# Mathematics of Financial Leverage

The mathematics of financial leveraging has always been very seductive to Real Estate Investors. This is more so at the time when markets soar. **With leveraging, one uses other people’s money to enhance his own profits by acquiring additional interests in real estate**. This enhancement process takes the form either of added equity, which is realized at the time the real estate asset is sold, or as additional cash-flow, as in the case of rental properties. Either way, mathematics of financial leveraging makes a compelling case for borrowing against home equity to invest.

**There are risks in leveraging that must be understood by an uninitiated investor**. For one thing, while leverage allows greater potential return to the investor than otherwise would have been available, the potential for loss is greater because if the investment loses value not only is a portion of that money lost, but the loan still needs to be repaid in its entirety.

It is therefore important to **understand the mathematics behind financial leveraging** to avoid making mistakes.

How much worth of real estate you can buy with $100,000? Clearly you can buy $100,000 worth of property in a cash deal. You can also buy property worth $200,000 by borrowing 50% of the purchase price. If you are more innovative you can buy $400,000 worth of property by taking out a 25% mortgage or better still you can buy $1,000,000 worth of property by taking out a 90% mortgage. This is interesting mathematics.

Let us say you buy a house of $100,000 in a cash deal with no borrowing. Let us assume that your tenant is paying $8000 in rent. The operating expenses that include the rates and maintenance cost come to $3000. You are now left with left with $6000 as cash flow from the rent. If your property appreciated by 10% during the year that is to $110,000. You will have a return of $16,000 ($5000 cash flow from rent + $10,000 in capital appreciation). This will mean that you will have a return of 16% on your investment of $100,000.

Now let us say that you decide to leverage your money and take out a mortgage of 90%. The bank will loan you $900,000 on your deposit of $100,000. You now have $1,000,000 and you decide to buy ten houses with each house valued at $100,000 as in the previous example. Let us assume that your rent of $80,000 from the 10 houses covers the expenses $30,000 ($3,000 X 10 houses) and the mortgage payment of $ 45,000 (5% interest only loan on $900,000). You will be left with $5000 cash flow from the rent. If your ten houses appreciate by 10% as in the last example to $1.1 million your return from your investment will be $105,000 ($5000 cash flow from rent + $100,000 in capital appreciation. This will result in a return of 105% on your initial investment of $100,000. This part of mathematics of financial leveraging that is so seductive to property investors

The after tax returns on a leveraged property will be much higher because you will be able to claim depreciation and maintenance costs on ten properties instead of one. Also the interest paid on borrowed funds of $900,000 can be claimed back to increase the tax refunds.

The above mathematics clearly shows how **you can increase your net returns dramatically by leveraging your money.**

But we should also **examine the downside mathematics of financial leveraging**. Let us say the property values went down by 10% in a year instead of going up in the previous example. In the case of a cash deal our loss will be $4000 for the year thereby giving us a negative return on investment of 4%. On the other hand we will suffer a loss of $95,000 or 95% of the value of the deposit in case of mortgage of 90%.

**The losses get amplified in case of a leveraged property. Is it advisable to risk financial leverage in buying property? The answer to that question is a simple YES.** This is because values of properties have appreciated steadily at 8% to 10% annually during the past 300 years. There are dips in the property cycle but these are far and few in between. If you have the capacity to buy and hold and manage your cash flow you will win in the end.

Please also read about mathematics behind Cash Flow Leveraging, Appreciation Leveraging, Risks involved with Leveraging and how you can contain these risks.

**Cash Flow Leveraging**

**Cash flow leveraging is about how borrowing can impact your cash flows from your rental properties**.

The first important thing to understand in cash flow leveraging is the capitalization rate. It is important to know how much the property is paying you. In its simplest form **capitalization rate is the net rental income from the property divided by the purchase price. **

Let us say you buy a property for $100,000. Let us assume gross income from this property is $14,000. Total expenses that include rates, insurance, maintenance & management come to $4,000. The net income from the property will be $10,000 ($14,000 minus $4,000). The net yield or cap rate on the property will be $10,000 (net rent) divided by $100,000 (purchase price) or 10% in this case.

**The next important thing to understand in cash flow leveraging is the cost of borrowing funds**. It is not a simple case of interest on your loans but must also into account the amortization cost and the loan period to work out the loan constant. Let us say that the cost of borrowing is 7%.

