Mortgages Analyzed

Payback Period

# What is Payback Period?

Payback Period is the length of time it takes to recover the initial investment from the cash flows generated by the investment. Stated differently, Payback period is the length of time it takes for an investment to reach break-even point. Beyond the break-even period, the cash flows from the investment represent profits.

For example, if you invest \$10,000 and you receive \$2,000 per year, the payback period is 5 years. At the end of the five years the initial investment has been returned and the project will start generating profits.

Payback Period is often used to compare different investment options, where the investment with a shorter payback period is more desirable than investment with a longer payback period. In mortgages, the most frequent use of payback period is to determine the time it takes to recover the cost of refinance.

## Decision Rule

The basic decision rule is to accept the investment if the payback period is less than the target payback period.

Source :www.MortgagesAnalyzed.com

# Formula of Payback Period

## Uniform Cash Flow

If the investment generates uniform cash flows, payback period is calculated by dividing the initial investment by the periodic cash flows.

Payback Period =
Initial Investment Periodic Cash Flows

Or,

P =
I CF
Source :www.MortgagesAnalyzed.com

Where,

 P = Payback Period I = Initial Investment CF = Periodic Cash Flows
Source :www.MortgagesAnalyzed.com

### Illustrative Example

You invest \$10,000 for an investment and you receive \$2,500 per year, payback period is 4 years as calculated below.

 Initial Investment (I) = \$10,000 Periodic Cash Flows (CF) = \$2,500

Therefore,

Payback Period =
10,000 2,500
=  4 Years
Source :www.MortgagesAnalyzed.com

## Uneven Cash Flows

If the cash flows are irregular, payback period is calculated by first calculating the cumulative cash flows and then using the formula below.

Or,

P =   n +
|CCFn| CFn+1

Where,

 P = Payback Period n = Last period of when cumulative cash flows were negative CCFn = Absolute value of cumulative cash flows at the end of the last period where the cumulative cash flows were negative, i.e. absolute value of cumulative cash flows at the end of period n CFn+1 = Cash flows in the period where the cumulative cash flows become positive, i.e. cash flows in the period n + 1
Source :www.MortgagesAnalyzed.com

### Illustrative Example

You invest \$10,000 for an investment and receive the yearly cash flows below.

 Year Cash Flows Year 1 \$500 Year 2 \$1,000 Year 3 \$3,000 Year 4 \$3,500 Year 5 \$4,000

First we need to calculate cumulative cash flows.

 Year Cash Flows Cumulative Cash Flows Year 0(Investment) \$10,000 -\$10,000 Year 1 \$500 -\$9,500 Year 2 \$1,000 -\$8,500 Year 3 \$3,000 -\$5,500 Year 4 (n) \$4,500 -\$1,000 Year 5 \$5,000 \$4,000

In this case,

 n = 4 CCFn = |-1,000| = 1,000 CFn+1 = 5000

Therefore,

P =   4 +
1,000 5,000
=  4 + 0.2 =  4.2
Source :www.MortgagesAnalyzed.com

# Uses of Payback Period

1. Comparing Investments: Payback Period can be used to compare and rank multiple investments. All things equal, investments with a shorter payback period are less risky and more desirable compared to investments with a longer payback period.
2. Evaluating Against Target Date: If you need the investment returned by a certain time period then payback period can be used to select investments where the investment's payback period is less than the target period. For example, if you need your investment back in three years, then any investment with a payback period of less than or equal to three years would be acceptable.
Source :www.MortgagesAnalyzed.com

# Advantages of Using Payback Period

1. Widely Understood: The biggest advantage of payback period is that it is widely understood. It is the simplest method for evaluating investments. When someone says, "you will get the money back in 5 years", they are using payback period.
2. Easy to Calculate: Payback Period is easy to calculate since it does not involve complex mathematics.
Source :www.MortgagesAnalyzed.com

# Disadvantages of Using Payback Period

1. Ignores Time Value of Money: Payback Period ignores the time value of money and treats payments from different periods as equal. This weakness become relevant when the payback period is very long or during periods of high interest rates.
2. Ignore Post Break-Even Money: The calculation does not consider the cash flows after the payback period. An investment with a shorter payback period may initially seem desirable, but the investment may not be the best choice if the total cash flows from the investment are less than the total cash flows from another investment that has a longer payback period.

