San Francisco Real Estate: “The Scoop”

Present Value, Future Value, and the Discount Rate

Definitions: 

Present Value (PV): Present Value is the amount that someone is willing to pay today in order to receive an anticipated cash flow in future years.   

Future Value (FV): Future Value is the value of an asset or cash at a specified date in the future that is equivalent in value to a specified sum today. 

Discount Rate: A Discount Rate is an interest rate used to determine what the right to collect future cash flows is worth today. In other words, it is the interest rate used to convert Future Value to Present Value. This rate is calculated by adding a risk-premium to the risk-free opportunity cost, which is the current yield on US government bonds. That risk-premium depends on the property’s unique characteristics.  

 In technical terms, a guideline rate for discounting an asset’s cash flow is the weighted average of the costs of debt and equity capital, also known as the weighted average cost of capital (WACC). For example, if a company’s cost of debt is 6% and its estimated cost of equity is 12%, and it plans to raise capital 80% by debt and 20% by way of equity, it computes the cost of capital at 7.2% as shown in the chart below. 

Sample Case: Calculating PV and FV Assume we have $200,000 to invest today, October 31st, 2007, at an interest rate of 6%: 

If you start with $200,000 in the bank on October 31st, 2007, and earn an interest rate of 6%, by the end of year 1, you will have $212,000.  By the end of year 2, you would have $224,720, and so on until the end of year 5, when you will have a balance of $267,645.  The $200,000 is your Present Value and the $267,645 is your Future Value.   

Alternatively, if an individual told you he could pay you $267,645 on December 31, 2010, what is the value of that money today?  If we agreed that current alternative investments could yield 6% per year over that time frame, we just work backwards to see that the value of $267,645 five years from now is equal to $200,000 today. In this case, the 6% is referred to as your discount rate.  The 6% an “interest rate” when it is used to calculate the future value of current interest bearing investment; but the same number is called a “discount rate” if it is used to calculate the present value of a future amount.  

Calculator: PV and FV on your HP 12c 

The following are the keystrokes to determine Present Value and Future Value using an HP12c Calculator:

HP12c Calculation:To determine Future Value:Enter:   $200,000 PV ($200,000 is your Present Value)            6 i (6% is your interest rate)            5 n (your investment is for 5 years)            FV (you now want to calculate Future Value) 

            Answer: 267,645 

HP12c Calculation:To determine Present ValueEnter:   $267,645 FV ($267,645 is your Future Value)            6 i (6% is your discount rate)            5 n (your investment is for 5 years)            PV (you now want to calculate Present Value) 

            Answer: 200,000

Net Present Value

 How an agent can use Net Present Value:   

Net Present Value {“NPV”) is a simple calculation for determining whether or not to invest. It compares the discounted present value of future cash flows with the price of the investment. It that present value is more than the price of the investment, it should be accepted. Otherwise, it should theoretically be rejected. 

NPV = PV – Equity Investment Sample Case: Calculating Net Present Value 

1. Calculate the expected cash flows over time that will be generated from the investment2. Determine the Present Value of the Cash Flows using a Discount Rate3. Subtract the initial investment 

Assume you invest $100,000 today in a property that yields $10,000 per year for the next five years. Assume you plan to sell the property for $125,000 at the end of year 5.  Let’s start by determining the PV of each year’s cash flow.  For year 1, the PV of $10,000 using a 7.2% discount rate is $9,328.  Using your calculator, you can derive this number by using $10,000 as FV, 7.2% as the interest rate (i), 1 as the n, and solve for PV.  Repeat this for years 2, 3, 4, and 5 where the only factor changing is the n and you will derive the $8,702, $8,117, etc.  Note that we sell the asset in year 5, so we will be deriving the PV for $135,000, which is the $10,000 in cash flow plus the $125,000 proceeds from the sale. 

The PV of this investment is $129,078, which is simply equal to the sum of the PV for each year’s cash flow. The NPV is simply the PV of the investment minus the initial investment, or $29,078.  Since this example shows a positive NPV, the project should be undertaken.  

Calculator: Calculating NPV on your HP 12c 

The following are the keystrokes to determine the Net Present Value on your HP12c.  Entries are based on the sample case above:  the “f” and “g” keys are the yellow and blue keys on the 12C that allow you to access the Cash Flow and NPV tool.

HP12c Calculation:To determine Net Present Value:Enter:   $100,000 CHS g Cfo ($100,000 is your initial equity investment (CF0) and CHS changes the sign to negative)            $10,000 g  CFj (10,000 is your Cash Flow in Year 1)$10,000 g  CFj (10,000 is your Cash Flow in Year 2)$10,000 g  CFj (10,000 is your Cash Flow in Year 3)$10,000 g  CFj (10,000 is your Cash Flow in Year 4)$135,000 g CFj ($135,000 is your Cash Flow in Year 5)5 n (your investment is for 5 years)7.2 I (7.2% is your interest rate)            f  NPV (you now want to calculate NPV) 

            Answer: 29,078 

Internal Rate of Return (IRR) 

How an agent can use Internal Rate of Return:   

Many people find the percentages of an Internal Rate of Return (“IRR”) easier to understand than the NPV. The IRR is the discounted value of the cash flows that the investor can expect, expressed as a percentage.  

It is calculated by setting the NPV to zero and calculating the discount rate. It shows the discount rate below which an investment results in a positive NPV (and should be made) and above which an investment results in a negative NPV (and should be avoided). In other words, it is the break-even discount rate, the rate at which the value of cash outflows equals the value of cash inflows. 

Another benefit from IRR is that it can be calculated without having to estimate the cost of capital.  When IRR is used, the usual approach is to select the projects where IRR exceeds the cost of capital (often called hurdle rate when used in the IRR context).  

Sample Case: Calculating Internal Rate of Return 

Using the example of NPV, we can see how IRR and NPV are related: 

Previously, we calculated an NPV of $29,078 for this investment. We decided to accept the investment because the NPV was positive; implying that our actual yield was higher than our required discount rate.  That actual yield is also known as the IRR, and we were correct – the actual yield, or IRR, is 13.80%. 

Accordingly, if we substitute the 13.8% rate as our discount rate, instead of the 7.2% rate, we will achieve a net present value of $0.  

Calculator: Calculating IRR on your HP 12c 

The following are the keystrokes to determine the IRR on your HP12c.  Entries are based on the sample case above:  the “f” and “g” keys are the yellow and blue keys on the 12C that allow you to access the Cash Flow and IRR tool.

HP12c Calculation:To determine Internal Rate of Return:Enter:   $100,000 CHS g Cfo ($100,000 is your initial equity investment (CF0) and CHS changes the sign to negative)            $10,000 g  CFj (10,000 is your Cash Flow in Year 1)$10,000 g  CFj (10,000 is your Cash Flow in Year 2)$10,000 g  CFj (10,000 is your Cash Flow in Year 3)$10,000 g  CFj (10,000 is your Cash Flow in Year 4)$135,000 g CFj ($135,000 is your Chas Flow in Year 5)5 n (your investment is for 5 years)            f  IRR (you now want to solve for IRR) 

            Answer: 13.80%