How The Numbers Work
By Robert Prouty and Darrell Roberts
In previous articles, we have discussed Cap Rate, Loan-to-Value (LTV), Debt Service Coverage Ratio (DSCR), Cash-on-Cash Return, Internal Rate of Return (IRR) and the Loan Constant. For any potential investor seeking to buy income-producing apartment property it is critical to understand how all of these factors are related and interact.
The cap rate is the main driver of any purchase price. Consider three different hypothetical properties: Property A, Property B and Property C. All three properties have the same net operating income (NOI) of $1,000,000.
Property A is a newer property located in an urban, in-fill location with high barriers to entry such as Los Angeles, CA. To enter this market an investor must pay a 5.00% cap rate (these cap rates are being used for illustrative purposes only).
Property B is located in a low barrier to entry market such as Dallas, TX. The property is located in a decent neighborhood and has had a stable operating history. To purchase this property an investor must pay a 7.00% cap rate.
Property C is also located in a low barrier to entry market such as Charlotte, NC. Unfortunately, the property is located in a challenging neighborhood. It has deferred maintenance and is subject to high vacancy and concession (free rent) levels. Its operations have been difficult and the cash flow is “not” stable. To purchase this property an investor will want a 9.00% cap rate.
The corresponding purchase prices based upon those cap rates are:
|
|
Property A
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Property B
|
Property C
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|
|
|
|
|
|
NOI
|
$1,000,000
|
$1,000,000
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$1,000,000
|
|
Cap Rate
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5.00%
|
7.00%
|
9.00%
|
|
Purchase Price
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$20,000,000
|
$14,285,714
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$11,111,111
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Three properties with the same NOI but yet three different purchase prices because of three different cap rates. As can be seen, the lower the cap rate the higher the purchase price and the higher the cap rate the lower the purchase price. One of the challenges an investor faces is to understand what cap rate is appropriate not only for a particular market but also for a particular property and its overall physical condition and operating performance levels
Unless an investor has the financial wherewithal to purchase a property for all-cash, she will need to apply for a loan. Loan parameters vary by lender but for this scenario we will assume the lender has a maximum loan-to-value (LTV) requirement of 80%. With the purchase prices outlined above, the maximum LTV loans are the following:
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Property A
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Property B
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Property C
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|
|
|
|
|
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Purchase Price
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$20,000,000
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$14,285,714
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$11,111,111
|
|
Maximum LTV
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80%
|
80%
|
80%
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|
Max LTV Loan
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$16,000,000
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$11,428,571
|
$8,888,889
|
There is one other loan constraint that must be considered and that is the debt service coverage ratio (DSCR). In this scenario, assume the bank also has a minimum DSCR of 1.25:1. The bank is willing to lend this money at 6.00% for 30 years. To calculate the possible mortgage under this constraint we must calculate the loan constant.
Loan Constant = [.06 / 12] / (1 – (1 / (1 + (.06 / 12]) ^ 360))
Loan constant = .07195 (rounded) or 7.195%
The NOI for each property is $1,000,000 and the minimum DSCR is 1.25:1. Knowing that a 1.25x DSCR means the NOI must be 125% greater than the debt service for the loan we can solve for the minimum annual debt service.
Net Operating Income = Annual Debt Service
DSCR
$1,000,000 = $800,000
1.25x
Therefore, $800,000 is the minimum annual debt service payment for each property. Using that we can figure our minimum DSCR loan by using the loan constant:
$800,000 = $11,118,832
.07195
Based upon the three properties NOI, we can summarize the debt service coverage loans:
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|
Property A
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Property B
|
Property C
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|
|
|
|
|
|
NOI
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$1,000,000
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$1,000,000
|
$1,000,000
|
|
Minimum DSCR
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1.25x
|
1.25x
|
1.25x
|
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Interest Rate
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6.00%
|
6.00%
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6.00%
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Amortization
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30 years
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30 years
|
30 years
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Constant
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0.07195
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0.07195
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0.07195
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Min DSCR Loan
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$11,118,833
|
$11,118,833
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$11,118,833
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Remember, the loan has two constraints. A maximum LTV and a minimum DSCR – whichever is less! As the chart below shows, Property A and Property B are constrained by the DSCR whereas Property C is LTV constrained.
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Property A
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Property B
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Property C
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|
|
|
|
|
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Max LTV Loan
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$16,000,000
|
$11,428,571
|
$8,888,889
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|
Min DSCR Loan
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$11,118,833
|
$11,118,833
|
$11,118,833
|
Obviously, these loan constraints have a large impact on the amount of equity necessary to purchase each property. In this example, the equity requirement is the highest for Property A and the lowest for Property C.
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Property A
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Property B
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Property C
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|
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Purchase Price
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$20,000,000
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$14,285,714
|
$11,111,111
|
|
Loan Amount
|
$11,118,833
|
$11,118,833
|
$8,888,889
|
|
Loan-to-purchase price
|
55.6%
|
77.8%
|
80%
|
|
Equity Requirement
|
$8,881,167
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$3,166,882
|
$2,222,222
|
The greater the equity requirement the lower the cash-on-cash returns and vice versa. Since Property A has the highest equity requirement it will also have the lowest cash-on-cash return. Consequently, Property C with the lowest equity requirement will have the highest cash-on-cash return. It should be noted that Property C is LTV constrained which means an investor must use the loan constant to calculate the annual debt service of the LTV constrained loan amount:
$8,888,889 x .07195 = $639,556
Knowing the correct annual debt services and the equity requirements for each property we can show the possible cash-on-cash returns an investor could expect.
