Investment Appraisal – Methods Accounting rate of return and Payback period

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1. Sir,i am from Pakistan and i understand the method of taking Average Balance Sheet Value But i have one question that,can we use the other way for taking the Average Balance Sheet value, like this one;
Add Year 1st+2nd+3rd+4th Balance Sheet Values And then Divide the Total with 4.(i have try this one and i got less then \$45000)
And if not then why not we can use this Method.
ThankYou.

• says

In real life there is no rule – you can do whatever you think is more sensible. What you suggest is fine, but even then you would have to decide whether to use opening balance sheet values each year or average values each year, or closing values – each would give different answers and there is no one ‘correct’ way.

However in the exam you will be expected to do it the way in the notes and lecture (unless you were specifically told to do different, which is very unlikely).

2. says

Sir, for the A.R.R part, why do we divide by 2 for the average balance sheet value? Should we divide by 4 as it has an expected life of 4 years?

• says

Suppose that this morning you had \$100 and you were spending all day so at the end of the day (10 hours later) you had nothing left.

What was the average amount of money in your pocket? Surely, on average you had \$50 – you would not divide by 10 and say that it was \$10.

Same example, but this time you still had \$20 left at the end of the day. In that case on average you would have had more money – (100 + 20) / 2 = on average \$60.

Hope that makes sense. If not then say and I will try and explain in another way

• says

Yup, makes sense with the above illustration, sir. Thank you very much

3. says

Hi John,

the lecture shows that payback time is 2.75 years, it’s simply add first 2 years cash inflow and a proportion of 3rd year cash inflow. However you didn’t take present value of these inflows into account. Actual payback time should be longer than 3 years if we convert these inflows to present value.

• says

But that is how we calculate the payback period – we do not discount the cash flows.

If you are asked for the ‘discounted payback period’ then you do discount the flows (and the discounted payback period will indeed be longer than the normal payback period).

4. says

Hi Sir
When we are calculating Average Book Value of the Asset, aren’t we supposed to calculate per annum? I got a bit confused and I actually calculated the depreciation in linear method. However, why do we calculate ARR in that way?
i.e. Average profit per annum from an investment/ Average Book Value of the Asset.

I would appreciate it if you could explain this a bit

Furthermore, I know this is nothing relating to PayBack Period. But don’t you think, the longer the Payback period, the lower the value of that money? As in the PV of the inflow decreses.

• says

In real life you might be more interested in the ARR year by year. However normally in the exam we simply calculate the average. It does not matter whether we depreciate on a straight line basis or some other way – in total the depreciation will be the difference between the cost and the scrap value, which method of deprecation we use.

With regard to the payback period, what you say about the present value may well be true. However, companies use a range of measures, and one big problem with NPV’s is that the further into the future we are estimating the cash flows, the more it becomes almost a guess. The shorter the payback period, the more certain we will be that we will really get the cash back.

• says

you have \$50000 in year two but you still need \$30000 to make \$80000.Therefore,30000/40000( ie the cash flows in the 3rd yr) = 0.75 yrs add 2yrs.Hope this helps

• says

Thanks Realhams – lovely explanation

5. says

I can never thank enough. Just watched all the chapter 7 lectures and they are so good and easy to understand. Thank you John thank you open tuition.

6. says

Dear jhon,
Once again a great job with this chapter, you have made F-9 so easy to comprehend. I have great understanding of calculations but have certain ambiguities in rationing behind NPV and ARR so I would appreciate if you can answer my uncertainty in number order as it makes easy for me to understand.
1) NPV for example 1 is (positive) 6660 and example 4 (negative) 9104. Other than being positive or negative does the value itself means anything at all, e.g. profit of 6660 or loss of 9140. Other than the sign of value, what does the value itself mean?
2) My previous understanding was that NPV calculates expected profit, but if it is not the case and we know for a fact that “NPV formula” DOES NOT take into consideration our expectations of cash needed to run the business or pay dividends or acquisition of other companies etc.
A) Why do we say that NPV needs to be positive and reject the project if NPV is negative? Even if NPV is negative how do we know the cash generated (cash flows) will not be sufficient to take care of cash needs since NPV Formula do not take into account our expected cash needs.
B) If NPV does not calculate expected profit and does not take account of our cash needs what is the purpose of NPV?
3) In example 8, we calculated profit considering only depreciation expense, but in real life are we going to consider raw material and labor costs associated with the machine? Because unless ALL expenses are deducted from revenue we cannot get net profit.
4) Suppose revenue generated by a machine in year two is 10,000 and expenses relating to this revenue are 1000 in running costs and 2000 in raw material used at this particular machine. Ignoring exam, for practical purposes can we use 7000 instead of 10,000 as a cash flow and will NPV then reflect net profit. Regardless of the debate whether ARR is better or this new method of calculating NPV, could it not be at least an alternative method to calculate expected profit.
5) Assume figures of Point-3 are result of an investment made in agricultural land (agricultural land does not depreciate) in this scenario could this new method of NPV used to calculate net profit and could it now be an alternative method to ARR.
6) Which book are you using to prepare f-9 lectures and which exam kit would you recommend e.g. Kaplan or BPP or any other?
Regards