**The difference between the cost of borrowing and the return from your investment property is called the spread.** In our example above we have borrowed money at 7% and are getting a net return of 10%. In this case we have a **positive leverage** or cash flow on the property.

If the return from property was lower than the cost of borrowing we will have a **negative leverage**. A **neutral leverage** will occur when the cost of borrowing is same as return from the property.

When you are buying a property for cash flow you have to **purchase only positively leveraged property**. If you do this the cash flow leverage will work in your favor.

Investors sometimes buy negatively or neutrally leveraged property in the hope that capital appreciation from the property will overcome the short term cash flow losses on the investment. In this case you will need to support the short fall in cash flow from other sources of income. This can become very worry some if the investor loses his job or suffers losses in his business that is supporting the negatively leveraged property.

**A positively leveraged property can turn into a negative leveraged property in case of loss of rental income or if the interest rates move up at the time of re-fixing the mortgage**. It is therefore prudent for you to allow for the vacancy rates or changes in the cost of borrowing.

No one can allow for all the contingencies that may occur in the future. But if you can work out your figures accurately for the first five years then chances of things going wrong with your investment are greatly reduced. This is because rents will normally go up to provide you with additional cash flow. In addition increase in capital value of the property will give you with an extra cushion of equity.

A negatively leveraged property will move into positive territory given time and a few rent reviews along the way.

As an investor **you will keep out of trouble if you apply cash flow leverage properly and make it a habit of buying only positively leveraged properties**. This is what Robert Kiyosaki and all savvy investors do. You must always concentrate on cash flow first and capital appreciation later.

You may like to read more about Appreciation Leverage, Financial Leverage, Mathematics behind Leverage, Risks involved with Leveraging and how you can contain these risks.

**Appreciation Leverage**

**Appreciation leverage happens when you borrow money at simple interest and invest it into a compounding investment such as real estate you can create great wealth for yourself**.

**Appreciation on properties compounds** where as interest on properties (though not exactly simple interest) are normally in fixed installments. If let us say you buy a property in a place where the historical appreciation is at 7% and you borrow money also at 7% interest only mortgage you will find that at the of thirty years your property would have gained in value by at least 3 times more than the interest you would have paid. And better still your tenant would have paid that mortgage.

As a thumb rule **if your interest on your mortgage is lower than the expected appreciation rate then you will have positive appreciation leverage**.

**The best properties are those that have positive cash flow leverage and positive appreciation leverage**. Such properties are sure shot winners.

In certain high capital growth areas you will have properties that have negative cash flow leverage but positive appreciation leverage. Depending upon your situation you might like to buy such a property if you have problems of excessive cash flow and a very high taxable income.

No savvy investor will buy a property that has both negative cash flow leverage and negative appreciation leverage. But I amazed at the number of people who are coaxed into buying such properties by savvy sales people. You should try and avoid such properties as a plague.

The **ultimate leverage** is when:

Cost of Borrowing < Capitalization Rate

Interest Rate < Appreciation

You may like to read about Financial Leverage, Cash Flow Leverage, Mathematics behind Leverage and Strategies to contain Leveraging Risk

**Understanding Leverage Risk**

Using Financial Leverage is an excellent way to accelerate your financial growth. But to be a savvy investor you have to understand the leverage risk and learn to manage those risks.

**More Leverage = More Financial Risk**

**Less Leverage = Less Financial Risk**

You must not let the leverage risk scare you away from real estate investing because **risk can be measured and controlled.**

**Where there is more volatility there is more risk**. Volatility refers to more frequent deviations from the standard. To understand risk you have to understand volatility.

**Real estate has the least volatility **when compared to other investment venues. A study carried out has shown that during the past 10 years real estate was ten times less volatile when compared to stocks which tend to fluctuate wildly on a daily basis. Yet there is hue and cry and everyone freaks out when real estate prices go down by five to ten percent.

**Even a highly leveraged real state is more stable than stocks**. This will imply that real estate has less leverage risk than most other investments.

Even though real estate is very stable leveraging does increase relative risk.

**More Leverage = More Returns = More Volatility = More Fluctuations in Cash Flow = More Fluctuations in Returns = More Risk**

Let us say you buy a house at a price of $100,000 with cash down. If the price moves up by 10% in one year then you will make a profit of 10% on your investment. In this example we are not taking cash flow into account. If the price moves down by 10% then you make a loss of 10% on your investment.