It is best to use Payback Period for comparing the different investment options an in conjunction with other measures for evaluating investments or loans. It should not be the only criteria when making investment decisions.

Source :www.MortgagesAnalyzed.com

# Payback Period in Mortgage Loans

## Evaluating Refinance Using Payback Period

The most frequent use of payback period is to determine the time it takes to recover the cost of refinance. Payback Period in the case of mortgage refinance is the time period it takes to recover the cost of refinance from the savings anticipated by the refinanced loan. The key decision is to ensure that the Payback Period on the refinanced loan is less than the Payback Period targeted by the borrower.

For example, assume the closing costs for a loan refinance is \$2,000 and the refinance will result in lowering the interest expense by \$250. The Payback Period for the refinance is 8 months (\$2,000/ \$250). The benefits of refinance will be achieved after the end of 8 months.

## Payback Period and Predatory Lending

Payback Period is an important indicator of predatory lending. If the loan is being refinanced multiple times where each refinance is before the payback period then the lender is most likely engaging in predatory lending. In other words, predatory lending is occurring if the loan is being refinanced successively in such a manner that the refinance costs exceed the total savings in interest expense by reducing the interest costs.

For example, assume a loan is refinanced where the monthly savings in interest is \$100 and the closing costs are \$3,000. The payback period is 30 months (3000/100) or 2 ½ years. After 2 years, the lender calls again in and urges the borrower to refinance with another loan that offers a monthly savings of \$300 from the existing loan at a cost of \$2,000. The lender will try to emphasize the \$300 monthly savings to the borrower. However, we know that the benefits of initial refinance are achieved after 2 ½ years. Performing the refinance again at the end of 2 years will mean the borrower is incurring a loss of \$600 on the initial refinance. Said differently, the true closing costs for the second refinance are \$2600, which comprises of \$2000 on the closing costs for second loan and \$600 on the unrecovered closing costs from the first refinance.

The borrower may end up becoming a victim of predatory lending if the loan is being constantly refinanced in such a manner that the benefits of refinance are never realized. Risk of predatory lending through refinances is higher in periods of declining rates.

Source :www.MortgagesAnalyzed.com

# Examples

## Example 1: Simple Refinance

A lender offers to refinance your mortgage which will reduce your interest cost by \$200 per month with closing costs of \$1,600.

With the given information, we can use the uniform cash flows formula. The initial investment is the closing costs and the cash flows are the monthly savings.

 I = \$1,600 CF = \$1,000
Payback Period =
1,600 200
=  8 months
Source :www.MortgagesAnalyzed.com

## Example 2: Refinance into a Fixed Rate Mortgage

You currently have a 30 year mortgage for a principal balance of \$100,000 at 6% that you obtained three years back. You are offered to refinance the loan into another 30 year fixed rate mortgage at 5% with a closing cost of \$1,400. Let us calculate the payback period. In case of a mortgage loan, the amortization causes unequal cash flows which means the payback period will be calculated using the unequal cash flows method.

