# NPV with Terminal Value

## NPV with Terminal Value Intro

Most projects require an initial investment and then eventually they give off positive net cash flows for a given period then stop like in the example below.

This example is for a mold that will be used to produce bumpers for a car model with a 4 year production run. When the car model gets updated, the mold is no longer useful and destroyed.

## Projects that give off perpetual net cash flows

Other projects can give off positive net cash flows that don’t stop and last forever. Think of an outdoor parking lot. After the initial investment, the parking lot can generate positive cash flows for 5, 10, 20, 100, etc. years. There’s no end to the net cash flows, the cash flows are perpetual.

## Calculating the NPV for a project with perpetual cash flows

If you keep the cash flows going for 250 years (including Year 0) and discount them, you’ll notice they get smaller and smaller as you go further in time until eventually they are a fraction of a penny like in year 249.

You could keep going another 500 or 5,000 years but the discounted cash flows are already so small that it wouldn’t really make a difference.

If you add up all those discounted cash flow you arrive at the NPV.

But there’s an easier way to calculate the NPV for investments that have perpetual cash flows by adding something to the cash flow called a terminal value.

Step 1: Calculate the Net Cash Flow (Cash Inflow minus Cash Outflow). The projection of net cash flows should go until you feel the project is stable and mature when the last year of your projection reflects that net cash flow that will be repeated every year forever. In this example the net cash flow of $180,000 in the final projection year (Year 4) represents that ongoing net cash flow that will be repeated each year thereafter forever. Step 2: Calculate the terminal value. Take the net cash flow in your last year of projection and divide it by the discount rate. =$180,000 / 10% = $3,600,000 Step 3: Add the net cash flow in your last year of projection plus the terminal value. This is your Net Cash Flow with Terminal Value. Step 4: Discount the net cash flows using the discount rate. Step 5: Add the discounted cash flows to arrive at the NPV with Terminal Value. (Notice that the NPV with Terminal Value is equal to the NPV with 500 years of net cash flows when rounded to the nearest penny.) ## NPV with Terminal Value with Growth What if you have a project in addition to giving off a positive supply of net cash flows forever will also increase every year at a given growth rate? There’s a simple formula that factors in the growth rate when calculating the terminal value. $Terminal Value with Growth Rate = \frac{Net Cash Flow in last year of projection * (1+ Growth Rate)}{(Discount Rate - Growth Rate)}$ $= \frac{180,000 * (1+ 1%)}{(7% - 1%)}$ =$3,030,000

All the examples provided above can download in the supporting file below.