Chapter 6: Estimating Cost Functions

Answers to Review Questions

R6.1 A: Estimation is prediction or forecast of resources (time, cost and materials) required to achieve or obtain an agreed upon scope of a project or a volume of a product.

R6.2. A: It is an indication of the degree to which the final cost outcome for a given project will vary from the original estimate cost.

R6.3. It is an amount added to an estimate to allow for items, conditions or events for which the state occurrence or effect is uncertain and that experience shows will likely result in additional costs.

R6.4 It is an algorithm or formula that is used to perform the costing operation. CER’s relate (Cost, Time, and Quantity) with quantity scope, execution strategies or other defining elements.

R6.5. A regression line intercepts the Y-axis at the fixed level.

R6.6 The account analysis approach requires that an experienced cost analyst to review the cost accounts and determine whether the costs in each account are fixed or variable. Then, the sum of all costs identified as fixed will be the estimate of total fixed costs. To determine the variable cost per unit, the sum of all costs identified as variable is divided by the measure of activity (e.g., number of units).

R6.7. The high-low method uses the historical data during several reporting periods; but, it uses only the data points corresponding to the highest and lowest levels of activity (output) to derive the algebraic equation for the total cost. The slope of the resulting equation is the variable cost and its y-intercept is the fixed cost. It ignores all other data points than the two extremes ones.

R6.8 Account analysis method of cost estimation is used to classify cost accounts as fixed or variable with respect to specific output level

AR6.9.When the cost is constant (fixed) the slope coefficient of a cost function equal to zero.

Chapter 6: Problem Solutions

P6.1: Solution a) F = $270,000 (total fixed cost)

V = $810,000 / 7,500 unit = $108 per unit b) Using the equation in part (a),

C = $270,000 + $108Q Total cost model, where Q is the production units.

C = $270,000 + $108(8,000) = $1,134,000 (total production cost of 8,000 units)

P6.2: Solution a) Fixed cost = F = $162,000. b) In the cost equation derived in part (a), substitute 8,000 units for Q, as follows:

Variable cost = V = $408,000 / 7,000 units = $58.29 per unit.

The total cost equation: C = $162,000 + $58.29X.

C = $162,000 + $58.29(8,000) = $628,320

Total production cost is estimated to be $628,320 in July.

P6.3: Solution

Cost A is variable as it remains constant on per unit basis.

TCB(10,000) = 10,000($12.00) = $120,000

TCB(20,000) = 20,000($8.50) = $170,000

Cost B is mixed cost per unit, as neither the per-unit cost nor the total is constant.

TCC(10,000) = 10,000($15.00) = $150,000

TCC(20,000) = 20,000($7.50) = $150,000

Cost C is fixed cost per unit, as the total remains constant

P6.4: Solution

V = (70,000 – 45,000) / (10,000 – 5,000) = $25,000 / 5,000 = $5 per unit

Using either the high point or low point, total fixed cost is calculated next:

F = TC(5,000 units) – VC(5,000 units) = $45,000 - $5(5,000) = $20,000

TC = $20,000 + $5Q

P6.5: Solution a) Variable cost per activity unit = (Change in cost)/(Change in Activity)

V = (136,700 – 5109,700) / (15,500 – 10,500) = $5.40/unit

Using either the high point or low point, total fixed cost is calculated next:

F = 136,700 - $5.40(15,500) = $53,300 OR

F = 109,700 - $5.40(10,500) = $53,300

TC = $53,300 + $5.40Q b) For the activity level of 15,000 units, the total cost is estimated to be: TC(15,000 = $53,300 + $5.40(15,000) = $134,300

P6.6: Solution a) Variable Cost Rate (Slope) = ChangeinTotalCost ChangeinActivityLevel

Using either the high point or low point, total fixed cost is calculated next: Fixed Cost = Total Cost – Total Variable Cost Fixed Cost (8,000) = $11,100 - $0.70(8,000) = $5,500 OR Fixed Cost (11,500) = $13,550 - $0.70 (11,500) = $5,500

The equation is: TC = $5,500 + $0.70Q or Y = $5,500 + $0.70X b) Total Cost = Fixed Cost + Total Variable Cost TC = $5,500 + $0.70(12,000)

Total Cost = $5,500 + $8,4000 = $13,900

P6.7: Solution a) High-Low Method

High Point: 4,900 machine hours  Total Cost = $5,195

Low Point: 6,500 machine hours  Total Cost = $6,075

Variable Cost Rate (Slope) = ChangeinTotalCost ChangeinActivityLevel = $6,075 $5,195 6,500 4,900 = $0.55 per hour

Using either the high point or low point, total fixed cost is calculated next:

Fixed Cost = Total Cost – Total Variable Cost

Fixed Cost (6,500) = $6,075 - $0.55(6,500) = $2,500

The equation is: C = $52,500 + $0.55Q or Y = $2,500 + $0.55X

P6.7: Solution (continued)

b) Regression Method

Plug the summation terms into the regression equations, as follows:

The