In the second example let us say you had taken a mortgage of 80%. This would imply that you have made a down payment of $20,000 on the property. Now if the price moves up by 10% i.e to $110,000 then you will make a profit of $10,000 on your investment of $20,000. This will equate to a return of 50%. Similarly if the price of the property went down by 10% you will make a loss of 50% on your investment.

This example clearly shows the amplification of leverage risk by a factor of five times if the property has a leveraging ratio of 5.

What happens to the leverage risk if your property is purchased with No Money Down deal with 100% mortgage? Your profits will be infinity if the property prices moved up. Similarly your loss will be infinity if the property prices went down. But what is your risk if you have no money in the deal?

A study conducted in 1978 found that leveraged real estate is the only investment that is fully protected against inflation. This is because when there is inflation rents go up and there is capital appreciation. However mortgages remain fixed if they are for long term.

Many investors only look at the upside of financial leverage. Savvy investors try and cover the down side of leverage by taking steps to control it if things go wrong.

**Leverage Risk Containment Strategies**

You can contain the leverage risk by following the under-mentioned guidelines:

**Reduce Financial Leverage Just Before the Market Peaks**

Most novice investors start to use maximum leverage when the market is about to peak. This is the time for you to reduce your leverage risk by selling a few properties to pay off your mortgage and increase your equity on the other properties.

**Increase Financial Leverage Just After the Market Bottoms Out**

This is the time when most people have deserted the real estate market. But it is exactly during this period that leveraging offers the best capital returns in the medium to long haul. Interest rates are low, so the cost of borrowing is minimized. Financial institutions are looking for customers and it is easier to cut a better deal or get incentives from them. Sellers too are more motivated and more flexible on prices and terms of contract.

You should use the equity in your properties to buy more property. You should increase your financial leverage to the maximum because during this period you will have positive cash flow properties reducing your borrowing risk.

**Buy Quality Properties**

Always buy quality properties. A house or multi-family dwelling that is well maintained and well kept will hold up value better in the long run, and will save you money in maintenance as well. When the markets are down it will be easier for you to find quality tenants willing and relocate into a nice-looking property. Quality properties reduce your leverage risk.

**Take the profits and pay down the debt**

Greed is always dangerous in any market. This is where most people fall. Do not keep reinvesting your profits to buy more property. That is like betting all winnings on every new roll of the roulette wheel. If you follow this strategy you will lose your winnings because sooner than later markets will move downward. If you do not stand on solid foundation you will lose your profits. The best and safest strategy is not to keep borrowing against your equity. Use cash-flow to pay down the loan or to wait for prices to increase and then sell for a profit to reduce your debt.

**Shop for the lowest possible interest rate**

Even though the interest is tax deductible you still have to pay some of it out of their own pocket. It is always advisable to shop for the best deal available, using the services of a good mortgage broker. If your loans are substantial the savings could amount to several thousand dollars every year.

**Make improvements to your property to increase cash flow**

Make improvements and add value to your property to increase the rents so that you have positive cash flow leverage on the property.

**Deposit Recycling to reduce Leverage Risk**

If you buy a property with no money down you have no personal risk as long as the purchase is structured in such a way that you have no personal liability.

It is not always possible to buy a property with no money down. At times you will be required to put some of your money into the deposit. Your aim should be to take out your personal money from the investment as soon as possible. You can then use this money to buy some more property. This is known as deposit recycling.

The best way to recycle your deposit is to firstly buy the property below market value and then make improvements to increase its value and cash flow. You should then refinance the property and take out your deposit as soon as possible. Your leverage risk becomes zero once you have none of your personal money in the property.

Once you recycle your deposit to reduce your stake in the property (eliminate leverage risk) you should allow the equity to build in the property through appreciation and repayment of loan through the cash flow generated from the property. Do not get greedy and keep taking out loans against the equity in the property.

**Reduce Leverage Risk as you grow older**

You can apply more leverage when you are young because time is on your side. In case things go wrong you can re-start once again. As you near your retirement age you should reduce leverage risk. Once you are retired leverage only to the extent to reduce your taxes.

**Leverage Risk as function of your personality **

Each one of us has a different risk profile. Some of us are comfortable at taking more risk than the others. You should study your risk profile carefully and take leverage risk to the extent you are comfortable with. You will have peace of mind.

You may also like to read about Cash Flow Leverage, Appreciation Leverage, Financial Leverage and Mathematics behind Leveraging.