/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 21 The controller of the Javier Com... [FREE SOLUTION] | 91Ó°ÊÓ

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The controller of the Javier Company is preparing the budget for 2018 and needs to estimate a cost function for delivery costs. Information regarding delivery costs incurred in the prior two months are: $$\begin{array}{lcc}\text { Month } & \text { Miles Driven } & \text { Delivery costs } \\\\\hline \text { August } & 12,000 & \$ 10,000 \\\\\text { September } & 17,000 & \$ 13,000\end{array}$$ 1\. Estimate the cost function for delivery. 2\. Can the constant in the cost function be used as an estimate of fixed delivery cost per month? Explain.

Short Answer

Expert verified
The estimated cost function for delivery is \(y = 0.65x + 2200\) based on the given data. The constant in the cost function (\(2200\)) can be used as an estimate of fixed delivery cost per month, as it represents the portion of delivery costs that do not change with miles driven.

Step by step solution

01

Calculate the cost per mile driven for each month

For August and September, divide delivery costs by miles driven to obtain the cost per mile. For August: \[\text{Cost per mile(August)} = \frac{\text{Delivery costs(August)}}{\text{Miles driven(August)}}\] For September: \[\text{Cost per mile(September)} = \frac{\text{Delivery costs(September)}}{\text{Miles driven(September)}}\]
02

Determine the average cost per mile

Calculate the average cost per mile driven by adding the cost per mile driven for August and September, then divide by 2. \[\text{Average cost per mile} = \frac{\text{Cost per mile(August)} + \text{Cost per mile(September)}}{2}\]
03

Use regression analysis to find the best fit line for delivery costs and miles driven

Regression analysis will give us a linear equation in the form \(y = mx + c\), where \(y\) represents delivery costs, \(m\) represents the slope (average cost per mile), \(x\) represents miles driven, and \(c\) represents the constant or fixed cost. To find the best-fit line, we'll plug in the given data points and solve for the constant.
04

Analyze the constant obtained in the cost function

Once we obtain the constant in the cost function, we'll analyze whether it can be used as an estimate of fixed delivery cost per month. We need to consider if the constant represents a fixed cost that does not change with the number of miles driven.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Delivery Costs Analysis
When analyzing delivery costs, it's important to understand how various factors contribute to the overall cost. Delivery costs can vary based on time, distance, and other operational variables. For the Javier Company, this means looking at how the number of miles driven impacts their total delivery expenses. We begin by categorizing these expenses into smaller components to understand which factors are fixed and which are variable. For example, in the context of the given exercise, observing delivery costs over August and September gives a clear view of how delivery expenses increased with more miles driven. Analyzing such data helps in strategizing future deliveries and optimizing costs.
Fixed and Variable Costs
Fixed and variable costs play a crucial role in determining delivery costs. Fixed costs refer to expenses that do not change with the level of activity. For instance, costs like salary for delivery staff or lease payments for delivery vehicles might remain constant, regardless of the number of deliveries made. Variable costs, on the other hand, fluctuate with the level of activity. Fuel consumption and maintenance costs often rise with an increase in miles driven, making them variable costs. By distinguishing between these two types of costs, businesses can better understand where savings can be made. In the exercise, identifying the fixed delivery cost was essential in predicting future expenses more accurately.
Regression Analysis
Regression analysis is a statistical tool used to identify relationships between variables. In the context of delivery costs, regression analysis helps in identifying how the costs change as the number of miles driven changes. The goal is to establish a cost function, which is an equation that best fits the observed data points. This function reflects two main components: the slope, which indicates the variable cost per mile, and the intercept, which is the estimated fixed cost. By applying this technique, companies like Javier can predict future costs with greater accuracy and make informed decisions about resource allocation.
Budget Preparation
Preparing a budget involves forecasting financial expenses and revenue. By estimating delivery costs accurately, companies can allocate resources more effectively for the upcoming periods. Using the cost function derived from regression analysis, businesses prepare a budget that accounts for both fixed and variable costs. This aids in setting realistic financial goals and maintaining profitability. Being aware of fixed and variable components allows companies to minimize cost overruns and manage cash flow efficiently. In the exercise, the cost function serves as a tool for creating a comprehensive budget for the year 2018.
Cost Accounting
Cost accounting focuses on capturing a company's entire cost of production by assessing the fixed and variable costs involved in each step of manufacturing. In the delivery context for Javier Company, cost accounting would involve not only the identification of these costs but also the allocation of expenses to different delivery operations. Accurate cost accounting ensures that the company can assess profitability at various levels, understand cost behavior, and make data-driven decisions. This systematic approach helps in setting prices, controlling expenses, and improving efficiency, thereby enhancing the overall financial health of the business.

