Question

is the new manager of the materials storeroom for

Parr

Manufacturing.

Mary

has been asked to estimate future monthly purchase costs for part​ #696, used in two of

Parr​'s

products.

Mary

has purchase cost and quantity data for the past 9 months as​ follows:

Month

Cost of Purchase

Quantity Purchased

January

$12,675

2,720 parts

February

12,110

2,820

March

17,426

4,095

April

15,825

3,724

May

13,025

2,912

June

14,022

3,321

July

15,290

3,688

August

10,094

2,262

September

14,970

3,552

Estimated monthly purchases for this part based on expected demand of the two products for the rest of the year are as​ follows:

Month	Purchase Quantity Expected
October	3,310 parts
November	3,750
December	3,040

1.	The computer in Mary​'s office is​ down, and Mary has been asked to immediately provide an equation to estimate the future purchase cost for part​ #696. Mary grabs a calculator and uses the​ high-low method to estimate a cost equation. What equation does she​ get?
2.	Using the equation from requirement​ 1, calculate the future expected purchase costs for each of the last 3 months of the year.
3.	After a few hours Mary​'s computer is fixed. Mary uses the first 9 months of data and regression analysis to estimate the relationship between the quantity purchased and purchase costs of part​ #696. The regression line Mary obtains is as​ follows:     y​ = $1,945.9 ​+ 3.71X Evaluate the regression line using the criteria of economic​ plausibility, goodness of​ fit, and significance of the independent variable. Compare the regression equation to the equation based on the​ high-low method. Which is a better​ fit? Why?
4.	Use the regression results to calculate the expected purchase costs for​ October, November, and December. Compare the expected purchase costs to the expected purchase costs calculated using the​ high-low method in requirement 2. Comment on your results.

Answer 1

Answer:

1.

The equation Mary gets is:

Purchase costs = $1,008 + ($4 x Quantity purchased)

That is y = $1,046 + $4x

2.

Month	Expected cost
October	14,286
November	16,046
December	13,206

3. As per the regression done , the actual estimate of fixed cost is low with all the provided data points. Here the variable rate is less, though the fixed cost is more for the regression line than for high-low cost equation done.

4.

Month	Expected cost
October	14,226.00
November	15,858.40
December	13,224.30

Calculation:

Here Mary will pick need to choose the highest point of activity, 4,095 (March) at $17,426 of cost, and the lowest point of activity, 2,262  parts (August) at $10,094

	Costdriver: Quantity Purchased	Cost
Highest observation of cost driver	4,095	17,426
Lowest observation of cost driver	2,262	10,094
Difference	1,833	7,332

The purchase cost is calculated as below

Purchase costs = a + b x Quantity purchased

So,

Slope Coefficient = $7,332/1833 = $4 per part

a = $17,426 ─ ($4 x 4095) = $1,046

The equation Mary gets is:

y = $1,046 + $4x

2.

Here we need to take the equation from requirement​ 1, we need to calculate the future expected purchase costs for each of the last 3 months of the year.

y = $1,046 + $4x

Here we need to replace the 'x' with the Purchase Quantity Expected

So,

Month	Purchase Quantity Expected	Formula	Expected cost
October	3,310	y = $1,046+ ($4 x 3310)	14,286
November	3,750	y = $1,046+ ($4 x 3750)	16,046
December	3,040	y = $1,046+ ($4 x 3040)	13,206

3.

Here we need to input the data provided for the first 9 months into the graphical format. Could do this by MS EXCEL or manually drawing it in a graph paper as below:

The regression line we got is same as the one mary have got rounded

y​ = $1,945.9 ​+ 3.71x

The regression line fits the data rightly as the distance between the regression line and observations is less. An r-squared value of greater than 0.97 which means, more than 97% of the cost change can be due to the change in quantity. Thus quantity purchased is correlated with purchasing cost for part #696.

The actual estimate of fixed cost is low with all the provided data points. Here the variable rate is less, though the fixed cost is more for the regression line than for high-low cost equation done.

4.

Here we need to take the equation from requirement​ 3, and we need to calculate the future expected purchase costs for each of the last 3 months of the year.

y = $1945.9 + $3.71x

Here we need to replace the 'x' with the Purchase Quantity Expected

So,

Month	Purchase Quantity Expected	Formula	Expected cost
October	3,310	y = $1,945.9+ ($3.71x 3310)	14,226.00
November	3,750	y = $1,945.9+ ($3.71x 3750)	15,858.40
December	3,040	y = $1,945.9+ ($3.71x 3040)	13,224.30