Mortgage refinancing: the interaction of break even period, taxes

Mortgage reﬁnancing: the interaction of break even

period, taxes, NPV, and IRR

Rich Fortin,

Stuart Michelson,

* Stanley D. Smith,

William Weaver

New Mexico State University, Las Cruces, NM 88003, USA

Stetson University, Deland, FL 32723, USA

Department of Finance, University of Central Florida, Orlando, FL 32816-1400, USA

Abstract

This paper develops a reﬁnance model that provides pertinent information for investors about

reﬁnancing their mortgage. We discuss the input variables and how to compute the breakeven number

of months when deciding to reﬁnance a mortgage. We incorporate the interest rate tax effects that are

normally ignored by investors when making their reﬁnancing decision. We also compute the net

present value and internal rate of return to allow one to analyze reﬁnancing as an investment decision.

Additionally we have developed an Excel model, complete with automated macros, to perform this

JEL classiﬁcations: G21; M5

Keywords: Mortgage; Reﬁnancing; Taxes; Breakeven; IRR; NPV; Simulation; Excel

1. Introduction

In this paper, we examine home mortgage reﬁnancing from a ﬁnancial analysis frame-

work. In particular, we examine the after-tax savings resulting from reﬁnancing while taking

into consideration the lost tax savings from the higher interest rate on the old mortgage. We

discuss the input variables required and how to compute the net present value (NPV), internal

rate of return (IRR), and breakeven period for the mortgage reﬁnancing decision. We

incorporate the interest rate tax effects that are normally ignored and we develop an Excel

* Corresponding author. Tel.: ⫹1-386-822-7376; fax: ⫹1-386-822-7491.

E-mail address: [email protected] (S. Michelson).

Financial Services Review 16 (2007) 197–209

model to perform this analysis and utilize Goal Seek to optimize the solution. We ﬁnd that

breakeven is about 35% to 40% longer when considering the effect of the lost interest tax

shield. The model we develop allows the user to compute the NPV and IRR based on their

speciﬁc investment horizon for the mortgage.

During the past 10 years, the cost of obtaining a mortgage has declined signiﬁcantly.

Figure 1 shows average points and fees associated with a 30-year ﬁxed-rate conforming

mortgage as a percentage of the loan amount over the 10-year period 1986 through 2006

(source: Primary Mortgage Market Survey, FHLMC, 2006). Points and fees have declined

from 1.8% in 1995 to 0.6% in 2005. The declining cost of obtaining a mortgage encourages

homeowners to reﬁnance by decreasing the cost of reﬁnancing.

Mortgage interest rates have also decreased. Figure 2 shows that current mortgage rates

are near recent historical lows. When current mortgage rates are lower than the rate on an

outstanding mortgage, the beneﬁts of reﬁnancing are enhanced (e.g., monthly payment

savings, faster payoff of the loan, etc.).

As the cost of a new mortgage declines relative to outstanding mortgage rates, the percentage

of new loans associated with reﬁnancing should increase. Figure 3 illustrates the recent percent-

age of home loans that are created through reﬁnancing. The reﬁnancing percentage is highly

negatively correlated with the current mortgage rate and the points and fees associated with a new

loan. In other words, as the beneﬁts increase and the costs decrease, reﬁnancing increases.

As a homeowner evaluates her decision to reﬁnance it is important to perform the analysis

correctly. Some ﬁnancial advisors recommend an easy approach, the payback or break-even

period method, which divides the cost of reﬁnancing by the monthly payment savings. The

homeowner compares this break-even period with the expected time that she will live in the

house. This method is easy to understand for the average homeowner who may not be

familiar with more sophisticated methods of ﬁnancial analysis.

The problems with this approach are that it ignores the time value of money, the potential

loss of some or all of the value of the mortgage interest tax deduction, and the differences

in the loan balances of the old and new loans. Our paper takes all of these factors into

0.5

1.5

2.5

1986 1991 1996 2001 2006

Year (December)

Percent Points & Fees

Fig. 1: Points and Fees as Percent of Home Loan

198 R. Fortin et al. / Financial Services Review 16 (2007) 197–209

account. In addition, we provide an Excel model for the ﬁnancial advisor or the homeowner

to use, which provides the IRR and the NPV as a function of the length of ownership.

