14. Growth Rates and Terminal Value

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To value assets that do not have a finite lifetime, we use the Terminal Value. Find out the various ways to calculate the Terminal Value for an asset in this lesson.

Lesson Notes

Terminal values

- Terminal values are used when we assume that cashflows will not stop at a point in time
- Examples of such assets include company stock, property purchases and annuities

How to value this type of asset

- Split the cashflow forecast into two time periods, the growth period and the stable period
- For the growth period, we discount each annual cashflow as before
- For the stable period, we use a terminal value that's discounted back to today

Ways to calculate the terminal value

Cost-based value: valued at the cost of replacement
Multiples: valued at a multiple of earnings based on market prices
Stable growth model: valued based on a stable growth in future cashflows

Equation for the stable growth model:
- TV = Terminal Value
- C = Cashflow in next period
- r = Discount rate
- g = constant growth rate


Up to now we've assumed that our investments end after a certain period of time. However, for many investments, including company stock, we may want to hold the investment for an indefinite period and in theory at least assume that the cash flows last forever. When valuing these types of investments, we use a concept called the terminal value. Our first step in this process is to split the cash flows from an asset into two parts. The first part is called the growth period which is usually the first five to 10 years. And the second part is the stable period after which cash flows grow at a constant growth rate. To calculate the value of an asset in the growth period, we follow the same steps as before discounting each annual cash flow back to its present value. To value the asset in the stable period, we use the terminal value. To calculate the terminal value, we have three different options. The first of these is the liquidation value. This is useful when there are some residual value in an investment which is best realized through a sale, for example, if a machine is close to the end of its useful life, our terminal value could be the income we receive from selling its parts and the scrap metal.

We can also use a multiples approach which is a market-based valuation method. If we were trying to calculate the terminal value for a company in five years' time, we could simply apply a price earnings multiple to its earnings at that point in the future to value the company and lastly we have the stable growth model which is theoretically consistent with income-based valuation or requires some judgment on the future. Given that we'll be covering liquidation values and multiples later in this course, I'm going to focus on the stable growth model in this lesson. To calculate the terminal value value for this method, we use the following formula where R is the discount rate, G is the consistent growth rate and C is the expected cash flow for the next period. To understand this in more detail, let's apply it to an example. Our example will be a company that we assume has a growth phase of six years and then enters a stable phase. To calculate the terminal value for this company, we'll use the formula I described earlier where R is the discount rate, G is the expected growth rate every year and C is the expected cash flow for the next period. When using the consistent growth model for calculating terminal value, you must be careful with the growth rate which must always be assumed to be lower than the growth rate of the economy because if it was greater, the company would ultimately be bigger than the economy. In this case, I'll assume the growth rate for the terminal value is 2%.

So, let's use our formula to calculate terminal value. I'll move to the year in which the terminal value will be calculated and my numerator will be the cash flow for the next period which is year seven. And that will simply be equal to the cash flow for year six multiplied by one plus the growth rate.

And then the denominator will simply be the discount rate minus the growth rate.

And this gives me a terminal value of 27.2 million. I must now discount the terminal value back to its present day value and to do this I'll simply change the discounted cash flows formula so that it sums together these two cells before discounting. I'll press F2 to jump back into the formula, I'll remove the I11 and I'll write equals sum, open the bracket and select my two cells.

I'll then copy and paste for the remaining cells.

And as you can see we now have a net present value of just under 17 million.

The terminal value makes up a huge proportion of the total value of the asset. For early-stage investments especially, where companies have a very fast growth stage and may run losses temporarily to realize that growth, almost all the value in the model will reside in the terminal value. Unfortunately the constant growth model is very dependent on the stable growth rate assumption. Off camera, I've created a one-row sensitivity table that shows the NPV for various stable growth rates. As you can see, quite a large range of NPV values are experienced for a set of plausible growth rates. For this reason, many analysts are wary of using the stable growth model for terminal value calculations. Instead, they often use a price earnings multiple to estimate terminal value. We'll learn more about the price earnings multiple in the next lesson when we leave income-based valuation and begin our look at market-based methods.