IRR Series, Part 4: The Net Present Value

Now we are getting somewhere in this crazy IRR calculation. We now know that the value of money decreases over time. We know that investments carry risk and that we need to account for that and the opportunity cost (how much we lose out by not putting our money elsewhere) when making an investment.

Let’s say we are making an investment in the form of a $100,000 loan to an acquaintance, so he can start a surgical mask factory. We have calculated the discount rate to be a rather large 18%. This is a risky venture, but if he can make better masks than other companies, there will be a huge market going forward and it is worth the risk to us if the rate of return is greater than 18%. We need to demand something more than this to have a reasonable likelihood of profit, but let’s say he told us he would pay us 18% per year going forward for the next five years.

We want to know how much all those annual payments are going to give us. The first year, we get $18,000 back but because it comes in the future and carries risk it is discounted at our discount rate. For the first year, the value we get is only worth what $14,760 is today.

18,000 / (1 + 0.18) = 14,760

This is a calculation similar to interest received on an investment, just that we are looking backwards. It is over one year, but going forward it will be less and less as that exponential gets larger. Here on out, I’m just going to say it is only worth such and such rather than talking about purchasing power all the time. In year 2, we have the 18,000 returned to us but it is discounted over two years now, so that is:

18,000 / (1 + 0.18) ^ 2 = 12,927

We add these two together to find what our two years of getting $18,000 back is worth to us today:

14,760 + 12,927 = $27,687

Over five years we can continue doing this or we can just use the formula:

NPV = Σ [Value returned each term / (1 + rate) ^ number of terms] from 0 to number of terms

We also need to account for the initial investment as well as the return we get at the end. In our example we have a hideous looking:

NPV = -100,000 + 18,000 / (1.18) ^ 1 + 18,000 / (1.18) ^2 + … + 118,000 / (1.18) ^ 5

Remember that we get $100,000 back plus the interest ($118,000) at the end of the last year.

The income per term doesn’t always have to be the same as in our example. We might predict our income to change over time and the equation still works, but it is pretty cumbersome. Spreadsheets can do this work for you, but teaching that is beyond the scope of this particular post.

Our NPV is now $0. That is what that 100k investment and those 18k payments are worth to us today. Even though we got interest checks totaling 5 x 18k = $90,000, since they come later and later, they are only worth $56,289 to us today. That 100k we get back at the end is only worth $43,711. Add it up and it is $100,000. But that’s what we had to pay to get into this deal. Our NPV is $0. This isn’t a coincidence. I designed this scenario to do that. We need to use this amount in making our decisions rather than the income of 90k. Sobering.

She really should be doing real estate math instead of playing around with her photos

The NPV is a way of comparing income streams to one another. It helps us decide, right now which deal is better for us over the long run, taking into account the discount rate. A higher discount rate, means the money paid to us later is worth less to us, and the NPV goes down. It is all based on making a good decision on the discount rate. But the NPV isn’t all fun and games for us.

The Net Present Value is the value today of the return on the investment that you get from the investment you make today.

Let’s make it simple. Here are two offers our acquaintance gives us:

  1. Loan $100,000 and he will pay back $16,000 yearly for five years and pay back the $100,000 at the end of five years. You’ll get a profit of $80,000.
  2. Loan $100,000 and he will pay back $25,000 yearly for three years and pay back the $100,000 at the end of three years. You’ll get a profit of $75,000.

To get to the NPV we take the yearly income/outflows and discount it per our 18% discount rate, then sum each discounted yearly income to arrive at the NPV. Keep in mind that we have a -$100,000 income when we first make our investment and we have a discounted $100,000 income when we are paid back. For scenario 1, we have an NPV of -$6,254. For scenario 2, we have an NPV of $15,220. Which investment is better?

The positive one! Making investment #1 today gives us a total of $80,000 profit, but over five years and discounted by our discount rate of 18% means we have a negative net present value. Even though we receive more dollars back in payments, #2 actually makes us money.

Many investors fail to note the time value of money and fail to account for risk. They get a big check at the end and never know that they really lost purchasing power. The NPV gives us a way to calculate this before making an investment.

Next Week

Scenario #1 gave us a loss. We got a gain from #2. There must be a combination of investment and returns that gives us a break-even. There must be a point where making even a penny more is a gain and a penny less is a loss. If we had that number, we could evaluate any deal based on our discount rate and quickly know if it was a viable deal for us or not. That number is the IRR. See you next week.

Dr. Equity