2. Relevant literature

With the home as one of the largest investments by many investors, the home buying

decision and the mortgage ﬁnancing as part of personal ﬁnancial planning have received

1986 1991 1996 2001 2006

Year (December)

Current Mortgage Rates -

Percent

Fig. 2: Conventional Conforming 30-year Fixed-Rate Mortgage

1986 1991 1996 2001 2006

Year (December)

Percent Refinancing

Fig. 3: Reﬁnancing Percentage of Home Loans

199R. Fortin et al. / Financial Services Review 16 (2007) 197–209

attention in this journal. Templeton, Main, and Orris (1996, 2002) provide a simulation

approach to choosing between ﬁxed and adjustable rate mortgages and investigate adjust-

able-rate mortgage pricing features, respectively. Zivney and Luft (1999) investigate the

feasibility of an individual hedging the interest rate risk involved in planning to take out a

mortgage at a future point in time. Lee and Hogarth (2000) investigate how consumers search

for information on a home mortgage loan. Waggle and Johnson (2003) examine the impact

of a single-family home on a family’s optimal asset allocation. Larsen (2004) examines the

impact of loan rates on direct real estate investment holding period returns. Only one paper

by Hoover (2003) in this journal has dealt with mortgage reﬁnancing. Before we look at the

Hoover article, we will review other articles related to mortgage reﬁnancing.

The literature on mortgage reﬁnancing from the borrower’s viewpoint includes several

interesting articles. Auster (1998) explains that homeowners must consider taxes, points and

closing costs, and use equal amortization schedules to ﬁnd the true cost savings of reﬁnanc-

ing. He maintains that when discounting the cash ﬂows, the appropriate discount rate is the

mortgage rate on the new loan. G-Yohannes (1988) illustrates that the decision to reﬁnance

should include a number of important factors, including: closing costs, interest rate on the

existing loan, interest rate on the new loan, holding period, opportunity discount rate, income

taxes, remaining balance, and the term of the new loan. Valachi (1982) uses the internal rate

of return to evaluate mortgage reﬁnancing. Followill and Johnson (1989) show that because

of the tax deductibility of the mortgage interest payment, the reﬁnancing decision must be

made from an after-tax perspective. They utilize a net present value model to analyze the

beneﬁts of reﬁnancing.

Bennett, Keane, and Mosser (1999) explain that the high number of loans that have been

reﬁnanced is not because of just being cost effective, but is also because of favorable

economic conditions. They observe that homeowners typically reﬁnance if the borrower’s

current rate exceeds the reﬁnance rate by 50 to 200 basis points. They also ﬁnd that the

mortgage interest rate spread explains about 72% of the reﬁnancing activity in the 1990

through 1998 period. Bennett, Peach, and Peristiani (2000) present a prepayment model that

incorporates the borrower’s creditworthiness, loan-to-value ratio, and market conditions.

Using a loan level dataset they develop a model that allows them to compute the minimum

interest-rate differential needed to justify reﬁnancing. Wetmore and Ndu (2006) use a Garch

model to explain changes in mortgage reﬁnancing over 1990 through 2001. They ﬁnd that

reﬁnancing activity is negatively related to the 30-year mortgage rate, that mortgage reﬁ-

nancing is a substitute for other investments, and that investors respond more quickly to

changes in interest rates than in the past.

Chen and Ling (1989) present a model of mortgage reﬁnancing in which the borrower is

viewed as the seller of a callable mortgage bond to the lender. They ﬁnd that it is

advantageous to “reﬁnance a ﬁxed-rate mortgage when the present value of interest savings

exceeds the reﬁnancing costs.” They also show that this minimum differential increases with

transaction costs, interest rate volatility, and expected holding period. Johnson and Randle

(2003) present a model for analyzing the feasibility of mortgage reﬁnancing. Their model

ﬁnds the breakeven number of months between the sum of the present value of the P&I

payment and unpaid balance for the old and new loans. As with previous authors, they ﬁnd

that it is mathematically the same to include the closing costs in the new loan balance as

200 R. Fortin et al. / Financial Services Review 16 (2007) 197–209

opposed to being “paid out of pocket.” Their model does not include the value of the lost

interest tax shield. Fortin and Michelson (2005) provide an Excel model to determine the

break-even period with and without these tax beneﬁts.

