Question: The chart below provides tax information for
a married couple under the new and old tax code.
Why is there no tax advantage
for purchasing a home under the new tax code?
Assume the old tax code was
in place for five years and total itemized deduction for our married couple
remained at $25,000. What is the net present
value of the tax advantage of purchasing a home and itemizing under the old
code for a fiveyear period?
(Assume the house is
purchased on January 1, 2018 and that the tax benefits are realized on, April
15 starting in 2019. Also assume the
cost of capital is 5 percent.)
Briefly discuss the potential
economic implications of the change on the tax code on the buy versus rent
decision, retirement savings, and migration of workers to new jobs.
Tax Situation


Old Code

New Code


Standard Deduction Married Couple

$12,700

$24,000

Total Itemized Deductions

$25,000

19,000

Tax Rate

28%

24%

Analysis: Homebuyers don’t benefit from the mortgage
deduction unless they itemize. This
married couple won’t itemize under the new tax code because itemized deductions
are lower than standard deduction.
Two methods are used to
calculate the NPV of the tax savings from purchasing a house under the old law.
The first involves
calculation of the discount factor 1/(1+r)^{t} for the five cash flows.
t is the difference in date of cash flow from
tax savings and date of initial house purchase and r the interest rate is 5
percent. The values of t were obtained
from the YEARFRAC function in Excel.
The NPV of the tax savings is
the sum product of annual tax savings and the discount factors. I get $14,702.
Calculation of NPV of tas savings under old law


Interest Rate


0.05


Date

Tax Savings

Years from house purchase

Discount Factor


1/1/18


1.28

4/15/19

$3,444

1.289

0.9391

2.29

4/15/20

$3,444

2.289

0.8943

3.29

4/15/21

$3,444

3.289

0.8517

4.29

4/15/22

$3,444

4.289

0.8112

5.29

4/15/23

$3,444

5.289

0.7726

NPV Tax Savings from House Purchas

$14,702

The other way to obtain the
NPV of the tax savings is from the XNPV function. I put $0 on the purchase date since the
problem only looks at the tax shield and does not consider costs associated
with the house purchase.
Second Calculation of NPV of Tax Savings


Date

Tax Savngs

1/1/18

$0

4/15/19

$3,444

4/15/20

$3,444

4/15/21

$3,444

4/15/22

$3,444

4/15/23

$3,444

XNPV

$14,703

The XNPV method gives us
$14,703.
The estimates differ by a
dollar probably because of the leap year impacting the YEARFRAC calculations.
Discussion of Implications: Most of the
political discussion of the tax changes has centered on limitations of mortgage
interest deductions and limitations of state local and property taxes. These issues are minor compared to the doubling
of the standard deduction, which eliminates any tax savings for most
homebuyers.
The elimination of the tax
savings for housing is important for three reasons. First, house equity is a major source of retirement
savings and delays in home purchases and lower home ownership rates will leave
many people with inadequate retirement savings.
Second homeownership locks in the cost of housing while housing costs
continue to increase for renters. Third,
the elimination of tax preferences for housing will discourage movement for new
jobs for many homeowners.
More on these topics will
appear shortly in my finance blog.
The bottom line of this work
is that the new tax code by discouraging home ownership will increase economic
uncertainty and ultimately increase poverty in America.
Authors Note: The problem presented in this post is
question number fifteen on the Excel Finance Function page.
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