The steps in calculating the payback period are:

1. Calculate the amortization for the old and the new loan. Remember, the new principal loan balance for the new loan will be the unpaid principal balance at the end of three years, which in this case is \$96,084.07.
2. Calculate the monthly savings based on difference in the interest cost of the two loans. The comparison starts from the date when the loan will be refinanced.
3. Calculate the cumulative savings.
4. Use the payback period formula for unequal cash flows to calculate the payback period.
Source :www.MortgagesAnalyzed.com

EXISTING LOAN NEW LOAN PAYBACK PERIOD CALCULATIONS

Period
Unpaid
Pricipal
Balance

Interest

Payment
Unpaid
Pricipal
Balance

Interest

Payment

Monthly
Savings

Cumulative
Savings

Cumulative
Cash Flows
1 96,084.07 480.42 599.55 96,084.07 400.35 515.80 80.07 80.07 -1,319.93
2 95,964.94 479.82 599.55 95,968.62 399.87 515.80 79.95 160.03 -1,239.97
3 95,845.21 479.23 599.55 95,852.69 399.39 515.80 79.84 239.86 -1,160.14
4 95,724.89 478.62 599.55 95,736.28 398.90 515.80 79.72 319.59 -1,080.41
5 95,603.96 478.02 599.55 95,619.38 398.41 515.80 79.61 399.20 -1,000.80
6 95,482.43 477.41 599.55 95,501.99 397.92 515.80 79.49 478.69 -921.31
7 95,360.29 476.80 599.55 95,384.12 397.43 515.80 79.37 558.06 -841.94
8 95,237.55 476.19 599.55 95,265.75 396.94 515.80 79.25 637.31 -762.69
9 95,114.18 475.57 599.55 95,146.89 396.45 515.80 79.12 716.43 -683.57
10 94,990.20 474.95 599.55 95,027.54 395.95 515.80 79.00 795.43 -604.57
11 94,865.60 474.33 599.55 94,907.68 395.45 515.80 78.88 874.31 -525.69
12 94,740.38 473.70 599.55 94,787.33 394.95 515.80 78.75 953.06 -446.94
13 94,614.53 473.07 599.55 94,666.48 394.44 515.80 78.63 1,031.69 -368.31
14 94,488.05 472.44 599.55 94,545.12 393.94 515.80 78.50 1,110.19 -289.81
15 94,360.94 471.80 599.55 94,423.26 393.43 515.80 78.37 1,188.57 -211.43
16 94,233.20 471.17 599.55 94,300.89 392.92 515.80 78.25 1,266.81 -133.19
17 94,104.81 470.52 599.55 94,178.01 392.41 515.80 78.11 1,344.93 -55.07
18 93,975.79 469.88 599.55 94,054.62 391.89 515.80 77.99 1,422.92 22.92
19 93,846.12 469.23 599.55 93,930.71 391.38 515.80 77.85 1,500.77 100.77
20 93,715.80 468.58 599.55 93,806.29 390.86 515.80 77.72 1,578.48 178.48
 n = 17 CCFn = |-55.07| = 55.07 CFn+1 = 77.99

Therefore,

P =   17 +
55.07 77.99
=  17 + 0.71 =  17.71 months

Payback Period is 17.71 months or approximately 17 months and 22 days. You will recover your closing costs in 17 months and 22 days. This is the time after which you will start realizing benefits of the refinanced loan.

Source :www.MortgagesAnalyzed.com

## Example 3: Refinance into an Adjustable Rate Mortgage

You currently have a 30 year fixed mortgage with an unpaid principal balance of \$100,000 at 6% that you obtained five years back. You are offered to refinance the loan into a 1 year adjustable rate mortgage at an initial rate of 5% with a closing cost of \$1,000. After 1 year the interest adjusts to 5.25%. The calculation of payback period will be similar to the previous example.

You currently have a 30 year mortgage for a principal balance of \$100,000 at 6% that you obtained five years back. You are offered to refinance the loan into a 1 year adjustable rate mortgage at 5% with a closing cost of \$1,400. After 1 year the interest adjusts to 5.25%. The calculation of payback period will be similar to the previous example, except that the amortization schedule will adjust after 1 year for the new loan.

