Net Present Value
When valuing a business, there is a lot of confusion between the terms net present value, present value, internal rate of return, and discount rate. We will try to dispel the mystery in all this terminology starting with net present value. First let’s clarify and say that the net present value and present value of a future cash flow stream are almost the same, but not quite. What is the difference? It is the inclusion or exclusion of the initial investment.Net Present Value
Simply put, the net present value is calculated by taking the present value of a future cash flow stream and subtracting from it the initial investment.Calculating
Let’s use an investor example to illustrate this. Assume you are considering buying a bond that has a face value of $10,000, pays an 8% annual coupon, matures in 4 years, and is currently trading at $9,500 (it is therefore trading at a discount). What would be the net present value? Let’s see.The initial investment today would be $9,500
At the end of year 1 to 4, you would receive a coupon payment of $800
At the end of year 4, you would receive the principal of $10,000.
Let’s say you have a return on investment threshold of 9% meaning you invest in securities that earn you a minimum of 9% over their life. Would you take this investment on? The first thing you would do is compute the present value of this bond using 9% as your discount rate. When you do this, the present value of the coupon payments is $9,676. How do you do this? The mathematical formula would be:
PV = FV divided by (1+R)t
where R stands for rate and t stands for the term. In this case, the future value is 10,000, R is 9%, and t is 4 years. Therefore you would have PV = 10,000 divided by (1+9%) to the 4 power. This formula would yield $9,676. However, if you want to easily compute this the present value then you can just use any number of PV calculators on the internet or use a financial calculator. With a financial calculator, you would punch in 10,000 for "FV, 800 for "PMT", 4 for "N", 9 for "I/Y", and the compute for "PV". Make sure your financial calculator is fully cleared first of previous calculations.
Ok great, so you now you know the present value is $9,676, what is the NET present value. It would simply be the difference between $9,676 and the initial investment of $9,500 or $176. If the net present value is positive, this means you that you would go forward with this investment whereas if negative, you would not go forward.
The reason the net present value is positive is because, in this case, the yield to maturity on the bond is actually higher than your 9% threshold. The actual YTM on the bond is 9.56%. Since the bond is being bought at a discount, the YTM is higher than the coupon rate. This is the rate that would make the future cash flow stream (being the coupon payments and bond principal) equal exactly $9,500. If you used 9.56% as your discount rate, the present value would be exactly $9,500 and the net present value would be zero (because the present value and the initial investment is the same).
