Question

Objectives: 1. To improve your quantitative literacy and critical thinking skills by completing a CVP problem with statistics and Excel 2. To improve your understanding of CVP and risk analysis by supplementing the basic CVP model with statistics Davy Company has decided to introduce a new product. The new product can be manufactured by either a capital intensive method or a labor-intensive method. The manufacturing method will not affect the quality of the product. Directly traceable incremental fixed factory overhead is expected to be $2,550,000 if the capital-intensive method is chosen and $1,650,000 if the labor-intensive method is chosen. Davy's market research department has recommended an introductory unit sales price of $35.00. Regardless of the manufacturing method chosen, the incremental marketing expenses are estimated to be $565,000 per year plus $2.00 for each unit sold. The estimated relevant manufacturing and marketing costs of the two methods follow: Direct Materials Direct labor Variable factory overhead Variable marketing expense Total variable costs Capital-intensive $4.00 $5.00 $3.00 $2.00 $14.00 Labor-intensive $4.50 $7.00 S3.20 $2.00 $16.70 Traccable fixed factory overhead Fixed marketing expense Total fixed costs $2,550,000 $565,000 S3.115.000 $1,650,000 $565,000 $2.215.000 Required: 1. Calculate the estimated break-even point in units) for the new product for each method. 2. At what level of sales in units will the operating incomes after tax of the two methods be equal? The tax rate is 15% 3. Given that the number of units sold is a normally distributed random variable with a mean of 300,000 and a standard deviation of 100,000 units, what is the probability that the level of sales will exceed the number identified in part 2? 4. Which method do you recommend that the company implement? Why?

Answer 1

	Capital Intensive	Labor intensive
Selling Price per unit (given)	35.00	35.00
Variable cost per unit (given)	14.00	16.70
Contribution per unit	21.00	18.30
Fixed Costs (traceable)	3115000	2215000

1. BEP (units) = Fixed Costs/Contribution Per unit

ie,

• Capital Intensive => 3115000/21 = 148333.33 or 148334 units for year, So, 148334/12 = 12361 units per month
• Labor Intensive => 2215000/18.30 = 121038 units for year. So, 121038/12 = 10087 Units per month.

2. Here we have to compute the Indifference Point =>

Let Quantity of Units be Q.

Profit = (Contribution * Quantity -Fixed Costs) * (1 - Tax)

So, (21Q - 3115000) * (1-0.15) = (18.30Q - 2215000) * (1-0.15) => 2.7Q = 900,000. So Q = 333,333 units.

Therefore @ 333,333 units Profits under both methods will be Equal.

3. Z = (X - μ)/σ

where X = desired level, μ = Mean, σ =Std. deviation.

So, Z = (333333-300000)/100000 = +0.33.

By looking into Z-table for 0.3 under column 3, we get p(Z<0.33) = 0.6293. So, p(Z>0.33) = 1 - 0.6293 = 0.3707.

Hence, Probability = 0.3707.

4. Based on indifference point in 2 above,

If Units to be produced are Less than 333,333 units, then Labor Intensive method to be used. (since lesser units to break even)

However if annual units to be produced are greater than 333,333 then Capital intensive units to be used. (since higher units to break even)