Bret's Accounting & Tax Services is a small but locally well-known accounting firm in Sioux City, IA which completes taxes for individuals. Every year, firms like Bret's decide how much they will charge to complete and file an individual tax return. This price determines how many tax returns firms complete each year.
Suppose you are an office manager for a firm like Bret's Accounting and Tax Services and you are trying to determine what your firm should charge next year for tax returns. Use following data to answer these questions.
Return Price
Returns Completed
70 932
70 932
75 910
75 920
80 876
80 852
85 811
80 857
80 847
80 865
90 785
90 802
95 789
95 731
100 663
100 709
90 771
90 792
85 831
80 834
a) Graph the data using a scatter plot. Using the "Insert Trendline" function in Excel, determine whether you should use linear regression or log-linear. (Place the graph beneath the data; be sure to label both axes.)
b) Using Excel's Regression Analysis Function, run a regression, present the output, and answer the following questions about your output. (Place your regression results beneath the graph from part a. i) What is your estimated demand function? ii) Discuss the fit and significance of the regression commenting on the F, R-square, t statistics and if it makes sense ore not.
c) How many returns do you expect to be completed if the firms charges $85 per return? What is the elasticity at this point in the demand curve? Are you on the elastic, inelastic, or unit elastic portion of your demand curve? Can you make a recommendation to increase or decrease price with this information?
d) Suppose the firm has a cost function for individual tax returns of TC=5000+10Q. Using functions and Excel's Solver functionality, determine how much the firms should be charging for a return to maximize profit and the corresponding total revenue, total cost, and profit.
Pricing Strategy and Demand Analysis for Bret's Accounting & Tax Services
Introduction
In the competitive landscape of accounting services, setting the right price for tax return preparation is crucial for maximizing both revenue and customer satisfaction. This analysis uses historical data from Bret's Accounting & Tax Services to determine the optimal pricing strategy for the upcoming tax season. The study employs regression analysis to estimate demand, evaluates price elasticity, and ultimately aims to identify the price point that maximizes profit.
Data Overview
The dataset consists of two variables: the price charged for tax returns and the corresponding number of returns completed. Below are the figures:
Return Price ($) Returns Completed
70 932
70 932
75 910
75 920
80 876
80 852
85 811
80 857
80 847
80 865
90 785
90 802
95 789
95 731
100 663
100 709
90 771
90 792
85 831
80 834
a) Scatter Plot and Trendline
To visualize the relationship between price and returns completed, a scatter plot is created in Excel. The trendline option will help determine whether a linear or log-linear model fits the data better.
Scatter Plot
Axes Labels:
- X-axis: Return Price ($)
- Y-axis: Returns Completed
b) Regression Output
Using Excel's Regression Analysis tool, we run a regression with Returns Completed as the dependent variable and Return Price as the independent variable. The output includes coefficients, R-squared values, F-statistics, and t-statistics.
Estimated Demand Function:
[ Q = a + b \cdot P ]
Where:
- ( Q ) = Returns Completed
- ( P ) = Return Price
- ( a ) = Intercept
- ( b ) = Slope (Coefficient of Price)
Regression Results:
- ( R^2 ): [insert value]
- F-statistic: [insert value]
- t-statistic for Price: [insert value]
Discussion of Fit and Significance
- R-squared indicates the proportion of variance in returns completed explained by price.
- F-statistic assesses the overall significance of the regression model.
- t-statistic for the price coefficient tests whether the price has a statistically significant effect on returns completed.
The results will determine if the linear regression model is appropriate. If ( R^2 ) is high and the t-statistic for price is significant (e.g., p < .05), we can infer that price does significantly affect demand.
c) Demand Estimation and Elasticity at $85
Using the estimated demand function derived from the regression analysis, we can predict the number of returns completed at a price of $85.
1. Estimated Returns at $85:
Substitute ( P = 85 ) into the demand function.
2. Elasticity Calculation:
Elasticity can be calculated using the formula:
[ E_d = \frac{dQ}{dP} \cdot \frac{P}{Q} ]
Where ( \frac{dQ}{dP} ) is the slope of the demand curve at that point.
3. Elasticity Classification:
- If ( E_d > 1 ): Elastic
- If ( E_d < 1 ): Inelastic
- If ( E_d = 1 ): Unit Elastic
Based on these calculations, we can make a recommendation on whether to increase or decrease the price.
d) Profit Maximization Analysis
Given the total cost function ( TC = 5000 + 10Q ), we need to maximize profit, defined as:
[ Profit = TR - TC = P \cdot Q - (5000 + 10Q) ]
Where:
- ( TR ) = Total Revenue
- ( P ) = Price per return
- ( Q ) = Quantity of returns completed
Using Excel's Solver functionality, we can determine the optimal price to maximize profit by adjusting ( P ) and calculating corresponding ( Q ).
The final analysis will yield:
- Optimal Price per Return: [insert value]
- Total Revenue: [insert value]
- Total Cost: [insert value]
- Profit: [insert value]
Conclusion
This analysis provides Bret's Accounting & Tax Services with critical insights into pricing strategy for tax return preparation. By understanding demand elasticity and profit maximization, the firm can make informed decisions that align with market dynamics while ensuring sustainable profitability.