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Property A
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Property B
|
Property C
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|
|
|
|
|
|
Loan
|
$11,118,833
|
$11,118,833
|
$8,888,889
|
|
Equity Requirement
|
$8,881,167
|
$3,166,882
|
$2,222,222
|
|
NOI
|
1,000,000
|
1,000,000
|
1,000,000
|
|
Annual Debt Service
|
$800,000
|
$800,000
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$639,556
|
|
Net Cash Flow
|
$200,000
|
$200,000
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$360,444
|
|
Cash-on-Cash
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2.25%
|
6.32%
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16.22%
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Property C illustrates what happens when a property is purchased at a cap rate above the borrower’s cost of capital. The cap rate was 9% whereas the loan constant was 7.195%. When this occurs the loan becomes LTV constrained versus DSCR constrained and thus increases the net cash flow for the investor and dramatically increasing the yield or cash-on-cash return.
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Both the iProfit Analyzer™ and the Apartment Acquisition Model™ easily calculates this information for you. An investor can modify all of the assumptions to determine when a transaction deserves better scrutiny or if the investor should walk away from a bad deal. |
Of course, this is not how the real world actually works. While a seller or a certain market may have come to expect a certain cap rate, a buyer’s cap rate should be determined by their investment requirements “not” dictated by the market. To better illustrate this, we will work backwards. Let’s have some fun!
Supposed Borrower A has $2,000,000 in equity to invest. He has several options for his money. First, he could invest in a savings account or certificate of deposit and earn 1% - 3% interest. His money would only be insured up to $250,000 by the FDIC. A second option would be to invest in US Treasury bills since they are AAA-rated (the lowest chance of default) which could yield 3% - 5%. Third, he could invest in the stock market and be exposed to volatility. Fourth, he could hire an investment adviser and look at alternative forms of investments which may have a high yield but also carry high risk.
Instead, Borrower A has decided he wants to purchase an income-producing apartment building as long as he can receive a 12% pre-tax cash-on-cash return ($240,000 net cash flow per year). From the properties listed above, the borrower may only pursue Property C assuming he can find the additional equity ($222,222) to purchase the property.
The best way to start is to know the likely loan parameters.
- Is the loan an 80% LTV or a 60% LTV?
- 1.25x DSCR or a 1.35x DSCR?
- Is the interest rate 6.50% or 5.75% amortized over 30 years with no interest only available?
Since each property will have a different NOI, the only thing Borrower A can decide is his price range based upon his $2,000,000.
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Maximum LTV
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80%
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60%
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Percent Equity Required
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20%
|
40%
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Equity
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$2,000,000
|
$2,000,000
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Max Purchase Price
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$10,000,000
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$5,000,000
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Based upon the borrower’s anticipated equity investment he is looking for a purchase price in the $5 million to $10 million range. Next, we calculate the anticipated loans and the loan constants.
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Max Purchase Price
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$10,000,000
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$5,000,000
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Less Equity
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($2,000,000)
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($2,000,000)
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Anticipated Loan
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$8,000,000
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$3,000,000
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6.50% Loan Constant = [.065 / 12] / (1 – (1 / (1 + (.065 / 12]) ^ 360))
6.50% Loan constant = .07585 (rounded)
5.75% Loan Constant = [.0575 / 12] / (1 – (1 / (1 + (.0575 / 12]) ^ 360))
5.75% Loan constant = .07003 (rounded)
With this we can calculate the required annual debt service and on the loans:
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LTV Loan
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$8,000,000
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$3,000,000
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Constant
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0.07585
|
0.07003
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Annual Debt Service
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$606,785
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$210,086
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Since Borrower A requires a 12% cash return on his equity, we can add the $240,000 to the annual debt service to determine the “necessary” NOI and debt service coverage ratio.
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Annual Debt Service
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$606,785
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$210,086
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Return
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$240,000
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$240,000
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NOI
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$846,785
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$450,086
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DSCR
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1.40x
|
2.14x
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Notice that the DSCR in both scenarios is significantly higher than the required 1.25x or 1.35x DSCR. Borrower A is looking for a property where the loan will be value constrained and not DSCR constrained in order to hit his required return (assuming there is no interest only period available). Based upon the maximum purchase prices and the required NOI, Borrower A is looking at the following cap rates:
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NOI
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$846,785
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$450,086
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Purchase Price
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$10,000,000
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$5,000,000
|
|
Implied Cap Rate
|
8.50%
|
9.00%
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Borrower A now knows that for his 12% return he is looking for properties in the 8.50% - 9.00% cap rate range (or higher) with a maximum purchase price of $10,000,000. He can then quickly size a transaction to estimate the NOI to see if it is worth his time to pursue further or walk away.
