The development of real estate in the form of a project is becoming increasingly competitive. I notice that almost daily with the implementation of our package for real estate developers Invantive Estate. It is important to properly compare projects including their contribution to the result. For example on the basis of net present value. In this way you can select the projects which promise the best results.

This blog lists some relevant basic concepts of financial mathematics. These basic concepts are useful for real estate developers, especially in the more complex projects because they help to determine if a development project meets the return requirements of the organization. The explanation is based on material from Scalar. With Scalar I have personally learned the fine art of real estate calculating. I hereby want to thank them for making this material available. Scalar regularly organizes courses which further elaborate on calculations on real estate projects. Topics such as 'residual land value' and 'financial gap 'are also discussed there.

Cash flow prognoses and turnover prognoses can be calculated on a large scale with just a few clicks of the mouse in Invantive Estate, on the basis fo the current prognosis end of work. A statistical study gives even further insight into the likelihood that the final result will be quite different from the forecast results, for example on the basis of Monte Carlo simulations. In this blog I will not address these kinds of valuation models. Such statistical research can be done with Monte Carlo simulations after you have used Microsoft Excel and Invantive Control to set up a mathematical model and filled it out for a project area.

Let us assume you would put € 100,- in a savings account at an interest rate of 10% per year. € 10, - of interest will be credited to your account by the bank after 1 year. So after 1 year you can withdraw € 110,-. In the figure below, this is displayed graphically.

This graphical representation is called a cash flow diagram in financial accountancy. Each arrow represents a cash flow that flows in or out of your account. Note that this concerns actual cash flows in comparison to book values, for example, which are not cash flows. Arrows pointing down represent cash flows that are going out, while arrows facing up represent cash flows going in.

The € 110,- that flows into your account after 1 year is called future value. It is said: the future value of € 100,- with an annual interest of 10% is € 110,- after 1 year. The following figure is a more general view of the previous figure.

Here C stands for the cash flow, r for the interest rate, t for the time period between the two cash flows and EW for the future value.

Imagine that you do not withdraw the € 110,- after 1 year, but rather leave it alone for another year. The bank will then add another 10% after that year over the amount of € 110,-. This would be € 11,- and is added to the € 110,-. You would then be able to withdraw € 121,- after 2 years. In other words: the future value of € 100,- with an annual interest of 10% is € 121,- after 2 years. See the figure below.

The formula to calculate this future value:

EW = 100 * (1 + 0,1) * (1 + 0,1) = 100 * (1 + 0,1)2 = 121

Or more generally:

EW = C * ( 1 + r )t

Here EW stands for the future value, C for the cash flow, r for the annual interest rate and t for the time period between the two cash flows. The rate is expressed as Hancock (=percentage divided by 100).

A concept that you may encounter is the net future value. That is the difference between the future values of all cash flows that come in and out of your account. You subtract the positive future values with the negative future values.

Imagine that you know that you will need to spend € 121,- in 2 years. What amount would you need to put on the bank to cover for this expenditure when the bank compensates you an annual 10% of interest?

It would not surprise you that you would need to put € 100,- on the bank to cover for this expenditure. It is said: the present value of a cash flow of € 121,- in 2 years with an interest rate of 10% is € 100,-.

Here C stands for the cash flow, r for the interest rate, t for the time period between the two cash flows and EW for the future value.

The formula to calculate this present value:

121 / (1 + 0,1) 121

CW = Division line = Division line = 100

(1 + 0,1) (1 + 0,1)2

Or generally:

CW = C / (1 + r)t

Here CW stands for the present value, C for the cash flow, r for the annual interest rate and t for the time period between the two cash flows. The rate is expressed as Hancock (=percentage divided by 100).

A concept that you may also encounter is the net present value. This is nothing more than the difference between the present values of all the cash flows that come in and out of your account. You subtract the positive present values with the negative present values.

The concept (net) present value is a very important concept which you will run into often. Cash flows that occur at different moments in time can be converted into 1 moment in time and subsequently added together. This allows for the possibility to judge whether long term revenue can balance out the costs of today. An example: You are contemplating to replace the boiler in your home by a more energy efficient boiler and you want to know if this is a good decision. You can then turn each of all the annual savings into present values. All these present values can then be added together. When the sum of all these present values is higher than the costs of the new boiler the investment would be accounted for.

What if your friend would ask you to lend him € 100,- and he would promise to pay you back € 121,- in 2 years. You also know that your bank pays an annual 5% interest reimbursement. What do you choose to do: put the money on the bank or lend it to your friend?

Because the numbers are the same as in the example task you know that your € 100,- will annually grow 10% if your friend pays you € 121,- back after 2 years. This is better than the interest reimbursement of 5% from the bank, so you would do better to borrow the money to your friend, provided he is as reliable as the bank. The 10% is called the internal rate of return. Because the calculations of internal yield in strongly variable cash flows is not reliable there is usually a return requirement included in the real estate calculations. The requirement indicates that the yield of the real estate object has to be at least equal to the yield of an alternative investment like that of a state loan. Whenever the real estate object fails to reach this yield it is no longer interesting as an investment to the investor. Because of the risk involved in an investment in real estate it is common that the return requirement is higher than that of a risk free investment like a state loan.

Whenever cash flows do not occur all at once on 1 point in time you also need to pay attention to cost and revenue increases. Imagine you would want to buy something in 2 years that is now priced at € 114,-. When you account for an annual increase in price of 3% you can calculate how much this would cost you in 2 years. This value is called the indexed value. The general cost increase is usually indicated with the term inflation. The cost and revenue increases can differ for each cash flow type. Build costs could rise with 4% per year for example, while rental income might increase with 3%. Indexed values can also be indicated as nominal values because these represent the actual amount that flow in or out of your account.

