Question

Winterstone Ltd produces a single product. Winterstone Ltd purchases a key part for this product from Brighton Ltd, which produces two versions of the part, Model A and Model B. Both models are suitable to use for the product, but they attract different costs for Winterstone Ltd. Data relevant to the two models are as follows:   

Model A

Variable cost per unit $8.00 Annual Fixed costs $1,969,500

Other information:

Model B

Variable cost per unit $6.40 Annual Fixed costs $2,230,050

   

Winterstone Ltd sells the product for $35 per unit.

1. Sales are subject to 5% sales commission.

2. Winterstone Ltd pays income taxes of 30%.

Required: Show all your workings.

1. How many units of the product must Winterstone Ltd sell to break even if Model A is selected?

2. Which of the two models would be more profitable if sales and production of the product were 95 000 units per year? (Ignore income tax)

3. Assume that Model B requires the purchase of additional equipment that is not reflected in the provided data. The equipment will cost $900,000 and will be depreciated over a five- year life by the straight-line method. How many units must the company sell to earn an after-tax profit of $1,338,960 if Model B is selected?

Answer 1

Answer:

1. Break even point in units if model A is selected,

Break even point(units) = Fixed cost / conribution margin per unit

Fixed cost = $1,969,500 (if model A is selected)

Calculation of contribution margin per unit

Selling price per unit		$35
Less: variable costs
1.Variable cost per unit for model A	$8
2.Sales commission@5% = 35*5%	$1.75
Total variable costs		($9.75)
Contribution margin		$25.25

So, Break even point(in units) = 1,969,500 / 25.25 = 78,000 units

2. Calculation of profits under each model.

	Model A	Model B
Number of units sold	95,000 units	95,000 units
	Per unit	95,000 units (per unit*95,000 units)	Per unit	95,000 units (per unit*95,000 units)
Sales	$35	$3,325,000	$35	$3,325,000
Less: variable cost
Variable cost for model	$8	$760,000	$6.4	$608,000
Sales commission @ 5% on sales	$1.75	$166,,250	$1.75	$166,250
Total variable costs	(9.75)	($926,250)	($8.15)	($774,250)
= Contribution margin	$25.25	$2,398,750	$26.85	$2,550,750
Less: Fixed cost		($1,969,500)		($2,230,050)
= Profit		$429,250		$320,700

* taxes are required to be ignored.

See, the profit is higher when Model A is selected. Selecting Model A will be profitable forWinterstone ltd.

3. Number of units to be sold for earning an after tax profit of $1,338,960 if model B is selected.

Required sales in units = (Fixed cost + Target profit before tax) / Comtribution margin per unit

a) Here, for model B, a new machine is purchased costing $900,000.

It's depreciation as per given data = 900,000 / 5 = $180,000

Depreciation is a fixed cost.

So, total fixed cost for model B = 2,230,050 + 180,000 = $2,410,050

b) Target after tax profit = $1,338,960

Income tax rate = 30%

So, profit before tax = 1,338,960 / (100 - 30)% = 1,338,960 / 70%

= 1,338,960 / 0.7 = $1,912,800

c) Contribution margin per unit = $26.85 (already calculated in the previous profit calculation table)

Now, let's apply the equation :

Required sales in units = (2,410,050 + 1,912,800) / 26.85 = 4,322,850 / 26.85 = 161,000 units

161,000 units to be sold for earning an after tax profit of $1,338,960

Let's check:

Sales	161,000 * 35	$5,635,000
Less: variable cost	161,000 * 8.15	($1,312,150)
=Contribution margin		$4,322,850
Less: fixed cost		($2,410,050)
=Profit before tax		$1,912,800
Less: income tax @30%	1,912,800 * 30%	($573,840)
Profit after tax		$1,338,960

Look at the profit after tax. We have met our after tax profit target by selling 161,000 units.