Our paper is an extension to the elegant closed-form equation model developed by Hoover

(2003) that computes the breakeven and NPV of mortgage reﬁnancing. The Hoover model

extends earlier work by Chen (1997), Rose (1992), and Johnson and Randle (1996, 2003) by

recognizing the importance of after-tax analysis and properly deﬁning the proper discount

rate. Our approach extends the Hoover model by relaxing the assumption made in the Hoover

paper that all loans are interest-only. Rather than a closed-form equation solution, our model

is iterative (made necessary by the changing proportion of principal and interest in most

mortgage payments each month) and has been programmed into Excel, which is much easier

to use than the algebraic closed-form approach. Because principal reduction loans are most

common, this is a signiﬁcant advancement. The iterative approach also results in an accurate

calculation rather than an approximation resulting from the closed-form model.

This paper incorporates the previously discussed factors. In addition, we provide an Excel

model for the ﬁnance professional or the homeowner to use that provides the IRR and the

NPV as a function of the length of ownership, as well as an after-tax breakeven period.

3. Data and methodology

Our primary objective is to examine the mortgage reﬁnancing decision, while considering

the lost tax shield from the interest payments on a higher interest rate mortgage. Rules of

thumb for reﬁnancing are not very accurate and the breakeven interest differential is higher

than one might think. Our analysis utilizes simulated data, over a representative sample of

differential mortgage rates over various reﬁnancing periods and using middle-income federal

tax rates. We also provide an Excel model that can be used by the reader to analyze mortgage

reﬁnancing for personal and professional use. The model allows the investor to modify the

mortgage balance, the term, the tax rate, the old mortgage interest rate, and the new mortgage

interest rate. A copy of the working model can be downloaded at www.drsm.org/

model1.html.

We ﬁrst discuss the basic inputs to the model, followed by a presentation of the Excel

model, and then provide a discussion of the results of the analysis of typical mortgage data.

The important input variables to the model are: mortgage balances, interest rates on the old

and new loans, number of remaining payments on the old loan, term of the new loan, closing

costs, and investor tax rate.

Using this data, we calculate the remaining balance on the old loan and use this amount

for the starting balance of the new loan, but also add the closing costs to the new balance.

Additionally, we calculate the monthly payment on each of the loans and then iteratively

perform a breakeven analysis. For each loan (old and new) we calculate the present value of

the future mortgage payments up to the breakeven month and the present value of the unpaid

balance. Following Auster (1998) and Johnson and Randall (2003), we assume that the

interest rate on the new mortgage is the opportunity cost of debt for this investor and the

relevant interest rate for computing present values is the interest rate on the new mortgage.

201R. Fortin et al. / Financial Services Review 16 (2007) 197–209

We take the sum of both of the PVs for each loan and then ﬁnd the breakeven number of

months for the two sums to be equal for the old loan and the new loan. We use Goal Seek

in Excel to perform this optimization.

The previous calculation does not consider the lost interest tax deduction. To ﬁnd the

breakeven while incorporating taxes, we perform a similar analysis as described above, but

also include the present value of the lost interest tax deduction. To do so, we calculate the

difference in the interest payment each month for the old and the new loans and then multiply

this value (each month) times the investor’s marginal tax rate. This incorporates the value of

the lost tax deduction because of lower interest payments on the new loan. We then ﬁnd the

present value of these monthly “tax deductions” over the breakeven period number of months

and use this value to penalize the new loan for the lost tax deduction, thus creating a longer

breakeven period.

As with previous authors, we ﬁnd that the results are mathematically identical when

including the closing costs in the new loan balance in contrast to being considered separately

during closing. We incorporate the closing costs in the new loan balance and, thus, compute

the breakeven between the old mortgage’s lower balance and the new mortgage’s higher

balance. The higher remaining balance on the new loan is offset by the lower P&I payments

and the higher payments towards the principal balance, due to the lower interest rate obtained

by reﬁnancing.

