Calculation of Compound Average Growth Rate(CAGR) of given Tax Analysis Data-Statistics Sample

QUESTION

 

Use the data in the spreadsheet below to complete the following tasks:
compute the compound average growth rate (CAGR) for personal income and each tax revenue source;
use the CAGR for personal income and the tax revenue sources to estimate the income elasticity of tax revenue of each tax revenue source;
use the income elasticity of tax revenue measures to assess the vertical equity of each tax revenue source;
develop a revenue forecast for each tax revenue source for FY 2017-FY 2021 and briefly defend the method used for the revenue forecast; and examine the 2003 and 2008 cigarette tax rate increases and estimate the tax rate elasticity of cigarette tax revenue.
Tax Analysis Data.xlsx
Draft a memorandum to provide all the information required above to me.
Formatting:
Microsoft Word Document.
Five-page maximum, excluding cover page, references, graphs, and tables (if needed).
Single spacing.
1-inch margins on all sides of the page.
Justified text alignment.
Arial 11 point font.
Use tables if they are helpful in presenting information. However, provide sufficient explanation of the information in any table or tables.
References in APA style
Memo cover page must be as follows:
TO: [Instructor Name]
FROM:
DATE:
RE: Tax Analysis.
Please submit the file by attaching it to the Submission Details page for the assignment. File must include student first and last name, course number, term and “Tax Analysis Memo” (e.g., Joe_Brown_402_Tax_Analysis_Memo.doc).
Country: United States of America

 

Fiscal Year   Personal Income (in millions) Gasoline Tax Revenue (in millions) Gasoline Tax Rate (cents per gallon) Sales Tax Revenue (in millions) Sales Tax Rate (% of sales price) Personal Income Tax Revenue (in millions) Personal Income Tax Rate (% of taxable income) Cigarette Tax Revenue (in millions) Cigarette Tax Rate (cents per pack)
1990 Actual $95,303.80 $395.73 $0.15 $2,136.70 5.0% $2,089.54 3.4% $112.74 $0.155
1991 Actual $99,501.82 $397.28 $0.15 $2,201.40 5.0% $2,183.97 3.4% $110.11 $0.155
1992 Actual $105,050.13 $399.94 $0.15 $2,264.10 5.0% $2,246.76 3.4% $111.26 $0.155
1993 Actual $112,850.37 $405.73 $0.15 $2,388.00 5.0% $2,412.47 3.4% $110.28 $0.155
1994 Actual $119,027.67 $420.24 $0.15 $2,601.40 5.0% $2,541.90 3.4% $113.38 $0.155
1995 Actual $126,121.52 $430.81 $0.15 $2,808.75 5.0% $2,767.74 3.4% $123.03 $0.155
1996 Actual $131,505.67 $437.10 $0.15 $2,966.15 5.0% $2,966.27 3.4% $123.72 $0.155
1997 Actual $139,189.28 $443.87 $0.15 $3,138.33 5.0% $3,197.12 3.4% $128.42 $0.155
1998 Actual $148,290.62 $455.57 $0.15 $3,278.77 5.0% $3,433.44 3.4% $127.97 $0.155
1999 Actual $157,512.38 $466.43 $0.15 $3,423.37 5.0% $3,699.32 3.4% $127.63 $0.155
2000 Actual $166,445.34 $464.15 $0.15 $3,687.40 5.0% $3,753.34 3.4% $125.15 $0.155
2001 Actual $174,492.64 $493.68 $0.15 $3,723.14 5.0% $3,779.81 3.4% $120.83 $0.155
2002 Actual $176,159.26 $480.81 $0.15 $3,798.49 5.0% $3,540.82 3.4% $123.21 $0.155
2003 Actual $179,844.47 $518.30 $0.165 $4,210.26 5.5% $3,644.16 3.4% $352.38 $0.523
2004 Actual $185,975.30 $582.61 $0.18 $4,759.45 6.0% $3,807.86 3.4% $338.72 $0.555
2005 Actual $192,417.29 $579.68 $0.18 $5,001.15 6.0% $4,213.21 3.4% $343.08 $0.555
2006 Actual $201,731.62 $570.49 $0.18 $5,336.78 6.0% $4,381.55 3.4% $355.52 $0.555
2007 Actual $211,520.59 $570.63 $0.18 $5,423.50 6.0% $4,615.60 3.4% $367.63 $0.555
2008 Actual $221,342.55 $553.46 $0.18 $5,738.83 6.83% $4,837.52 3.4% $525.27 $0.960
2009 Actual $222,409.35 $535.89 $0.18 $6,205.64 7.0% $4,313.76 3.4% $516.76 $0.995
2010 Actual $222,655.79 $540.70 $0.18 $5,963.87 7.0% $3,875.57 3.4% $482.01 $0.995
2011 Actual $235,095.65 $543.04 $0.18 $6,269.74 7.0% $4,585.55 3.4% $478.61 $0.995
2012 Actual $248,276.33 $534.70 $0.18 $6,631.95 7.0% $4,765.46 3.4% $456.17 $0.995
2013 Actual $257,025.75 $529.62 $0.18 $6,805.07 7.0% $4,972.81 3.4% $461.64 $0.995
2014 Actual $260,361.12 $527.29 $0.18 $7,003.66 7.0% $4,896.32 3.4% $447.56 $0.995
2015 Actual $272,529.30 $540.08 $0.18 $7,278.60 7.0% $5,232.98 3.35% $439.26 $0.995
2016 Actual $282,505.53 $556.82 $0.18 $7,306.33 7.0% $5,218.17 3.3% $443.21 $0.995
2017 Forecast $293,030.27                
2018 Forecast $306,316.99                
2019 Forecast $321,482.04                
2020 Forecast $336,868.54                
2021 Forecast $352,200.15              