Notice, during both examples, there was no IRR calculation example. As we have written before, IRR is entirely dependent upon the borrower’s assumptions and is heavily weighted to the sale of the property when the initial investment is returned. Consider four scenarios if Borrower A purchases the $10,000,000 property with his $2,000,000 investment.
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$1 million Gain on Original Equity
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||
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Year
|
Return
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Cash-on-Cash
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|
Investment
|
($2,000,000)
|
|
|
1
|
$240,000
|
12%
|
|
2
|
$240,000
|
12%
|
|
3
|
$240,000
|
12%
|
|
4
|
$240,000
|
12%
|
|
5
|
$240,000
|
12%
|
|
6
|
$240,000
|
12%
|
|
7
|
$240,000
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12%
|
|
8
|
$240,000
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12%
|
|
9
|
$240,000
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12%
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|
10 - Sale
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$3,000,000
|
150%
|
|
IRR = 14%
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||
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Return of Equity Multiple = 1.58x
|
||
In the above scenario, the Borrower receives his 12% annual cash-on-cash return and sells the property in Year 10 that returns his original $2,000,000 equity plus an additional $1,000,000. Total IRR is 14% for the hold period. The Return of Equity Multiple is 1.58x, which means the investor was repaid his initial $2,000,000 investment plus 1.58x times his investment or $3,160,000.
|
Return of Original Equity
|
||
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Year
|
Return
|
Cash-on-Cash
|
|
Investment
|
($2,000,000)
|
|
|
1
|
$240,000
|
12%
|
|
2
|
$240,000
|
12%
|
|
3
|
$240,000
|
12%
|
|
4
|
$240,000
|
12%
|
|
5
|
$240,000
|
12%
|
|
6
|
$240,000
|
12%
|
|
7
|
$240,000
|
12%
|
|
8
|
$240,000
|
12%
|
|
9
|
$240,000
|
12%
|
|
10 - Sale
|
$2,000,000
|
100%
|
|
IRR = 11%
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||
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Return of Equity Multiple = 1.08x
|
||
What happens if the Borrower sells his property for just enough to return his original equity investment? His IRR drops to 11% and the Return of Equity Multiple drops to 1.08x as indicated in the chart above.
|
$1 million Loss on Original Equity
|
||
|
Year
|
Return
|
Cash-on-Cash
|
|
Investment
|
($2,000,000)
|
|
|
1
|
$240,000
|
12%
|
|
2
|
$240,000
|
12%
|
|
3
|
$240,000
|
12%
|
|
4
|
$240,000
|
12%
|
|
5
|
$240,000
|
12%
|
|
6
|
$240,000
|
12%
|
|
7
|
$240,000
|
12%
|
|
8
|
$240,000
|
12%
|
|
9
|
$240,000
|
12%
|
|
10 - Sale
|
$1,000,000
|
50%
|
|
IRR = 8%
|
||
|
Return of Equity Multiple = 0.58x
|
||
Here the Borrower still received his 12% cash-on-cash return but when he sold the property he received only 50% of his original investment. This loss translates into an IRR of only 8% and a Return of Equity Multiple of 0.58x.
|
Loss of Original Equity
|
||
|
Year
|
Return
|
Cash-on-Cash
|
|
Investment
|
($2,000,000)
|
|
|
1
|
$240,000
|
12%
|
|
2
|
$240,000
|
12%
|
|
3
|
$240,000
|
12%
|
|
4
|
$240,000
|
12%
|
|
5
|
$240,000
|
12%
|
|
6
|
$240,000
|
12%
|
|
7
|
$240,000
|
12%
|
|
8
|
$240,000
|
12%
|
|
9
|
$240,000
|
12%
|
|
10 - Sale
|
$0
|
0%
|
|
IRR = 2%
|
||
|
Return of Equity Multiple = 0.08x
|
||
Finally, in this example, the Borrower sold the property but was unable to receive any proceeds from the sale thus wiping out his equity. While he received a 12% cash-on-cash return his IRR and Return of Equity Multiple for the property was only 2% and 0.08x, respectively. If he had known this was a potential outcome he would have been better off with a savings account. The only worse scenario would be if the Borrower had to pay the seller additional money to purchase the property. In that case, the IRR would have been negative.
What any potential investor should realize is that a cap rate is a function of your equity requirements and the debt parameters for the property, not what a sales broker states. If a buyer cannot see how the property will provide the necessary return, the buyer should walk away and look at another property.
The debt parameters have a direct impact on the amount a borrower can purchase and his potential equity returns. While these parameters can change from lender to lender and from market to market, a buyer should have a basis for his assumptions when sizing a transaction.
Lastly, the IRR calculation can easily be manipulated. Proper due diligence at the beginning of a transaction is necessary to fully understand the operation of the property and the underlying market and submarket. It may be impossible to accurately predict cash flows in Year 9, but that does not mean a buyer should not have a reasonable basis for his assumptions rather than an input to solve for a certain return.
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If you would like further information on how all of these concepts are important when looking at purchasing property, please contact us at www.ApartmentAnalyticsSoftware.com. |
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