For NPV, one ﬁrst selects the year at which to compute the NPV. At that year, we ﬁnd the

present value of the difference in principal and interest payments, the present value of the

difference in remaining balances, and the present value of the lost interest deduction. One

would normally select the year based on how long the homeowner anticipates holding the

mortgage and the result would be a positive or negative NPV decision. For IRR, the

computation is similar to NPV, except we now solve for the rate of return.

Algebraically, our calculations are accomplished as follows:

To ﬁnd the present value of the principal and interest payments at the breakeven year (m),

compute the following for the old loan and the new loan, where loan indicates the payment

is for either the old loan or the new loan.

P&I

⫽

冘

n⫽1

n⫽m

PMT

loan

(1 ⫹ i

new

/12)

(1)

To ﬁnd the present value of the remaining balance at the breakeven year (m) for the old loan

and the new loan, where loan indicates the payment is for either the old loan or the new loan.

Remaining Balance

⫽

冘

n⫽m⫹1

n⫽360 or (180)

PMT

loan

(1⫹i

loan

/12)

(2)

Then ﬁnd the sum of both present values for the P&I and the Remaining Balance for both

the old loan and the new loan. Excel’s Goal Seek will be used to ﬁnd the breakeven number

of years in which these two sums are equal. Alternatively, algebraically, ﬁnd m (breakeven

month), such that:

202 R. Fortin et al. / Financial Services Review 16 (2007) 197–209

P&I (old loan)

⫹ PV

Remaining Balance (old loan)

⫽ PV

P&I(new loan)

⫹

Remaining Balance (new loan)

(3)

This equation is used to ﬁnd the breakeven month (m), not incorporating the value of the

interest deduction.

To incorporate the value of the lost interest deduction:

lost deduction

⫽

冘

n⫽1

n⫽m

冋

冘

n⫽1

n⫽m

Interest payment

n, old loan

⫺

冘

n⫽1

n⫽m

Interest Payment

n, new loan

册

⫻ Tax Rate

(1 ⫹ i

new loan

/12)

(4)

Then adjust the sum of the present values (above) used to ﬁnd the breakeven, by including

the lost interest deduction:

P&I(old loan)

⫹ PV

Remaining Balance(old loan)

⫽ PV

P&I(new loan)

⫹

Remaining Balance(new loan)

⫹ PV

lost deduction

(5)

This equation is used to ﬁnd the breakeven month (m), including the value of the interest

deduction.

4. The Excel model

Table 1 presents the Excel model developed to perform the breakeven analysis and Table

2 provides examples of the results. Table 3 shows the formulas used to build the model. The

inputs are in the shaded cells (original loan amount, loan term, interest rates, remaining

number of payments, tax rate, and closing costs). The monthly payments are calculated using

the PMT function. The model calculates the remaining balance of the old loan using a lookup

(VLOOKUP function) that references the amortization table. The present value of the P&I

payments is calculated using the PV function to discount the mortgage payments using the

new loan interest rate as the discount rate. The present value of the unpaid balance is

computed using the PV function to discount the P&I payments from the end of the loan up

to the breakeven month. These two values are summed (PV of P&I and PV of Remaining

Balance) separately for the old and the new loan. We then use the Goal Seek Analysis Tool

to ﬁnd the breakeven period number of months to cause these two sums to be equal, using

the difference cell, D23.

As indicated in Column G of Table 1, Goal Seek can be used to ﬁnd the breakeven number

of months. Goal Seek is the simplest form of a linear program, in that there is only one

constraint. To use Goal Seek, go to Tools, Goal Seek, and then ﬁll in the three blanks in the

dialogue box. For Set Cell, specify cell D23 and for Value, specify 0. For Changing Cell,

203R. Fortin et al. / Financial Services Review 16 (2007) 197–209

Table 1.