 

 

ANSWER

 

MEMO

The following is the CAGR of the sources:

Personal Income (in millions)

Gasoline Tax Revenue (in millions)

Gasoline Tax Rate (cents per gallon)

Sales Tax Revenue (in millions)

Sales Tax Rate (% of sales price)

Personal Income Tax Revenue (in millions)

Personal Income Tax Rate (% of taxable income)

Cigarette Tax Revenue (in millions)

Cigarette Tax Rate (cents per pack)

CAGR

4.27%

1.32%

0.70%

4.84%

1.30%

3.58%

-0.11%

5.41%

7.41%

The CAGR has been calculated using the values for 1990 and 2016. The formula used is the following:

CAGR = (Final/ Initial)^(1/Number of periods)

The formula used is a standard formula and is used by all the industries in calculating the CAGR.

Tax elasticity is the proportionate increase in the adjusted tax revenue, without any discretionary change, relative to GDP. Well what does the above statement mean, It just means how much will the tax revenue increase without any change in the tax rate(either increase or decrease) with the proportionate change in GDP. Hence, tax buoyancy shows the association between economy’s performance and the government’s ‘happiness’ (tax revenue). it indicates the high sensitiveness of tax revenue realization to GDP growth.

The CAGR was then used to calculate the Elasticity of tax revenue which has a few methods of calculations available in the literature. Among them the two most widely accepted methods are log gain method and absolute gain method. The main difference both the methods is that we use the natural log of the change instead of the absolute change in the logarithmic method. That is done to normalise the data in the absence of sufficient data to support the analysis. As we have 26 data points for each tax source and that is enough to support the analysis we will be using the absolute change method. The formula used for that is the following:

Tax elasticity for a particular source = (Change in tax/change in Income)*(Income or the GNP/Tax)

Here as we are not calculating the tax elasticity for a single period but for a much longer period of time thus we will be using the CAGR instead of the change in the tax rates over just the last year. The Results of the tax elasticity are as follows:

Personal Income (in millions)

Gasoline Tax Revenue (in millions)

Gasoline Tax Rate (cents per gallon)

Sales Tax Revenue (in millions)

Sales Tax Rate (% of sales price)

Personal Income Tax Revenue (in millions)

Personal Income Tax Rate (% of taxable income)

Cigarette Tax Revenue (in millions)

Cigarette Tax Rate (cents per pack)

Elasticity

157.1747335

258778.43

43.87018383

1231695.436

45.44688335

-230177.6515

807.4273158

493163.2135

Now as we have the elasticity of each source which are the ones associated with the absolute values and not the tax rates we will use that to calculate the associated vertical equity. In simpler terms vertical equity is the incremental equity that is associated with each tax rate. This is done to make the people who can afford to pay more ay a higher tax rate than the people who cannot afford to pay the same higher tax rate. The Vertical equity is calculated as the percentage of the total equity instead of a calculation of the absolute number. The actual calculation is done by dividing unity by the elasticity and then dividing it by the tax rate. Following is the equity calculations:

