# Discounted Cash Flow Further Aspects, Capital Rationing

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1. says

Dear John,

Regarding your example on part c (non-infinitely divisible) if we calculate NPV per invested \$:
ABC NPV – 143 Total cost – 1400 NPV per \$ – 0.102
ABD NPV – 157 Total cost – 1500 NPV per \$ – 0.10466
ACD NPV – 143 Total cost – 1200 NPV per \$ – 0.119
BCD NPV – 136 Total cost – 1300 NPV per \$ – 0.10461
We should chose fraction ACD with highest NPV per \$ at the same time we save (no borrow thereby less cost of capital) \$400

My question is can I get on exam the same marks for this type of answer or is it better your answer ABD higher NPV?

Thank you!
Anzor

• says

We always want the highest total NPV, and the only correct answer is ABD.
Remember that the NPV is the surplus after repaying the borrowing (together with interest).

To explain, here is a very very basic illustration.
Suppose you could borrow \$10 and get back \$20 – a surplus of \$10 ignoring interest.
Alternatively, you could borrow \$100 and get back \$120 – a surplus of \$20 ignoring interest.
Which would you prefer? The first one gives surplus of \$1 per \$1 (10/10) and the second one only gives a surplus of \$0.20 per \$. (20/100).
However, surely you would prefer the second and end up with a surplus (cash profit) of \$20 after repaying the borrowing as opposed to a surplus of only \$10.

The only problem (and this is only relevant for a written part of a question) is that we are assuming that the returns are certain. If there is uncertainty then by choosing the second one we are taking more risk. However for the numbers part of questions we would always assume certainty.

• says

Thank you John!
That is clear.

Best regards,
Anzor

2. says

Now that the F9 exam has a multiple choice component, will it now be necessary to read the text book from cover to cover.

• says

If you watch all our lectures (together with the lecture notes) then you will have enough to pass the exam well.

What is essential is that you have a current edition of Revision Kit and that you practice all of the questions.

3. says

Hi Mr Moffat
Thanks to yourself and Open Tuition for the lectures.
A question regarding the answer to example 1(c) if I may (this question was asked by louise06111 back in Feb-12 but, and no disrespect to tameablebunchy, I’m not convinced by the answer given at that time, but I may be missing something).
The answer given to 1(c) in the lecture, is to choose the projects giving the greatest NPV, being A, B and D. However, A, C and D give the highest return per \$ invested (\$0.113 per \$ invested compared to £0.105 per \$ invested, if my maths are correct).
Using the same sort of logic, take this example (a spurious one but it’s simply to make the point):
A – cost \$10000, NPV \$1000
B – cost \$2000, NPV \$999
Assuming a capital restriction of \$11000, and the projects are not infinitely divisible, A has the greater NPV, but B has much better return on investment. Surely B would be the better choice?
What am I missing?
Thanks again for the assistance you provide.

• says

The NPV is the cash surplus we end up with (after accounting for interest).

To take your examples, if you invest in project A then you end up with a cash surplus of \$1000 (the amount not invested earns nothing.
If you take project B, then you end up with a cash surplus of \$999 (the remaining \$9,000 of the cash available earns nothing).

I would prefer to end up with a surplus of \$1000 than a surplus of \$999

(If we could invest all our money in B (i.e. 9.5 B’s) then certainly B would be better – we would end up with a much bigger cash surplus. However, that is not the case – we either invest in just one A or just one B)

• says

Of course, the interest on the source of the capital in the first place (cost of capital) is already being accounted for in coming to the NPV, so choosing to ‘borrow’ the additional capital in the first place is the better option as it gives a greater NPV.
Knew I was missing something.
Thanks again.
Regards

• says

If the projects were all mutually exclusive, it would mean that you could only do one of them – then you would simply select the project with the higher NPV.

If just 2 of them were mutually exclusive then you need to do the exercise twice. (If, for example, A and B were mutually exclusive, then you would do as normal first as though only A, C and D were available, and then as though only B, C and D were available. Whichever of the two solutions gave the higher NPV would be the best.

There is no such term as mutually inclusive. If they are all available, then it is the normal solution. I suppose what you could have (although extremely unlikely indeed for the exam) was that if, for example, we were to do A then we would be forced to do B. If that did happen, then you would treat A and B as being one project (simply adding them together) and then continue as normal. However, I do not think there is any chance at all of that being relevant for the exam.

4. says

Could we in the exam say that the amount of 100\$ leftover can be used as working capital in the projects so as to avoid the trap of fast expansion and working capital cash management?

5. says

Hey all.

I have a question regarding investment appraisal,
When do I add Working Capital Recovery in DCF?.
I have noticed that some times it is added and sometimes it is just ignored.?

6. says

Thank You So much Sir, An Excellent Lecture It Refreshed My memories Learning Limiting Factor Analysis and Throughput Accounting

7. says

Hi John,
After listening to this lecture I finally fully understand capital rationing! Thank you for simplifying for me!!

8. says

I feel am studying F5! It reminded me of key factor analysis and throughput accounting! Feels good that I still remember the stuff after the exam lol!

• says

I’m studying F5 as well, so I’m finding F5+F9 an amazing combination 😀

9. says

Please assist.. Dec 2009…Q 3. I wanna calculate part a TERP not the way it has been calculated in the answer somebody let me know the other optional method we have..

10. says

thanks f9 has been eased for me instead of calming things i real understand the concept open tuition is far better than these colleges were we pay heavily and get sub standard lectures with out you i don’t know how i would have made it thankes

• says

Completely agree!!!! I have got no problem with paying money, in fact my study is half funded by my company, yet am so not gonna pay to have less quality lectures, that would be stupid! I can understand paying for a higher quality, but less quality! O.o! Opentuition is far better than the institute I was going to, it feels bad to be paying and then come to a free resource to understand everything you did not understand in the classes you have been paying for!!

11. says

Dear tutor,
Regarding part(c) of Eg1, I am confused.
We choose ABD combination which gives the highest total NPV, but why don’t we analyse the efficiency as we do in part(b)?
ABC: 1400 input, we get 143 output, the efficiency is 10.21%;
ABD: 1500 input, 157 output, 10.46%;
ACD: 1200 input, 136 output, 11.33%;
BCD: 1300 input, 143 output, 11.00%.
(OMG, I hope I’ve made it clear~)
From my view I may think ACD is the most efficient investment combinations and I am wondering whether I got something wrong. Can you please help check my thought? Thx a lot.

• says

@louis06111,

part B is infinitely divisible, this means you can do a fraction of a project, therefore you start with the highest NPV first and so forth what capital is left is invested into a fraction of the project B which 66.6666%.

With part C, capital is restricted to 1600 so you choose the best option that will return highest NPV per project because these projects are non infinitely divisible you have to choose the best option so you only have to borrow or use the amount of cash that is needed.

The key is to find the highest return/NPV for investment

• says

@tameablebunchy,
Thanks a lot for your time and effort,
It does help!