CDEF G HIJ

Exhibit 1

Fixed Rate Level Payment Home Loan Loan Amortization Model

Breakeven Months For New Loan With and Without Taxes

Old Loan New Loan

Input Values:

Input Values

Initial Loan Amount, Old Loan $100,000 NA Goal Seek Cells

Original Loan Term

360 240

fter-Tax Rate

Annual Interest Rate 7.00% 6.00% 4.32%

Remaining Number of Payments 240 240 Goal Seek:

Remaining Loan Balance $85,812 Set cell: D23 or D31

New Loan Amount $86,812 Set to value: 0

Monthly P&I Payment $665 $622 Changing cell: C19 or C26

Closing Costs, New Loan

NA $1,000

Tax Rate

28% 28%

Macros:

Ctrl T - first breakeven

Calculations without any tax effect:

Ctrl G - Tax breakeven

Breakeven Number of Months (m) 14.74 14.74

PV of P&I Payments at (m) $9,429 $8,815

PV of Remaining Balance at (m) $77,383 $77,997

PV of All Cash Flows at (m) $86,812 $86,812 NPV at 36 Months

Difference $0 $674.61

Calculations with Tax Effect:

IRR at 36 Months

Breakeven Number of Months (n) 20.42 20.42 49.83% annualized

PV of P&I Payments at (n) $13,077 $12,225

PV of Remaining Balance at (n) $76,430 $76,925

PV of All Cash Flows at (n) $89,508 $89,150

PV of Interest Deduction Difference at (n) $357

Difference with Interest Tax Deduction

Table 2.

Exhibit 2

Months to Breakeven, NPV, and IRR when Refinancing

Old mortgage amount

$100,000 $100,000 $100,000 $100,000

Old mortgage remaining balance

$85,812 $85,812 $85,812 $85,812

New mortgage amount (unpaid balance

plus closing costs)

$86,812 $86,812 $86,812 $86,812

Old mortgage term (months)

360 360 360 360

Months left on old mortgage

240 240 240 240

New mortgage term (month)

240 240 240 240

Interest rate old mortgage

7.00% 7.00% 7.00% 7.00%

Interest rate new mortgage

6.00% 6.50% 5.50% 5.00%

Closing costs on new mortgage

$1,000 $1,000 $1,000 $1,000

Investor tax rate

28% 28% 28% 28%

Old mortgage P&I monthly payment

$665 $665 $665 $665

New mortgage P&I monthly payment

$622 $647 $597 $573

Months breakeven w/o taxes 14.74 31.44 9.63 7.15

Months breakeven w taxes 20.42 44.23 13.30 9.69

NPV $0 $0 $0 $0

IRR 4.32% 4.68% 3.96% 3.60%

204 R. Fortin et al. / Financial Services Review 16 (2007) 197–209

specify C19. These values specify that you require Goal Seek to optimize such that C22 and

D22 (the PV of All Cash Flows, old loan and new loan) are equal, by varying the values in

C19 (the Breakeven Number of Months). Notice that the breakeven number of months is the

time-period used in computing the present values of P&I payments and remaining balance.

When computing breakeven while considering the tax effect of the lower interest deduc-

tion, the logic is similar to the previous breakeven calculation. The primary difference is that

cell C30 also incorporates the PV of the lost interest deduction, penalizing the new loan for

the difference. To use Goal Seek for the breakeven computation that incorporates the interest

tax deduction, the procedure is similar to the non-tax case, just change the cell references.

The Set Cell is D31, Value is zero, and Changing Cell is C26. We have also developed

macros to allow automatic operation of Goal Seek. Simply depress Control-T to compute the

ﬁrst breakeven value and depress Control-G to compute the tax adjusted breakeven value.

We have also provided macro buttons in rows 2– 4 (not shown on the exhibit) that can also

be used to run the two macros.

To compute NPV and IRR, input the number of months one expects to hold the mortgage

in Cells H22 and H25. The resulting NPV and IRR will appear in Cells G23 and G26 that

are generated by referencing a lookup (VLOOKUP) from the amortization table, where the

NPV and IRR are computed for every month in the mortgage. The values for NPV and IRR

are exact for each whole month, but not continuous, so NPV will not be exactly zero when

20.42 is entered in cell H22. The program enters the value of 20.42 as 20 and the

corresponding NPV is ⫺26.67. If you enter 21 in cell H22 the NPV is ⫹19.14. You can see

that an NPV of zero would fall between the two values. A similar situation exists for IRR

when entering values for months in cell H25. At 20 months the IRR is ⫺1.55% and at 21

months the IRR is 4.59%. The after-tax discount rate of 4.32% in cell E10 falls between those

two values.

Figure 4 presents a graph showing how NPV increases as the mortgage term increases.

