## Monday, December 18, 2017

### NPV of five-year housing tax break under old law.

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 five-year 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.