Personal Income (in millions)

Gasoline Tax Revenue (in millions)

Gasoline Tax Rate (cents per gallon)

Sales Tax Revenue (in millions)

Sales Tax Rate (% of sales price)

Personal Income Tax Revenue (in millions)

Personal Income Tax Rate (% of taxable income)

Cigarette Tax Revenue (in millions)

Cigarette Tax Rate (cents per pack)

Vertical Equity

3.53%

32.56%

66.68%

0.12%

For the calculation of the forecast of the revenue sources the vertical equity percentage has been used. We have used the forecasts for the actual revenue which are already given. The same forecast has been used and the percentage of those forecast have been used by multiplying the same with the vertical equity percentage. Instead on increasing the actual tax rates only the revenue forecast has been used as the vertical equity already entails the elasticity of the CAGR of each revenue source. The following are our forecasts:

Personal Income (in millions)

Gasoline Tax Revenue (in millions)

Gasoline Tax Rate (cents per gallon)

Sales Tax Revenue (in millions)

Sales Tax Rate (% of sales price)

Personal Income Tax Revenue (in millions)

Personal Income Tax Rate (% of taxable income)

Cigarette Tax Revenue (in millions)

Cigarette Tax Rate (cents per pack)

2017

$621.45

$7,792.73

$5,526.65

$453.65

2018

$649.63

$8,146.08

$5,777.24

$474.22

2019

$681.79

$8,549.37

$6,063.25

$497.70

2020

$714.42

$8,958.55

$6,353.45

$521.52

2021

$746.94

$9,366.27

$6,642.61

$545.25

In case of the cigarette tax rates there has been a steep jump in the tax rate from 2003 to 2008. Due to that reason we There is a need to re-evaluate the elasticity for the same header in the above-mentioned time range. The methodology and the formulas used for these are the same and there in no change in the procedure. The following are the results for cigarette tax rates:

Cigarette Tax Revenue (in millions)

Cigarette Tax Rate (cents per pack)

CAGR

8.31%

12.91%

Elasticity

820.6523181

697630.5956

Vertical Equity

0.13%

We can see that there is a significant difference in the elasticity of the cigarette tax rate when we used the data for the range of 2003 to 2008. There is also a change in the vertical equity percentage. Thus, in that time range there was a larger focus on cigarette tax rates compared to the time before and after the given range.

 

  Personal Income (in millions) Gasoline Tax Revenue (in millions) Gasoline Tax Rate (cents per gallon) Sales Tax Revenue (in millions) Sales Tax Rate (% of sales price) Personal Income Tax Revenue (in millions) Personal Income Tax Rate (% of taxable income) Cigarette Tax Revenue (in millions) Cigarette Tax Rate (cents per pack)  
CAGR 4.27% 1.32% 0.70% 4.84% 1.30% 3.58% -0.11% 5.41% 7.41%  
Elasticity   157.174733475285 258778.430013385 43.8701838329252 1231695.43649471 45.4468833460668 -230177.651461721 807.427315834461 493163.213499239  
Vertical Equity   3.53%   32.56%   66.68%   0.12%    
2017   $621.45   $7,792.73   $5,526.65   $453.65    
2018   $649.63   $8,146.08   $5,777.24   $474.22    
2019   $681.79   $8,549.37   $6,063.25   $497.70    
2020   $714.42   $8,958.55   $6,353.45   $521.52    
2021   $746.94   $9,366.27   $6,642.61   $545.25    
                     
                  Cigarette Tax Revenue (in millions) Cigarette Tax Rate (cents per pack)
                CAGR 8.31% 12.91%
                Elasticity 820.652318126306 697630.595577225
                Vertical Equity 0.13%

REFERENCES

  • YILMAZ, E., & SÜSLÜ, B. (2015). The calculation of weighted price elasticity of tax: Turkey (1998-2013). Çankırı Karatekin Üniversitesi Iktisadi Ve Idari Bilimler Fakültesi Dergisi, 5(1), 337-346.
  • Jacob, M. (2016). Cross-base tax elasticity of capital gains. Applied Economics, 48(28), 2611-2624. doi:10.1080/00036846.2015.1125438
  • Anderson, J. E., & Shimul, S. N. (2018). State and local property, income, and sales tax elasticity: Estimates from dynamic heterogeneous panels. National Tax Journal, 71(3), 521-546. doi:10.17310/ntj.2018.3.04

 

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