Question

CVP—sensitivity analysis. Joan’s Beauty College is considering introducing a new nail design seminar to run on an annual basis with the following price and cost characteristics:

Tuition	$405.00 per Student
Variable Costs (polish, supplies, etc.)	$185.00 per Student
Fixed Costs (advertising, instructor’s salary, insurance, etc.)	$29,480 per Year

Required:

2a. What enrollment enables Joan’s Beauty College to break even?

Break even = 29,490/(405-185)= 134

134 enrollment enable’s Joan’s Beauty College to break even.

2b. How many students will enable Joan’s Beauty College to make an operating profit of $35,750 for the year?

(29,480+35,750)/(405-185)= 296.5

It will take 297 students to enroll for Joan’s Beauty College to make a operating profit for the desired income of $35,750.

2c. Assume that the projected enrollment for the year is 350 students for each of the following situations:

(1) What will be the operating profit for 350 students?

((405-185) x 350) – 29,480 = $47,520

The operating profit for 350 students will be $47,520.

(2) What would be the operating profit and changecompared to the results from c(1)if the tuition per student (that is, sales price) (show amount change & %)

(i).decreased by 10 percent?

47,520 – (405*350*.10) = 47520 – 14,175 = $33,345 operating profit

Operating profit decrease % = (47,520 – 33,345)/ 47,520 = 29.83%

Operating profit change in amount is $14,175.

(ii). Increased by 20 percent?

47,520 + (405*350*.20) = 47,520 + 28,350 = $75,870 operating profit

Operating profit increase % = 28,350 / 47,520 = 59.66%

Operating profit change in amount is $28,350.

(3) What would be the operating profit and changecompared to the results from c(1)if variable costs per student (show amount change & %)

(i) increased by 10 percent?

(ii) Decreased by 20 percent?

(4) Suppose that fixed costs for the year are 10 percent lower than projected, whereas variable costs per student are 20 percent higher than projected. What would be the operating profit(loss)for the year

Answer 1

Since in the question itself answer for 2a, 2b, 2c(1) and 2c(2) are given, answer for 2c(3) and 2c(4) is as follows

3) (i) Variable cost per student increased by 10%

Profit as per c(1) = $47,520

Less: Increase in Variable cost = $6,475 (350 students * (185*10%))

   $41,045

Operating profit decrease % = (47,520 – 41,045)/ 47,520

=6,475/47520

= 13.626%

Operating profit decrease % = 13.626%

Operating profit change in amount is $6,475.

3) (ii) Variable cost per student decrease by 20%

Profit as per c(1) = $47,520

Add: Decrease in Variable cost = $12,950 (350 students * (185*20%))

   $60,470

Operating profit Increase % = (60470 - 47,520)/ 47,520

=12,950/47520

= 27.25%

Operating profit Increase % = 27.25%

Operating profit change in amount is $12,950.

4) Profit as per c(1) =    $47,520

Add: Decrease in fixed cost = $2,948 ($29,480*10/100)

Less: Increase in Variable Cost = $12,950 (350 students * (185*20%))

Operating profit = $37,518

Operating profit decrease by $10,002.