There are four basic concepts of financial mathematics: Compound Growth, Present Value, Net Present Value (NPV) and Internal Rate of Return (IRR). Their definition was the subject of Bayfield Training’s second webinar, Introduction to Financial Mathematics, held on 20 February 2019. It was hosted by Andri Rabetanety, a senior lecturer at Glion Higher Education for MSc in Hospitality, Real Estate and Finance and financial modelling trainer at Bayfield Training who says financial mathematics is vital for decision-making.

Within corporate finance financial mathematics provides the framework for quantifying the costs and benefits of a project or investment, allowing those involved to decide whether it’s worthwhile, he explains. “If we look at a project or an investment from an economical view we are going to take the benefits – that is whatever positives are going to come out of the project be they revenue or clients or anything that is a positive – and we are going to deduct all the potential costs and see if from this calculation a margin and a profit arises,” he says. If the answer is yes then it makes sense to do the project. “When corporate finance comes into play is where we think about this project in terms of valuation and how much this project will be financially worth to me as an investor,” he says.

#### Understanding the Time Value of Money – Compounding and Discounting

As part of this, the impact of time and when benefits and costs will be received needs to be understood. This is the concept of Time Value of Money, thinking about time as a currency and summarised by the idea that £100 today is not worth the same as £100 tomorrow, explains Rabetanety. This is explained by the concept of compounding (compound growth) and discounting (present value).

#### Compound Growth

With compounding the idea is that £100 could be invested today and generate a return (interest) at a certain rate. If that money is kept in that account then the interest will also earn interest. “That’s where we define the concept of compounding – when you are going to invest and earn interest on interest and net out with more than the simple interest at each period. At the end of the investment period, I’m going to have an amount of money composed of my initial investment and the interest and that will become my future value,” he says.

#### Present Value

In the reverse concept of discounting, we look at the £100 to be received in the future and look at what value it may have today to understand the present value of investments. “To do that I need to think about an alternative world where I had this £100 available and I had the opportunity to invest that £100 at a certain rate. By receiving £100 in the future I lost the opportunity to invest this £100 right now. So if I think about the value that this money in the future will represent to me I need to reduce that value by the interest that I lost by not investing that money now. That’s why we talk about discounting the value – losing the opportunity to invest today that amount,” he says.

#### Explaining the formulas

Rabetanety used the webinar to explain the formulas in more detail and how they apply to the real estate industry before moving to the two performance indicators and decision criteria used for both.

#### Net Present Value

“Now we are equipped with the discounting formula we can use it for any type of project,” he says. “If you lay down through time all the cash flow of your project you can then discount each net cash flow to today and if you do that and then sum all expected value of all expected cash flow, positive and negative, you get your net present value (NPV) of your project,” he says. This should either be 0 or positive, the latter required to add value to the firm. “The key decision criteria is when you look at an NPV of a project the NPV needs to be positive. When it is positive it shows that the project has a positive value for the investor,” says Rabetanety.

#### Internal Rate of Return

The other performance indicator to be considered is the internal rate of return (IRR) – an annualised rate of return of your investment which can be the same or equal to the target rate for investability. “The key decision criteria is that the IRR needs to be higher than the required rate of return expected by the investor,” he says.

##### Conclusion

All four concepts are sufficient to help you build a basic annual cash flow in Excel. Most other mathematical concepts for DCF where needed are just variations in these. If you’re comfortable with these four you should have all the tools to start building and understanding financial models.

The next in the series is An Introduction to Property Valuations which take place on 20 March at 11am GMT.