 + $5 × 7,200 = $16,000 + $36,000 = $52,000.

Two cautions a grader expects you to know: the estimate is only valid inside the relevant range (5,000 to 9,000 hours), and because the method uses just two data points it is less reliable than a regression on all four months. The January and April observations fall close to the line (predicted $48,000 and $53,500 against actual $48,500 and $54,200), which suggests the fit is reasonable here.

Answer: (a) $5 per machine-hour, $16,000 fixed per month; (b) Y = $16,000 + $5X, giving $52,000 at 7,200 hours.

First convert totals to actual rates. Materials: $23,940 ÷ 6,300 kg = $3.80 per kg. Labour: $22,050 ÷ 1,050 h = $21.00 per hour. Standard quantities allowed for 2,000 stools: materials $2{,}000 \times 3 = 6{,}000$ kg; labour $2{,}000 \times 0.5 = 1{,}000$ hours.

(a) Materials price variance isolates paying a different price for the quantity purchased:

$$(AP - SP) \times AQ = (3.80 - 4.00) \times 6{,}300 = -1{,}260$$

Paying $0.20 less per kg than standard saves money, so $1,260 F.

(b) Materials quantity variance isolates using a different amount, priced at standard so the price effect is excluded:

$$(AQ - SQ) \times SP = (6{,}300 - 6{,}000) \times 4.00 = 1{,}200$$

Using 300 kg more than allowed costs more, so $1,200 U. (Check: the total materials variance is $23,940 − $24,000 = $60 F, and $1,260 F − $1,200 U = $60 F.)

(c) Labour rate variance:

$$(AR - SR) \times AH = (21.00 - 20.00) \times 1{,}050 = 1{,}050$$

Workers were paid $1 per hour above standard: $1,050 U.

(d) Labour efficiency variance:

$$(AH - SH) \times SR = (1{,}050 - 1{,}000) \times 20.00 = 1{,}000$$

Fifty hours more than allowed were used: $1,000 U.

(e) Linking the variances. A favourable price variance paired with an unfavourable quantity variance is the classic sign that purchasing bought cheaper, lower-grade hardwood. Poorer wood splits or has more defects, so more kilograms are consumed per stool, and the extra cutting and rework also helps explain the unfavourable labour efficiency variance. The purchasing department's saving ($1,260) was more than used up on the shop floor ($1,200 + $1,000), which is why variances should be evaluated together rather than one department at a time.

Answer: (a) $1,260 F; (b) $1,200 U; (c) $1,050 U; (d) $1,000 U; (e) cheaper, lower-quality materials leading to more waste and slower work.