One can see graphically how the breakeven number of years is equal to the point at which

Table 3.

EF G HI

Exhibit 3

Fixed Rate Level Payment Home Loan Loan Amortization Model

Breakeven Months For New Loan With and Without Taxes

Old Loan

New Loan

Input Values:

Input Values

Initial Loan Amount, Old Loan

$100,000

Goal Seek Cells

Original Loan Term

360 240

fter-Tax Rate

Annual Interest Rate

7.00%

6.00% =D10*(1-D16)

Remaining Number of Payments

240

Goal Seek:

Remaining Loan Balance

=VLOOKUP($C$9-$C$11,A35:E395,5)

Set cell: D23 or D31

New Loan Amount

=C12+D15

Set to value: 0

Monthly P&I Payment

=PMT(C10/12,C9,-C8)

=PMT(D10/12,D11,-D13)

Changing cell: C19 or C26

Closing Costs, New Loan

$1,000

Tax Rate

28%

Macros:

Ctrl T - first breakeven

Calculations without any tax effect:

Ctrl G - Tax breakeven

Breakeven Number of Months (m)

15 =C19

PV of P&I Payments at (m) =PV($D$10/12,C19,-$C$14)

=PV($D$10/12,D19,-$D$14)

PV of Remaining Balance at (m)

=PV($C$10/12,$C$11-C19,-$C$14)*(1/(1+D10/12))^C19 =PV($D$10/12,$D$11-D19,-$D$14)*(1/(1+D10/12))^C19

PV of All Cash Flows at (m)

=SUM(C20:C21) =SUM(D20:D21)

NPV at 240 Months

Difference =C22-D22

=VLOOKUP(H22,K35:W395,11)

Calculations with Tax Effect:

IRR at 240 Months

Breakeven Number of Months (n)

=C26

=VLOOKUP(H25,K36:W398,13)

annualized

PV of P&I Payments at (n)

=PV($E$10/12,C26,-$C$14)

=PV($E$10/12,D26,-$D$14)

PV of Remaining Balance at (n)

=MAX(PV($C$10/12,$C$11-C26,-$C$14),0)/((1+E10/12)^C26) =MAX(PV($D$10/12,$D$11-D26,-$D$14),0)/((1+E10/12)^D26)

PV of All Cash Flows at (n)

=SUM(C27:C28)

=SUM(D27:D28)

PV of Interest Deduction Difference at (n)

=VLOOKUP(C26,K35:P395,6)

Difference with Interest Tax Deduction

=C29-D29-C30

205R. Fortin et al. / Financial Services Review 16 (2007) 197–209

NPV is zero and the point where the IRR is equal to the discount rate (after-tax interest rate

on the new loan). The graph updates as one changes the input variables.

5. Results and discussion

Table 2 presents example results of the model shown in Table 1. We have varied the

mortgage amount, term, and interest rate to provide a sample of scenarios for discussion. The

table presents the results for a $100,000 original mortgage, $85,812 remaining balance, and

$86,812 new mortgage including closing costs of $1000. The remaining balance is computed

based on the number of months remaining in the mortgage. The new loan amount is the

remaining balance of the old loan, plus closing costs. The mortgage principal and interest

payments are computed based on the term, mortgage amount, and interest rate. Note that the

number of months remaining on the old mortgage and the term on the new mortgage are the

same. This is not a requirement of the model; we simply utilize the same number of months

to allow the reader to more easily compare the old and new loan. In general, the variables

that create a longer breakeven include: longer term mortgage, lower initial interest rate,

smaller difference in old and new interest rates, and lower principal balance on the mortgage.

On a $100,000 mortgage, a one percentage decrease in interest rates requires about one

year to breakeven (15 months), when not considering taxes and about two years when the lost

tax deduction is included (21 months). When reviewing a one-half percentage difference in

mortgage rates, the break-even is much longer. The breakeven is three years (32 months)

NPV vs Term of Mortgage

-2000

-1000

1000

2000

3000

4000

5000

6000

0 50 100 150 200 250 300 350

Months

of Mortgage

NPV ($)

Fig. 4: NPV vs Term of Mortgage

206 R. Fortin et al. / Financial Services Review 16 (2007) 197–209

without the lost interest tax deduction. However, when also considering taxes, the breakeven

is about four years (45 months), about 40% longer. A larger decrease in interest rates

provides much faster breakevens. A one and one-half percentage difference provides a

14-month breakeven (incorporating taxes) and a two percentage difference provides a 10

month breakeven. Even though both breakevens are fairly rapid, they are still about 40%

slower than the equivalent breakeven not incorporating the tax effect.