• says

The NPV is measuring the cash surplus or deficit from investing in a project, after accounting for the interest.
It does not measure profitability.
The future cash needs are not relevant at all. If an investment generates a cash surplus then it is worth borrowing money to invest in it – we will be able to repay the borrowing together with interest and end up with a surplus.

The reason it is cash that is so important (rather than profits) is that it is cash that is needed to pay dividends and it is cash that is need for further investment. Therefore in theory the object should be to invest in projects that give cash surpluses.

The cash flows we look at are the net cash flows after charging all cash expenses (i.e. the cash profit).
Your point 4 is not a new method – we look always look at the operating cash flows (which means the net cash flow after all cash expenses).

This chapter of the notes is just going through the arithmetic as revision of Paper F2. You should watch the next chapter which goes through how we get the cash flows – this is the important bit for the exam (the arithmetic for discounting etc. is just following rules and was already examined in F2).

I do not use a book to prepare lectures – I have been teaching it for 40 years

The books by all the approved publishers are fine.

• says

Will you consider labor and raw material used to generate cash flows from a particular machine in its cash expenses.(not talking about the whole company jut the machine/project under investigation)
You mentioned two points in your reply, first that NPV does not measure profit but later mentioned that my point 4 is not a new method because cash flows are net operating cash flows after deducting all cash expenses does this include cost of raw material, labor and other costs related to this particular machine. If yes than it means NPV is net profit (not for the whole company but only for this particular investment).

• says

Wow Mr John! 40 years!! Very impressive!!! Surely it does appear in your performance that you are a master at teaching, yet I didn’t know you have been teaching for 40 years. It is great that highly experienced tutors such as yourself would offer free tuition like this.

Great job!

7. says

am failing to access most of the lectures .feed back saying “shockwave flash has crashed”. how can i get over this?

8. says

Why didn’t we take the scrap value of 10k in 4th year as a cash inflow (like we did in example 1), so the total operating cash flow would be 110.000? Also, why didn’t we then say that the balance at the end of 4th year would be 0, so the average book value would be (80.000 + 10.000) / 2 = 40.000 ? It’s a bit confusing because the example is the same as example 1, but here we treat the scrap value differently.

• says

@crnimeda, For the accounting rate of return, we are not looking at cash flows. The ARR is an accounting measure (average profit per the accounts as a percentage of the average balance sheet value).
With regard to the second point, if the asset was worth nothing at the end of its life, then the average value would indeed be 40,000. However it is worth 80,000 and the start, and still worth 10,000 at the end, and so the the average value is higher at 45,000.

You cannot compare it with example 1 – it is a different way of appraising that is common in real life because shareholders etc are interested in profits. Example 1 looks purely at cash flows.

• says

@cris1993, it isn’t relevant for DCF – it’s a different approach
. However, it is a common way of appraising and can be examined in F9.

• says

@neil.farrow, Because is a simple avarage calculation, you have to values 80,000 and 10,000. The mathematical avarege is (80+10)/2. Don’t think about net book value.

• says

But why do you divide it by 2

9. says

I just love this Lecturer. He gets straight to the point and makes it look easy. Thank you Sir!!

10. says

I am happy with this lecturer as he made this so easy. I have always done it the wrong way.

Thanks

11. says

I can not play any vedio lecture of F9 as server is not available.
Can any one help me?

12. says

What about if the project rquires a working capital at the beginning or anytime within the project life span? How would you compute the payback period? Do you have to add the working capital to the initial investment cost in determining the payback period?

• says

@richoab, Interesting question

Best to ignore the working capital.
The reason is that we assume that we get back the working capital whenever the project finishes.