3.8 Investment appraisal

Full video class on YouTube, summary and notes on Instagram, class extracts on TikTok, text below. Have fun!

The main point of this class is to learn to see whether investment is worth pursuing.

In the IB Business Management course, investment is a purchase of an asset that will potentially generate future earnings. Investment appraisal refers to quantitative techniques that are used to evaluate the pros and cons of investment opportunities. The three investment appraisal techniques that we’ll learn in this class are:

1. Payback period (PBP)
2. Average rate of return (ARR)
3. Net present value (NPV) (HL only)

As always, I suggest you make notes in a systematic manner by filling in the table below. If you can fill in the entire table, it means you are the boss of investment appraisal.

Payback period (PBP) is the length of time required for an investment to recover its initial cost of investment (principal) in terms of profit. In some industries (for example, IT and hi-tech), assets become outdated in a short time, so for these industries calculating PBP is really important. If an asset becomes obsolete before the end of payback period, then there is no point in purchasing it.

Let’s see how to calculate payback period. We’ll start off with a simple example. The formula for PBP is as follows:

PBP = initial investment cost ÷ cash flow from investment per period

If a delivery scooter for a pizza restaurant is worth $1200 and it’ll bring $600 per year (after variable costs are paid, e.g. maintenance), then PBP is 2 years ($1200 ÷ $600 = 2).

However, most of the time, it is not as straightforward as in the example above. Let’s see a more complicated example. The formula would be:

PBP = additional cash inflow needed ÷ annual cash flow in the next year ⨉ 12 months (+ no. of years)

The formula might seem really complicated now, but believe me it is much simpler than it looks. Just read the following text carefully.

Suppose that a pizza restaurant is now considering purchasing pizza oven ABC that is worth $5,000. It’s expected to generate the following cash flows in the first four years: $3,000, $1,500, $1,500 and $1,000.

The first thing we have to do is to outline annual net cash flows (CF) and cumulative net cash flows for each year of investment. It is really important to start counting with “year 0”, which refers to the point when the purchase is made. See the table below for annual and cumulative cash flows.

Tip: In financial statements, negative figures are taken into brackets. For example, instead of "-$5,000" accountants record "($5,000)".

What we do next is look back at the formula and identify additional cash flow needed (in green), annual cash flow in the next year (in blue) and count the number of full years until investment pays off (in red). Again, see the table below with all the necessary figures:

Tip: Mind the difference between these words: cash flow, net cash flow, return. Sometimes, you have to subtract costs from cash flow before calling it “net cash flow” or “return”.

Now calculating payback period should be really simple. Let’s see the pros and cons of payback period as of an investment appraisal technique.

On the one hand, payback period is simple, easy, and quick to calculate. It is super helpful for industries where assets quickly become outdated, for example, IT. Overall, payback period is a quick way to check the viability of the investment project or to compare several investment opportunities. If you are not sure whether to pursue investment project A, B or C, then see which one pays back sooner and go for it.

However, payback period, as an investment appraisal technique, only takes time into account. It ignores overall project profitability. In addition, annual and cumulative cash flows for the coming years are just a prediction, it is impossible to know them certainly, which makes payback period quite unreliable. So, on the downside, PBP is too simplistic to be the only investment appraisal technique to rely on. Luckily, we learn two more in this class! Keep reading.

Average rate of return (ARR) is average profit on investment expressed as a percentage of the initial investment (capital costs). So, if PBP shows time, then ARR shows percentage. After calculating ARR, managers usually compare it to the interest rate in the banks. Depositing money in a bank has almost no risk, but pursuing an investment project is quite a risky thing to do. That is why, if ARR for an investment project is just slightly higher than the interest rate offered by the banks, perhaps this investment project is not a good idea. In addition, many companies develop their own benchmarks for ARR (called criterion rate) that are used to assess the viability of different investment opportunities.

Now let’s see how to calculate ARR. The official IB formula from the subject guide is:

ARR = (total returns – capital costs) ÷ years of use ÷ capital costs ⨉ 100

Let’s continue the pizza theme and calculate ARR for a pizza restaurant again. Suppose pizza oven XYZ is worth $5,000. This time, the expected returns for the five years of its lifespan are estimated to be $3,000, $2,500, $2,000, $1,500 and $1,000 accordingly.

First of all, let’s calculate the total returns:

Total returns = $3,000 + $2,500 + $2,000 + $1,500 + $1,000 = $10,000

Now we have all the date we need for the formula.

ARR= (total returns – capital costs) ÷ years of use ÷ capital costs ⨉ 100 = ($10,000 – $5,000) ÷ 5 ÷ $5,000 ⨉ ⨉ 100 = 20%.

Then, ARR is compared to criterion rate and interest rate and investment decision is made. The example of the entire step-by-step calculation is summarised below:

Tip: Mind the difference between these words: cash flow, net cash flow, return. Sometimes, you have to subtract costs from cash flow before calling it “net cash flow” or “return”.

As you can see, calculating average rate of return is quite simple. In the exam, you will even be provided with the formula… Let’s see the pros and cons of ARR as of an investment appraisal technique.

The advantages of ARR are similar to those of PBP. On the one hand, calculating ARR is simple, easy and quick. In addition, ARR goes further in time than PBP, because it takes account of profitability for the entire lifespan, not only of the time until the investment pays off. So, overall, ARR is another quick way to check the viability of the investment project or to compare several investment opportunities.