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Most popular questions from this chapter

Describe the account analysis method for estimating a cost function.

\((\mathrm{CPA}, \text { adapted })\). The vertical axes of the graphs below represent total cost, and the horizontal axes represent units produced during a calendar year. In each case, the zero point of dollars and production is at the intersection of the two axes. Select the graph that matches the numbered manufacturing cost data (requirements 1-9). Indicate by letter which graph best fits the situation or item described. The graphs may be used more than once. 1\. Annual depreciation of equipment, where the amount of depreciation charged is computed by the machine-hours method. 2\. Electricity bill-a flat fixed charge, plus a variable cost after a certain number of kilowatt-hours are used, in which the quantity of kilowatt-hours used varies proportionately with quantity of units produced. 3\. City water bill, which is computed as follows: The gallons of water used vary proportionately with the quantity of production outputt 4\. cost of direct materials, where direct material cost per unit produced decreases with each pound of material used (for example, if 1 pound is used, the costis S10; if 2 pounds are used, the costis \$19.98 3 pounds are used, the cost is \(\$ 29.94\), with a minimum cost per unit of \(\$ 9.20\) 5\. Annual depreciation of equipment, where the amount is computed by the straight-line method. When the depreciation schedule was prepared, it was anticipated that the obsolescence factor would be greater than the wear-and- tear factor. 6\. Rent on a manufacturing plant donated by the city, where the agreement calls for a fixed-fee payment unless 200,000 labor-hours are worked, in which case no rent tis paid. 7\. Salaries of repair personnel, where one person is needed for every 1,000 machine-hours o o less (that is, 0 to 1,000 hours requires one person, 1,001 to 2,000 hours requires two people, and so on 8\. cost of direct materials used (assume no quantity discounts).) 9\. Rent on a manufacturing plant donated by the county, where the agreement calls for rent of \(\$ 100,000\) to be reduced by s1 for each direct manufacturing labor-hour worked in excess of 200,000 hours, but a minimum rental fee of \(\$ 20,000\) must be paid.

Nandita Summers works at Modus, a store that caters to fashion for young adults. Nandita is responsible for the store's online advertising and promotion budget. For the past year, she has studied search engine optimization and has been purchasing keywords and display advertising on Google, Facebook, and Twitter. In order to analyze the effectiveness of her efforts and to decide whether to continue online advertising or move her advertising dollars back to traditional print media, Nandita collects the following data: 1\. Nandita performs a regression analysis, comparing each month's online advertising expense with that month's revenue. Verify that she obtains the following result: Revenue \(=\$ 51,999.64-(0.98 \times \text { Online advertising expense })\) 2\. Plot the preceding data on a graph and draw the regression line. What does the cost formula indicate about the relationship between monthly online advertising expense and monthly revenues? Is the relationship economically plausible? 3\. After further thought, Nandita realizes there may have been a flaw in her approach. In particular, there may be a lag between the time customers click through to the Modus website and peruse its social media content (which is when the online ad expense is incurred) and the time they actually shop in the physical store. Nandita modifies her analysis by comparing each month's sales revenue to the advertising expense in the prior month. After discarding September revenue and August advertising expense, show that the modified regression yields the following: Revenue \(=\$ 28,361.37+(5.38 \times \text { Online advertising expense })\) 4\. What does the revised formula indicate? Plot the revised data on a graph. Is this relationship economically plausible? 5\. Can Nandita conclude that there is a cause-and-effect relationship between online advertising expense and sales revenue? Why or why not?

A firm uses simple linear regression to forecast the costs for its main product line. If fixed costs are equal to \(\$ 235,000\) and variable costs are \(\$ 10\) per unit, how many units does it need to sell at \(\$ 15\) per unit to make a \(\$ 300,000\) profit? a. 21,400 b. 47,000 c. 60,000 d. 107,000

When using the high-low method, should you base the high and low observations on the dependent variable or on the cost driver?

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