# Capitalization Rate

The capitalization rate for CAUV values uses a combination of interest rates and equity rates along with a specified term of years for the lean and split between equity appreciation and interest costs.

## Update Dates

Data source for the interest is from Farm Credit Services for a 25-year term on a loan \$75,000 and over while the equity rate comes from USDA-ERS which has updates each year in February (should be considered “official”), August, and November. It is not clear if the Farm Credit Services produces their historical values of interest rates on a 25-year term loan or when this value is selected by the ODT.

## Calculations

The calculation procedure of the capitalization rate has had a few changes since 2005, which can be summarized for each year as follows:

Tax Year Interest Rate Equity Rate Loan Pct. Term Sinking
2005 1999-2005 1999-2005 60% 15 year 5 year
2006 2000-2006 2000-2006 60% 15 year 5 year
2007 2001-2007 2001-2007 60% 15 year 5 year
2008 2002-2008 2002-2008 60% 15 year 5 year
2009 2003-2009 2003-2009 60% 15 year 5 year
2010 2004-2010 2004-2010 60% 15 year 5 year
2011 2005-2011 2005-2011 60% 15 year 5 year
2012 2006-2012 2006-2012 60% 15 year 5 year
2013 2007-2013 2007-2013 60% 15 year 5 year
2014 2008-2014 2008-2014 60% 15 year 5 year
2015 2009-2015 2009-2015 80% 25 year 5 year
2016 2010-2016 2010-2016 80% 25 year 5 year
2017 2011-2017 1991-2015 80% 25 year 25 year
2018 2012-2018 1992-2016 80% 25 year 25 year
2019 2013-2019 1993-2017 80% 25 year 25 year
2020 2014-2020 1994-2018 80% 25 year 25 year
Future current-6 years ago 2lag-26 years ago 80% 25 year 25 year
Years 7 Olympic 25 Average

The capitalization rate requires the knowledge of an interest rate on a loan and an equity rate as well as the term and debt percentage for determining from the Mortgage-Equity Method. But it can be defined as:

\begin{aligned} {CAP_t} &= {Loan \%}_t \times {Annual Debt Service}_t + \\ & {Equity \%}_t \times {Equity Yield}_t - \nonumber \\ & {Buildup}_t + \nonumber \\ & {Tax Additur Adjustment}_t \nonumber \end{aligned}

The $${Loan \%}_t$$ plus $${Equity \%}_t$$ must equal one and is currently an 80% to 20% ratio respectively. Prior to 2015, the values were based on 60% loan and 40% equity appreciation.

$${Annual Debt Service}_t$$ is a debt servicing factor based on a 25-year term mortgage with an associated interest rate. The interest rate used for a particular year is based on a 7-year Olympic average where the value for the loan interest rate came from a 25-year mortgage from Farm Credit Services (FCS). Prior to 2015, a 15-year term was used instead of 25 and there were no lags in this formula. For example, the 2017 interest rate used comes from FCS values between 2011 and 2017. The formula for calculating the debt servicing factor with $$r$$ as the interest rate (from FCS) and $$n$$ the term length (currently 25) is:

${Annual Debt Service} = \frac{r \times (1 + r)^n}{(1 + r)^n - 1}$

Next, the $${Equity Yield}_t$$ needs to be calculated – which is simply the interest rate associated with equity that a farmer may hold. Prior to 2017, the equity yield was a 7-year Olympic average of the prime rate plus 2% from the Wall Street Journal’s bank survey – with no lag for the values. In 2017, the ODT switched the equity yield to be a two year lagged 25-year average of the “Total rate of return on farm equity” from the Economic Research Services of the USDA. For example, the 2017 value used the ERS’s values from 1991 to 2015.

Then, the equity buildup associated with a set time frame needs to be calculated. The equity buildup formula involves an associated interest rate (the $${Equity Yield}_t$$ is used here as $$r$$) and a time-frame $$n$$, which is set at 25 years currently (prior to 2017, this was set at 5 years of equity buildup):

${Buildup}_t = {Equity \%}_t \times {Mortgage Paid \%}_t \times \frac{r}{(1 + r)^n - 1}$

For 2017 and beyond, the $${Mortgage Paid \%}_t$$ is assumed to be 100%. However, prior to 2017 this value needed to be calculated as the percentage of mortgage paid after 5 years. The mortgage term was needed to determine what the mortgage paid after 5 years would be. For 2015 and beyond the mortgage terms have been for 25 years while prior to 2015 the mortgage term was for 15 years. The formula for calculating the percentage of the mortgage paid off after 5 years is:

${Mortgage Paid \%}_t = \frac{ \frac{1}{ (1 + r)^{n-5} } - \frac{1}{ (1 + r)^n} }{ 1 - \frac{1}{(1 + r)^n} }$

Where $$r$$ is the interest rate and $$n$$ is the term of the loan.

And finally, the $${Tax Additur Adjustment}_t$$ needs to be calculated. The tax additur is added onto the capitalization rate as a way to proxy for property taxes as a ratio to market value. The statewide average effective tax rate on agricultural land, as determined through table DTE27, from the previous tax year is used in calculation for the tax additur in question. The statewide average effective tax rate is expressed in terms of mills and the tax additur is then expressed as:

${Tax Additur Adjustment}_t = \frac{0.35 \times {Statewide Millage}_{t-1} }{1000}$

## Current Projections

Year ODT Value Expected Low High
2010 7.8% 7.8% 8.0% 7.7%
2011 7.6% 7.6% 7.8% 7.4%
2012 7.5% 7.5% 7.7% 7.2%
2013 6.7% 6.7% 7.0% 6.6%
2014 6.2% 6.2% 6.6% 6.2%
2015 6.6% 6.6% 6.9% 6.4%
2016 6.3% 6.3% 6.6% 6.2%
2017 8.0% 8.0% 8.2% 7.8%
2018 8.0% 8.0% 8.1% 7.8%
2019 8.0% 8.0% 8.2% 7.9%
2020 - 7.9% 8.1% 7.8%
2021 - 7.8% 8.0% 7.7%
2022 - 7.8% 8.0% 7.7%