Dear John, thank you for your lectures, they are great 🙂 I have a question with regards to the units of production. Your example above is 15,000 per year, but what if i have different numbers of units per year, do i add the total and continue following the rest of the equation? Thank you

Thank you for your reply. My scenario is for 5 years with different units per year, i add the total of all units and use the cumulative pv table at 12% for 5 years, is this correct? Thank you once again

No – you can only use the annuity tables if there is an equal cash flow each year. If the units change each year then you discount using the present value tables for each year separately.

sir you said that the rule to obtain sensitivity is npv/ pv of flows affected. what would happen if say more than one flows get affected ? will pv of of both the flows be added up and substituted in the formula you mentioned to get sensitivity?

I used Discount factor at 17% and NPV is -2231, IRR is 16.41 (15%+(5329/7560 x 2%) So Sensitivity of capital= (16.41-15) / 15 x 100% = 9.4% Am I right? Thanks sir.

If there are more than one critical factors, hence the investment has high uncertainty. Can we decide after sensitivity analysis that we should not go ahead with this investment as we may most probably lose money?

To further confirm our decision, should we perform some of the below analysis:? 1. Probability analysis – Expected values 2. Using risk-adjusted discount RATE 3. Adjusted payback PERIOD 4. Simulation

So before accepting an investment from the proposed investments/projects, we do the above analysis to assess its risk and then decide to accept it or not.

You are correct, except that you will not automatically decide not to do a project – it is just that the more uncertainty there is the more you might decide not to risk going ahead.

It is not a problem in the exam – you accept or reject based on whether the NPV is positive or negative. But for written parts you must be able to discuss the relevance of uncertainty.

You certainly have to read the question carefully. In the lease buy question it is made very clear that the scrap value is only relevant if the machine is purchased. In the sensitivity question is says that the final scrap value is 15,000, and scrapping can obviously only occur at the end of the projects life!

Hello, Mr. Moffat! I got the overall idea, but confused with sensitivity for sales volume. Can we use PV of revenue instead of contribution? Follow the same logics: if sales volume fall by 10%, revenue fall by 10% and PV fall by 10%. Same as for contribution. Why don’t we have the same answer as for contribution, if everthing else remain constant? (The question appeared while practicing specimen exam for Sept.2016, question 2). Thank you in advance!

It depends whether increasing the flow is what will cause problems (in which case it is + ) or whether the flow decreasing will cause problems ( in which case it is – )

Mr. Moffat, am I correct in saying that when calculating the PV for Cash inflow in Question 1 (a) only using contribution and not price can only be done if price (and variable cost) remain constant?

Something that worries me is that I understood the whole lecture but I got parts iv and v wrong because in both cases I divided the NPV by the fixed costs (15,000) in part iv and by the scrap value (15,000) in part v and consequently got the wrong answer.

But my understanding was that I wanted to know the percentage change in fixed costs or scrap value because that would ultimately bring the present value of that particular flow down by the same percentage resulting in a NPV of zero and that’s what we are doing, aren’t we. Where am I wrong then?

For the NPV to end up at zero, the PV of the relevant flow has to change by the amount of the current NPV.

So, for example, if the NPV is 100, and the PV of the fixed costs is 1,000. Then for the NPV to fall by 100 to zero, the PV of the fixed costs will have to increase by 100. In percentage terms this is 100/100 = 10% It is always the NPV divided by the PV of the flows that change (expressed as a %).

It should be clear that it would be silly to divide a % by a PV. For cost of capital we have to go back to the basis logic and divide the change needed (0.84) by the current value (15)

Hi John, permit me ask you this question. how do you go about calculating the sensitivity of the price. I mean the percentage of the price change that will lead to the NPV falling to zero thank you

For this particular example we can not, because we do not know the estimated selling price. In general terms you would take the same approach as the others i.e. express the NPV as a % of the present value of those cash flows that would change (which in the same of the price would be the sales revenue flows).

you mean NPV/ present value of sales revenue? this will give me the percentage change in sales revenue. I am preparing for P4 and there is this question Dec 2012 question that asked for this. when i tried going through the solution i didnt understand how it was solved. If use this your approach i will get the percentage change in sales revenue but the question asked for sales price

But surely, if the sales price changes by 10% then the revenue changes by 10% as well! (I know it could be affected by other things, but with sensitivity we can only consider one item at a time)

One other thing is that if there is tax in the question, then the flows that will change if the selling price changes will be the revenue and the tax on the revenue. So you need the net PV of these two. Then express the NPV of the project as a % of it.

