Chapter 15, Problem 4CE

Refer to Cornerstone Exercise 15.3. Choctaw Company provides the following additional information so that total productivity can be valued:

Required:

1. 1. Calculate the cost of inputs in 20x2, assuming no productivity change from 20x1 to 20x2.
2. 2. Calculate the actual cost of inputs for 20x2. What is the net value of the productivity changes? How much profit change is attributable to each input’s productivity change?
3. 3. What if a manager wants to know how much of the total profit change from 20x1 to 20x2 is attributable to price recovery? Calculate the price-recovery component, and comment on its meaning.

To determine

Compute the cost of inputs for the profile 20x2, if there is no change from productivity profile 20x1 to 20x2.

Explanation of Solution

Productivity measurement: The productivity measurement refers to the quantitative assessment of the changes in the productivity.

Profile measurement and analysis: The profile measurement and analysis refers to the computation of a set of operational partial productivity measures and their comparison to the corresponding set of base period, for the assessment of the nature of changes in productivity.

Calculate the cost of inputs for the profile 20x2:

Particulars	Amount ($)
Cost of labor (3)	$1,260,000
Cost of materials (4)	$6,300,000
Total PQ Cost	$7,560,000

Table (1)

Working Notes (1):

Compute the base period productivity ratios for profile 20x1:

Compute the Labor Productivity Profile for 20x1:

$\begin{array}{c}\text{Labor Productivity Profile = }\frac{\text{Number of Units produced}}{\text{Labor hours used}}\\ =\frac{\$540,000}{108,000\text{ hours}}\\ \text{= }5.00\end{array}$

Working Notes (2):

Compute the Material Productivity Profile for 20x1:

$\begin{array}{c}\text{Material Productivity Profile = }\frac{\text{Number of Units produced}}{\text{Materials used}}\\ =\frac{\$540,000}{2,160,000\text{ lbs}}\\ \text{= }0.25\end{array}$

The Labor Productivity Profile is 5.00 and Material Productivity Profile is 0.25 for 20x1.

Working Notes (3):

Calculate the cost of labor:

$\begin{array}{c}\text{Labor cost = }\frac{\text{Number of units produced}}{\text{Labor Productivity Profile }}\times \text{ Wages per labor hour}\\ \text{= }\frac{\text{450,000}}{5\left(\text{1}\right)}\times \text{\$14}\\ \text{= 90,000}\times \text{\$14}\\ =\text{\$1,260,000}\end{array}$

Working Notes 4):

Calculate the cost of materials:

$\begin{array}{c}\text{Material cost = }\frac{\text{Number of units produced}}{\text{Material Productivity Profile }}\times \text{ Cost per pound of material}\\ \text{= }\frac{\text{450,000}}{0.25\left(2\right)}\times \text{\$3}\text{.50}\\ \text{= 1,800,000}\times \text{\$3}\text{.50 }\\ \text{= \$6,300,000}\end{array}$

To determine

Compute the actual cost of inputs for the profile 20x2. Indicate the net value of productivity changes and identify the profit change attributable to productivity change of each unit.

Explanation of Solution

Profit-linked productivity measurement and analysis: The profit-linked productivity measurement and analysis is the ascertainment of the amount of change in profit, from the base period to the current period, due to the various changes in the productivity.

Calculate the current cost of inputs for the profile 20x2:

Particulars	Amount ($)
Cost of labor (5)	$1,575,000
Cost of materials (6)	$5,250,000
Total Current Cost	$6,825,000

Table (2)

Working Notes (5):

Calculate the cost of labor:

$\begin{array}{c}\text{Labor cost = }\frac{\text{Number of units produced}}{\text{Labor Productivity Profile }}\times \text{ Wages per labor hour}\\ \text{= }\frac{\text{450,000}}{5\left(\text{1}\right)}\times \text{\$14}\\ \text{= 90,000}\times \text{\$14}\\ =\text{\$1,260,000}\end{array}$

Working Notes (6):

Calculate the cost of materials:

$\begin{array}{c}\text{Material cost = }\frac{\text{Number of units produced}}{\text{Material Productivity Profile }}\times \text{ Cost per pound of material}\\ \text{= }\frac{\text{450,000}}{0.25\left(2\right)}\times \text{\$3}\text{.50}\\ \text{= 1,800,000}\times \text{\$3}\text{.50 }\\ \text{= \$6,300,000}\end{array}$

Compute the profit linked productivity measure:

Input	A	$\text{B=}\frac{\text{450,000}}{\text{A}}$	C	$\text{D=}\left(\text{B×C}\right)$	E	$\text{F=}\left(\text{E×C}\right)$	$\text{G=}\left(\text{D}-\text{F}\right)$
Labor	5	90,000	$14	$1,260,000	112,500	$1,575,000	($315,000)
Materials	0.25	1,800,000	$3.50	$6,300,000	1,500,000	$5,250,000	$1,050,000
Total				$7,560,000		$6,825,000	$735,000

Table (3)

The Net productivity change is $735,000.

The Labor productivity change is ($315,000).

The materials productivity change is $1,050,000.

To determine

Compute and describe the price recovery component.

Explanation of Solution

Price-recovery component: The price-recovery component refers to the differences amongst the changes in the total profit with the changed in the productivity effects.

Compute the profit linked productivity measure:

Particulars	Profile 20x1	Profile 20x2	Amount ($)
Revenues	(7) $10,800,000	(8) $9,900,000	(9) ($900,000)
Costs	(10) $8,640,000	$6,825,000	(11) $1,815,000
Total Profit	$2,160,000	$3,075,000	$915,000

Table (4)

Working Notes (7):

Calculate the Revenues for Profile for 20x1:

$\begin{array}{c}\text{Revenues = Number of units produced }\times \text{ Selling price}\\ \text{= 540,000}\times \text{\$20}\\ =\text{\$10,800,000}\end{array}$

Working Notes (8):

Calculate the Revenues for Profile for 20x2:

$\begin{array}{c}\text{Revenues = Number of units produced }\times \text{ Selling price}\\ \text{= 450,000}\times \text{\$22}\\ =\text{\$9,900,000}\end{array}$

Working Notes (9):

Calculate the changes in revenues:

$\begin{array}{c}\text{Revenues = Revenues for Profile 20x1 }-\text{Revenues for Profile 20x2}\\ \text{= \$10,800,000}-\text{\$9,900,000}\\ =\left(\text{\$900,000}\right)\end{array}$

Working Notes (10):

Calculate the cost of inputs for Profile 20x1:

$\begin{array}{c}\text{Cost of inputs = }\frac{\text{Labor hours used}}{\text{Wages per labor hour}}\text{+}\left(\begin{array}{l}\text{Materials used (lbs}\text{.)}\times \\ \text{Cost per pound of material}\end{array}\right)\\ \text{= }\frac{\text{108,000}}{\$12}+\left(\text{2,160,000}\times \text{\$3}\text{.50}\right)\\ =\text{\$8,640,000}\end{array}$

Working Notes (11):

Calculate the changes in cost of inputs:

$\begin{array}{c}\text{Costs = Costs for Profile 20x1}-\text{Costs for Profile 20x2}\\ \text{= \$8,640,000}-\text{\$6,825,000}\\ =\text{\$1,815,000}\end{array}$

Compute the Price-recovery component:

$\begin{array}{c}\text{Price-recovery component = }\left(\begin{array}{l}\text{Total profit change}-\\ \text{Profit-linked productivity change}\end{array}\right)\\ \text{= \$915,000}-\$735,000\\ =\$180,000\end{array}$

The Price-recovery component is $180,000.