Let's say you have two projects in front of you and you'd like to know if your firm should invest in these projects. How can you compare their performances? Obviously, one option is to keep your money in your savings account, GIC, bond, or stock market. Let's assume that your money is currently parked in an account earning 5%.
A basic concept in finance is that money today is worth more than the same amount of money tomorrow. This is because, if nothing else, you can invest the money in your savings bank account and earn interest on it. Or, instead of lending it to someone else to get the same amount of money next year, you can use it for your own enjoyment now. So, money today is worth more than the same amount of money tomorrow. Now, Let's say you have $1,000 and your money earns 5% annual interest sitting in an investment account. This means next year this time, you will have $1,050 in that account.
Total amount next year (FV) = Cash Amount Today (PV) + Interest on the cash (I)
FV = PV + I
FV = PV + (PV x r) = PV x (1+ r)
We say that the present value of the $1,050 is $1,000 today assuming 5% interest rate.
Net Present Value (NPV) is the sum total of all present values of future cash amounts (cash-flows) in an investment. Mathematically, we represent the above definition with the following formula:
NPV = CF1 + CF2 + ... + CFn
The money that is invested is flowing out of the account and is therefore considered a negative number. The money that is earned during the investment period is flowing in and is considered a positive number. In this very simple example, the NPV is:
NPV = -$1,000 + $1,050 = $50
NPV tells us that if the present value of all future cash-flows in a business or a project, less the amount of the investment made on that business or project, is bigger than 0, the business has made money and so that business or project is a viable business. A negative NPV means the business is losing money, so that business or project is not to be invested in.
Discount Rate
Note that in the above example, the NPV is calculated based on the interest rate of 5%. This interest rate has many names: opportunity cost, discount rate, user cost, etc. It is a number less than 100%, which means converted to a decimal, it is a number less than 1. When you are calculating the present value of a cash flow in future, you are converting the cash flow that is a bigger number back to today's value, which is a smaller number, using the interest rate number between 0 and 1, hence the number is called the discount rate. So, discount rate is the interest rate used in the NPV calculation to convert the future cashflow values to today's value. In the above example, the discount rate of 5% tells us that the value of $1,050 next year from now is equal to $1,000 today. To get the formula for the present value in our simple example, we use our formula above and solve for PV this time
FV = PV x (1 + r)
PV = FV / (1 + r)
| # |
Year 0 |
Year 1 |
| Cash-flow |
-$1,000 |
$1,050 |
| Present Value |
-$1,000 |
$1,050/( 1 + 0.05 ) = $1,000 |
| Net Present Value (NPV) = $0.00 |
So, at 5%, the NPV of the investment is $0.00! This is a special case. The interest rate that makes the NPV zero is called IRR, Internal Rate of Return. The word internal in finance means that the calculation excludes the external factors such as inflation, etc.
Now, let's say that a real estate developer comes to you and offers you the following cash flow scenario. Based on the interest rate of 5% you have if you were to invest your money in a bank account, your NPV would look like this:
| # |
Year 0 |
Year 1 |
Year 2 |
Year 3 |
Year 4 |
| Investment |
-$1,000,000 |
$80,000 |
$80,000 |
$80,000 |
$80,000 |
| Present Value |
-$1,000,000 |
$80,000/(1+0.05)^1 |
$80,000/(1+0.05)^2 |
$80,000/(1+0.05)^3 |
$1080,000/(1+0.05)^4 |
|
= -$1,000,000 |
= $76,190.48 |
= $72,562.36 |
= $69,107.00 |
= $888,518.67 |
| Net Present Value (NPV) |
$0.00 |
Based on 5% interest rate, your net present value, the value of the developer's offer makes you $106,378.51. This means you would make $106,378.51 more than what you would have made investing your money in an account with 5% interest. So, this is a great deal for you given the alternative.
In short, the positive NPV means take the deal! When NPV is 0, you should see what other factors such as unknown risks, etc. are suggesting for each investing alternative. The negative NPV means take the other deal with the yield equal to the interest rate used in your NPV calculation
So, what would the IRR be for the above sequence of payments? The formula for IRR is:
If you do the calculations, you'll see that the interest rate that makes the NPV equal to zero is 8%. So, IRR for the above sequence of payments is 8%
Problem with IRR
IRR does not take the timing of the payments into consideration, so the calculation of IRR assumes annaul interest rate. This is generally not a problem with commercial real estate modelling as we are interested in IRR as annual interest rate anyway. But, it is good to be aware of this pitfall. To overcome this, XIRR was developed to take the timing of cash flows into consideration. In a XIRR calculation, both the list of payments and list of cash flow events should be taken into consideration.
Conclusion
Both NPV and IRR are financial tools to evaluate investment opportunities. There are, to be sure, other metrics such as ROE (Return on Equity) and ROI (Return on Investment) we can use to compare differnt commercial real estate opportunities to each other. But, IRR gives us a more global metrics that can help us compare different kinds of investments to each other, say one in commercial real estate and the other in stock market or investing as an angel investor.
