Question

​(Forecasting

inventories​)

Findlay Instruments produces a complete line of medical instruments used by plastic surgeons and has experienced rapid growth over the past 5 years. In an effort to make more accurate predictions of its financing​ requirements, Findlay is currently attempting to construct a​ financial-planning model based on the percent of sales forecasting method.​ However, the​ firm's chief financial analyst is concerned that the projections for inventories will be seriously in error. She recognizes that the firm has begun to accrue substantial economies of scale in its inventory investment and has documented this fact in the following data and​ calculations:

YEAR	SALES​ ($000)	INVENTORY​ ($000)	​% OF SALES
2014	​$14,000	​$1,070	7.64​%
2015	17,000	1,110	6.53​%
2016	16,500	1,100	6.67​%
2017	19,000	1,130	5.95​%
2018	24,000	1,190	4.96%
			Average 6.35​%

.

a. Plot​ Findlay's sales and inventories for the past 5 years. What is the relationship between these two​ variables?

b. Estimate firm inventories for

2019​,

when firm sales are projected to reach

​$40

million. Use the average percentage of sales for the past 5​ years, the most recent percentage of​ sales, and your evaluation of the true relationship between the sales and inventories from part a to make three predictions.

a.​ Findlay's sales and inventory balances for the past 5 years are plotted in the figure below.

The image is a graph that shows the sales and the inventory balances for a firm for the past five years. The horizontal axis measures sales in thousands of dollars; the axis values range from 10,000 thousand dollars to 40,000 thousand dollars, in increments of 5,000 thousand dollars. The vertical axis measures inventory in thousands of dollars; the axis values range from 1,000 thousand dollars to 1,500 thousand dollars, in increments of 100 thousand dollars. There are five points marked on the graph. The first point corresponds to sales of 14,000 thousand dollars and inventory of 1,070 thousand dollars. The second point corresponds to sales of 17,000 thousand dollars and an inventory of 1,110 thousand dollars. The third point corresponds to sales of 16,500 thousand dollars and an inventory of 1,100 thousand dollars. The fourth corresponds to sales of 19,000 thousand dollars and an inventory of 1,130 thousand dollars. The fifth point corresponds to sales of 24,000 thousand dollars and inventory of 1,190 thousand dollars.

Which of the following best defines the relationship between these two​ variables?  ​(Select the best choice​ below.)

A.

A parabolic function.

B.

A logarithmic cylinder function.

C.

A hyperbolic function.

D.

A linear function.

E.

An exponential function.

b. Use the average percentage of sales for the past 5 years to make the prediction. What are the​ firm's projected inventories for

2019

when the sales are projected to reach

​$40

​million?

​$nothing  

​(Round to the nearest​ dollar.)Use the most recent percentage of sales to make the prediction. What are the​ firm's projected inventories for

2019

when the sales are projected to reach

​$40

​million?

​$nothing  

​(Round to the nearest​ dollar.)Use your evaluation of the true relationship between the sales and inventories from part a to make the prediction. What are the​ firm's projected inventories for

2019

when the sales are projected to reach

​$40

​million?

​$nothing

​ (Round to the nearest​ dollar.)

Answer 1

Answer:

a) Plot between inventories and sales for last 5 years is shown below. Inventory is on the Y axis, whereas Sales is on the X axis. The relation between inventory and sales is clearly linear as shown in the plot.

b) Forecast for 2019 inventory using average percentage of sales

Average percentage of inventory with respect to sales is calculated for last 5 years. This number is used as the percentage value to calculate inventory estimation for 2019. Estimated sales for 2019 is given as $40 million. Estimated inventory for 2019 using this method comes out to be $2.539 million. Calculations are shown below.

c) Forecast for 2019 inventory using latest percentage of sales

Most recent percentage of inventory with respect to sales is used as the percentage value to calculate inventory estimation for 2019. Estimated sales for 2019 is given as $40 million. Estimated inventory for 2019 using this method comes out to be $1.983 million. Calculations are shown below.

c) Forecast for 2019 inventory using regression

To find out more accurate relation between inventory and sales, regression analysis is carried out. The relation between inventory and sales is satisfied using following equation.

Sales = 83.75 * Inventory - 75700 (both sales and inventory numbers in 000')

Estimation of 2019 inventory using this method comes out to be $1.381 million. Calculation and regression details are shown below.