The steps in calculating the payback period are:

1. Calculate the amortization for the old and the new loan. Remember, the new principal loan balance for the new loan will be the unpaid principal balance at the end of five years, which in this case is \$93,054.36.
2. Calculate the monthly savings based on difference in the interest cost of the two loans. The comparison starts from the date when the loan will be refinanced.
3. Calculate the cumulative savings.
4. Use the payback period formula for unequal cash flows to calculate the payback period.
Source :www.MortgagesAnalyzed.com

EXISTING LOAN NEW LOAN PAYBACK PERIOD CALCULATIONS

Period
Unpaid
Pricipal
Balance

Interest

Payment
Unpaid
Pricipal
Balance

Interest

Payment

Monthly
Savings

Cumulative
Savings

Cumulative
Cash Flows
1 93,054.36 465.27 599.55 93,054.36 387.73 499.54 77.54 77.54 -1,322.46
2 92,920.08 464.60 599.55 92,942.55 387.26 499.54 77.34 154.88 -1,245.12
3 92,785.13 463.93 599.55 92,830.28 386.79 499.54 77.14 232.02 -1,167.98
4 92,649.50 463.25 599.55 92,717.53 386.32 499.54 76.93 308.95 -1,091.05
5 92,513.20 462.57 599.55 92,604.32 385.85 499.54 76.72 385.66 -1,014.34
6 92,376.22 461.88 599.55 92,490.63 385.38 499.54 76.50 462.16 -937.84
7 92,238.55 461.19 599.55 92,376.48 384.90 499.54 76.29 538.46 -861.54
8 92,100.19 460.50 599.55 92,261.84 384.42 499.54 76.08 614.54 -785.46
9 91,961.14 459.81 599.55 92,146.73 383.94 499.54 75.87 690.40 -709.60
10 91,821.39 459.11 599.55 92,031.14 383.46 499.54 75.65 766.05 -633.95
11 91,680.95 458.40 599.55 91,915.07 382.98 499.54 75.42 841.47 -558.53
12 91,539.80 457.70 599.55 91,798.51 382.49 499.54 75.21 916.68 -483.32
13 91,397.95 456.99 599.55 91,681.47 401.11 513.51 55.88 972.56 -427.44
14 91,255.39 456.28 599.55 91,569.07 400.61 513.51 55.67 1,028.23 -371.77
15 91,112.12 455.56 599.55 91,456.17 400.12 513.51 55.44 1,083.67 -316.33
16 90,968.13 454.84 599.55 91,342.78 399.62 513.51 55.22 1,138.89 -261.11
17 90,823.42 454.12 599.55 91,228.90 399.13 513.51 54.99 1,193.88 -206.12
18 90,677.99 453.39 599.55 91,114.52 398.63 513.51 54.76 1,248.64 -151.36
19 90,531.82 452.66 599.55 90,999.63 398.12 513.51 54.54 1,303.18 -96.82
20 90,384.93 451.92 599.55 90,884.25 397.62 513.51 54.30 1,357.48 -42.52
21 90,237.31 451.19 599.55 90,768.36 397.11 513.51 54.08 1,411.56 11.56
22 90,088.94 450.44 599.55 90,651.96 396.60 513.51 53.84 1,465.40 65.40
23 89,939.84 449.70 599.55 90,535.05 396.09 513.51 53.61 1,519.01 119.01
24 89,789.99 448.95 599.55 90,417.63 395.58 513.51 53.37 1,572.38 172.38
Source :www.MortgagesAnalyzed.com

 n = 20 CCFn = |-42.52| = 42.52 CFn+1 = 54.08

Therefore,

P =   20 +
42.52 54.08
=  20 + 0.79 =  20.79 months

Payback Period is 20.79 months or approximately 20 months and 24 days. You will recover your closing costs in 20 months and 24 days. This is the time after which you will start realizing benefits of the refinanced loan.

Source :www.MortgagesAnalyzed.com

Updated: May 09, 2017

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The length of time it takes to recover initial investment from the investment's cash flows generated by the investment
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