Here C stands for the cash flow, s for the increase, t for the time period between two cash flows and IW for the indexed value.

The formula to calculate this indexed value:

IW = 114 * (1 + 0,03) * (1 + 0,03) = 114 * (1 + 0,03)2 = 121

In general terms:

IW = C * (1 + s)t

Here IW stands for the indexed value, C for the cash flow, s for the annual increase and t for the time period between the two cash flows.

The increase is expressed as Hancock (=percentage divided by 100).

The term price level is used to indicate whether a cost or revenue item applies at a certain moment or point in time. When you ask for a construction budget for a building this will always have a price level. This means that the price is valid for that date. If you realize the building on another point in time then you will also have to adjust the price according to the increase in price (=indexing).

Imagine you know that you have to purchase something in 2 years that costs € 114,- at this moment (current price level or t=0). What amount would you need to put on the bank to cover for this expense when the bank compensated you an annual 10% of interest and you expect an annual price increase of 3%?

In this case you need to index the purchase price to the year in which the purchase is taking place since there is a price increase twice:

IW = 114 * (1 + 0,03)2 = 121

This amount will be made in cash:

CW = 121 / (1 + 0,1)2 = 100

You would need to put € 100,- in the bank to be able to do this purchase.

The interest that you would normally receive on your savings account is partly a refund for delayed consumption, but it is also partly a refund for the inflation (or currency devaluation). Imagine that all the prices rise annually with 3% and your income rises annually 3% as well. In essence your purchasing power remains equal since you will use that 3% extra income to pay for purchases that cost 3% more. When you include the inflation in your calculation you are calculating nominally. You then index amounts (where necessary) with the inflation and use the nominal interest (interest including inflation) to calculate the present values and future values. You can also exclude the inflation. In that case you would calculate realistic. You would therefore need to use the realistic interest (interest excluding inflation) to calculate the present values and final values. In this blog calculations are done nominally.

At time t=3 there is a cash flow of € 3.000,- (price level t=1) and on time t=8 there is a cash flow of € -6.000,- (price level t=1).

What is the total present value and the total future value of both cash flows? Assume a nominal interest of 8% and a yearly cost increase (inflation) of 3%.

It is a good habit to always draw the cash flow diagram:

This example for calculating the cash flows has been developed in 2 ways:

•Algebraic calculations on cash flows

•Calculating the cash flows with a Microsoft Excel spreadsheet.

The cash flow of € 3.000,- has a price level t=1 but takes place on t=3. This amount first has to be indexed for 2 years with a 3% increase per year. For this we use the general formula for the calculation of the indexed value:

IW = C * (1 + s)t

When the data is entered into this formula:

IW = 3.000 * (1 + 0,03)2 = 31.83

Subsequently you calculate the present value. Calculated with the general formula for determining the present value:

CW = C / (1 + r)t

Entered into the formula:

CW = 3.183 / (1 + 0,08)3 = 2.527

For the calculation of the present value of the cash flow of € -6.000,- the formulas for indexing and getting the present value are combined into 1 formula:

CW = -6.000 * (1 + 0,03)7 / (1 + 0,08)8 = -3.987

Both present values can be added together:

NCW = 2.527 - 3.987 = -1.460

The net present value would be € -1.460.

For the calculation of the future value the amount of € 3.000,- needs to be indexed first as well.

IW = 3.000 * (1 + 0,03)2 = 3.183

Subsequently the future value is calculated according to the general formula for determining the future value:

EW = C * (1 + r)t

Entered into the formula:

EW = 3.183 * (1 + 0,08)5 = 4.676

The cash flow of € -6.000,- takes place on t=8 and this is the same moment the future value is determined. This means that the future value of this cash flow is equal to the indexed value (this is also the case for the present value of a cash flow on t=0):

EW = -6.000 * (1 + 0,03)7 = -7.379

Both of the future values can be added together:

NEW = 4.676 - 7.379 = -2.703

The net future value would be € -2.703,-.

In the picture below you can see how the detailed version with the aid of a spreadsheet program would look like. It is smart to enter all unique data in unique cells. Subsequently you indicate to these unique cells in the calculations. In the example this can be seen in the list of data. The most important formulas in this spreadsheet are all treated one by one below.

Cell |
Formula |
Explanation |
---|---|---|

B13 |
=C4*(1+C7/100)^2 |
In this cell the cash flow of € 3.000,- is indexed. Because this amount has the price level t=1 the amount is indexed with 3% per year for 2 years. |

C18 |
=C5*(1+C7/100)^7 |
In this cell the cash flow of € -6.000,- is indexed. Because this amount has the price level t=1 the amount is indexed with 3% per year for 7 years. |

D10 |
=SUM(B10:C10) |
In this cell the year balance is calculated. This formula is copied up to and including cell D18. |

E10 |
=D10/(1+$C$6/100)^A10 |
In this cell the year balance is made into a present value. The required interest is used and the result is dependent on the year in which the cash flow is taking place. The reference to the interest is made absolute by the dollar signs. This formula is copied up to and including cell E18. |

E19 |
=SUM(E10:E18) |
This cell displays the net present value. |

F10 |
=D10*(1+$C$6/100)^(8-A10) |
In this cell the future value of the year balance is calculated. The required interest is used and the result is dependent on the year in which the cash flow is taking place. The year of the cash flow is subtracted off the time of the last cash flow (t=8). This formula is copied up to and including cell F18. |

F19 |
=SUM(F10:F18) |
This cell displayed the net future value. |

I hope that with this short introduction into financial arithmetic you will be able to better appreciate the merits your projects. Any questions? Leave a comment below, and we will answer your questions.