On the other hand, ARR ignores timings of returns. For example, two investment opportunities may have the same ARR but different PBP. In addition, total returns and lifespan (years of use) of an investment project are just a prediction. So overall, on the downside, average rate of return, as an investment appraisal technique, is too simplistic to be the only tool to rely on (same as PBP).

Based on the pros and cons of PBP and ARR, we may conclude that PBP + ARR = ❤️. They make a great combo and should be used together for appraising investment opportunities.

Net present value (NPV) is the difference between present values of future cash flows and original cost of investment (principal). As always, it might sound difficult but in fact it is not. First of all, we have to establish that cash is a depreciating asset because it loses its value over time. 100 years ago you could buy way more things for $100 than now. Why is that? Mainly because of inflation that makes cash lose its value over time. Thus, we may conclude that in the future the we can afford less things for $100, compared to today.

Simply speaking, if the interest rate offered by the banks in your country is 5%, then it means that $100 today will be the same as $105 one year later. Of course, it is not as simple as that, but we’ll leave the complexities to those of you who study Business and Economics in university and we’ll focus on the basics now.

So far, we’ve established that present value is today’s value of future cash. In order to calculate present value, we need to multiply the sum by a discount factor from the table below:

The table above is easy to use. By the way, it will be provided to you when you take an exam (for HL students only). For example, let’s say your lovely grandma gave you $1,000 for your birthday and you want to save it for 2 years. You also know that interest rate these days is around 6%. So, you look for the cell in the table on the intersection of 2 years (that’s how long you want to save your grandma’s gift for) and 6% (that’s the current interest based on your research). Thus, the discount factor is 0.8900. Now we multiply your cash by the discount factor and we have the following: $1,000 ⨉ 0.8900 = $890. Now you know that 2 years later, for $1,000, you will be able to afford as much as you can afford today for $1,000. In other words, $890 is the present value of the future (2-years later) $1,000. So maybe you’d better spend it now or invest it into something that will multiply your grandma’s gift.

Now, net present value is a sum of present values minus original cost of investment, as the formula below states:

NPV = Sum of present values – Original cost

In order to understand it, let’s get back to my favourite thing in this class — the pizza restaurant! So, as you remember, it’s considering purchasing a pizza oven XYZ that is worth $5,000. The expected returns for the five years of its lifespan are $3,000, $2,500, $2,000, $1,500 and $1,000. The interest rate is currently 6%. Let’s outline a simple table that will help us calculate net present value of this investment.

Hopefully, you remember that discount factor is something that you can find in figure 4 (remember that discount tables in figure 4 have to be provided to all HL students who are taking BM exam). Now, once we calculate present values of all the future net cash flows, let’s apply the formula:

NPV = Sum of present values – Original cost = 8,669.85 – 5,000 = $3,669,85.

NPV is positive. Thus, investment is worth pursuing. If it was a negative number, then investment is not worth pursuing.

The example of the entire step-by-step calculation is summarised below:

Tip: Mind the difference between these words: cash flow, net cash flow, return. Sometimes, you have to subtract costs from cash flow before calling it “net cash flow” or “return”.

For example, if the estimated cash flows from the pizza oven would be $3,000, $2,500, $2,000, $1,500 and $1,000, as in the example above, but the case study also stated that maintenance costs of the oven are $500 per year, then net cash flows (or returns) that we include in the table in figure 5 should be $2,500, $2,000, $1,500, $1,000 and $500 accordingly.

As you can see, calculating net present value is a little bit more complicated than calculating payback period and average rate of return, but it is still pretty easy. On top of that, in the exam, you will even be provided with the formula and discount tables… Now let’s see the pros and cons of NPV as of an investment appraisal technique.

On the one hand, it includes both time and cash value. As you remember, PBP was only about time, and ARR was only about rate, but NPV takes account of a combination of factors. In addition, NPV is quite flexible in its use: discount factor may alter based on the state of economy, and thus calculation may be altered quickly as well. Overall, NPV is a widely used technique that takes account of several factors at the same time (profitability, economy, time).

On the other hand, as I mentioned before, NPV is relatively difficult to calculate, compared to PBP and ARR. In addition, it is still somewhat inaccurate because interest rate is highly unlikely to remain unchanged throughout the entire project lifespan… So overall, NPV is too simplistic to be the only tool to rely on (same as any other investment appraisal tool — PBP or ARR).

Based on the pros and cons of all investment appraisal techniques (PBP, ARR, and NPV), we may conclude that PBP + ARR + NPV = ❤️. They make a great combo and should be used together for appraising investment opportunities (especially if you are a Higher Level student, haha).

Tip: Once again, remember the different things that different investment appraisal techniques show: PBP shows time, ARR shows rate (percentage) and NPV shows monetary value. Mind the units of measurement for these three techniques.

In the end, I will just emphasise that investment appraisal is a quantitative tool. So, for a balanced investment decision, qualitative factors (reputation, brand image, gut feeling) should be considered too.

Make sure you can define all of these:

1. Investment
2. Investment appraisal
3. Payback period (PBP)
4. Principal
5. Average rate of return (ARR)
6. Capital costs
7. Criterion rate
8. Net present value [HL]
9. Present value [HL]
10. Discount factor [HL]