Chapter 15, Problem 4CE

1.

To determine

Compute the cost of inputs for the profile 2015, if there is no change from productivity profile 2014 to 2015.

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 2015:

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 2014:

Compute the Labor Productivity Profile for 2014:

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

Working Notes (2):

Compute the Material Productivity Profile for 2014:

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

The Labor Productivity Profile is 5.00 and Material Productivity Profile is 0.25 for 2014.

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:

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

2.

To determine

Compute the actual cost of inputs for the profile 2015. 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 2015:

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.

3.

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 2014	Profile 2015	Changes 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	(12) $915,000

Table (4)

Working Notes (7):

Calculate the Revenues for Profile for 2014:

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

Working Notes (8):

Calculate the Revenues for Profile for 2015:

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

Working Notes (9):

Calculate the changes in revenues:

$\begin{array}{c}\text{Revenues = Revenues for Profile 2015 }-\text{Revenues for Profile 2014}\\ \text{= \$9,900,000}-\text{\$10,800,000}\\ =\left(\text{\$900,000}\right)\end{array}$

Working Notes (10):

Calculate the cost of inputs for Profile 2014:

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

Working Notes (11):

Calculate the changes in cost of inputs:

$\begin{array}{c}\text{Costs = Costs for Profile 2015}-\text{Costs for Profile 2014}\\ \text{= \$6,825,000}-\text{\$8,640,000}\\ =\text{\$1,815,000}\end{array}$

Working Notes (12):

Calculate the changes in total profit:

$\begin{array}{c}\text{Changes in Total profit = Profile of 2015}-\text{ Profile of 2014}\\ \text{= \$3,075,000}-\text{\$2,160,000}\\ =\text{\$915,000}\end{array}$

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.