In this model, the NPV and IRR are calculated for each year of the mortgage. Therefore,

an investor can use the model to determine how long they will need to hold the mortgage to

have a positive NPV or high enough IRR, based on their horizon. For example, if an investor

is planning on retaining this mortgage for 36 months using the 6% new mortgage rate, the

resulting NPV is $674.61 and the IRR is 49.83%. This conﬁrms that over a 36-month

horizon, reﬁnancing would be a good investment decision. When we review the NPV and

IRR at the breakeven point, the result is known beforehand. At the breakeven, the NPV

should be zero and the IRR will be the after-tax rate of return. Table 2 conﬁrms that this is

true. Therefore, under all of our scenarios, the NPV is zero and the IRR decreases as the new

mortgage interest rate decreases. Note that in this model, we present the breakeven as a

whole number (we do not present fractional months), so there is some round off when

comparing breakeven, NPV, and IRR.

The data illustrate that at least a one-percent interest rate differential is necessary to

achieve a reasonable breakeven. Longer-term mortgages also tend have a faster breakeven

because more interest is saved by reﬁnancing. Similar results are found when including the

effect of the lost interest deduction, although the breakeven periods are about 40% longer.

Because the average mortgage holder tends to move or reﬁnance every three to ﬁve years,

one must evaluate their speciﬁc breakeven very carefully. All of the scenarios presented

break even in less than ﬁve years. If an investor is considering moving or reﬁnancing after

only three years, he or she would need a one percentage or larger interest rate decrease to

breakeven.

6. Conclusion

This paper provides homeowners with relevant information about what is likely the largest

single asset in their overall ﬁnancial portfolio. We discuss the input variables required and

how to compute the NPV, IRR, and breakeven period for the mortgage reﬁnancing decision.

We incorporate the interest rate tax effects that are normally ignored and we developed an

Excel model to perform this analysis and utilize Goal Seek to optimize the solution. We ﬁnd

that breakeven is about 35% to 40% longer when considering the effect of the lost interest

tax shield. The model we develop allows the user to compute the NPV and IRR based on

their speciﬁc investment horizon for the mortgage. A free copy of this Excel model is

available at: www.drsm.org/model1.html.

A ﬁnancial planning website (CCH 2007) states “A rule of thumb is that your new loan

should have an interest rate that is at least 1% less than your present mortgage before you

consider reﬁnancing. Also, you must plan on owning your home for a long enough period–

generally ﬁve years is required–to at least breakeven when it comes to the costs and fees

207R. Fortin et al. / Financial Services Review 16 (2007) 197–209

incurred in obtaining a lower interest rate.” This is fairly typical advice that a client receives

from a ﬁnancial planner. The model that we develop in this paper allows a ﬁnancial planner

to easily apply the information when advising their clients. The ﬁnancial planner can

compute an accurate breakeven period, NPV, and IRR of reﬁnancing. The lost tax beneﬁt of

reﬁnancing at a lower interest rate is also incorporated in the model. The Excel spreadsheet

allows the ﬁnancial planner to customize the variables (including mortgage interest rate, tax

rate, mortgage term, and closing costs) for their client’s speciﬁc situation. If the ﬁnancial

planner wishes to quote rules of thumb, he or she can indicate that a one-percentage decrease

in mortgage rates will result in a one to two year break-even. The reason for considering the

lost interest deduction is that breakevens are about 35% to 40% longer when these deductions

are incorporated. In addition, longer term mortgages break even much faster when consid-

ering the lost interest deduction because the interest savings is greater. In conclusion,

ﬁnancial planners need to stop using rules of thumb and take the time to compute the actual

beneﬁts to their client. Our model easily allows this to be accomplished.

Acknowledgment

The authors thank Bruce Bagamery at Central Washington University for his helpful

comments and suggestions at the 2006 Academy of Financial Services Annual meeting.

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