Thanks John, an issue here,when we are calculating the sensitivity of change on for example part (iii) which is contribution p.u, why do we put that negative sign yet in our table the final value was a positive??

Now the F9 carries a MCQ do I need to read the text book from cover to cover, or your notes, lectures and the kit will be sufficient to help me pass the exam.

Hello Sir, why lower the sensitivity—> the more worried about item.? how about the higher sensitivity, is the higher sensitivity more optimal? could u plz explain it again. thanks

Its not really a question of calling it the optimum.

The problem is that we are making a decision on forecasts of cash flows, and therefore the actual cash flows may turn out to be different – if they are different then the NPV might turn out to be negative and then we will have made the wrong decision.

The higher the sensitivity the less the chance is of that flow changing enough to affect the decision. However if the sensitivity is low, then it means that even just a small change in the flow will affect the decision. Therefore the lower the sensitivity the more risk we are taking and therefore the more we will try to estimate the flow accurately (or else maybe decide not to take the risk).

The PV of the scrap is 1845. This would have to fall by 5329 to end up with a NPV of zero.

So in percentage terms this is a fall of 5329/1845 x 100% = 289%

However (as I do state in the lecture) this is ridiculous because it would mean that the scrap value would have to be negative! Usually, obviously the most it can fall is 100% down to zero. So you would state that the scrap is not sensitive at all.

(The only time it could possibly be relevant is if there were a possibility of us having to pay money to scrap the machine, which is very unlikely)

What you have to ask yourself is will it make the NPV worse if it gets higher or lower.

So, for example, as far as the revenue is concerned, we are only worried if it should fall – so the sensitivy is negative (it measures the percentage fall that we can afford). But as far as the cost of capital is concerned, we are only worried if it should increase – so the sensitivity is positive (it measures the percentage increase that we can afford).

Hey John, Why u didn’t do cost of captial sensitivity? However I done it by my self and the IRR comes = 15.842%. I took 20% as another npv that resulted in ($26306).

Now as per your formulae: NPV/PV of changes x 100% = 15%/15.842% x 100% = ~95%

At present the NPV is 5329, and we need to know the % fall in sales volume that will give NPV of zero.

If the sales volume per year falls, then the contribution per year falls, and therefore so too will be present value of the contribution flows. At present the present value of the contribution flows is 241189 – we need this to fall by 5329, which is a 2.2% fall.

Wow, couldn’t be better. Nevertheless, if a question asked us to evaluate sensitivity for sales volume, sales price and variable cost it appears we would have the same change in the variables (for all of them) if we only calculated the PV for contribution only and not the independent variables i.e. separate PV for sales price and variable cost respectively. What I want to know is that wont such an approach limit us on the marks awarded?

Sales price will have a different effect (and therefore a different sensitivity) than sales volume (with sales volume the contribution per unit remains the same, but if sales proie changes then the contribution per unit changes). So too will the variable costs.

i am confused about the last part cost of capital sensitivity?? please can anyone tell me in detail the whole working including IRR please help me out….

@adeel15, you can easily understand this if you went back to the video on the IRR. I have found it to be easy actually. Remember that the IRR gives you the cost of capital that will result into NPV of Zero. Compare that IRR (which you must calculate with the information in the question) with the cost of capital (we have been given). The difference in percentage terms is the sensitivity on cost of capital.

@tiffanytoon, The cost of capital is 15%. For a NPV of 0, the cost of capital would have to be 15.84% (the IRR). So we can afford the cost of capital to change by 0.84 (15.84 – 15) from an existing 15.

In percentage terms, this is a change of 0.84/15 x 100 = 5.6%

@amytan, On the right hand side of the bar at the bottom of the screen is a symbol with 4 little arrows. If you click on it, then the video should be full screen.

hi. i used the same approach for sensitivity for qn dec 01 tower railways inc. i got 2003/10771 X 100% = 18.6% 🙁 no where near their ans. of 20.87% or fall in px of $2.50. Moreover their explanations n calculations are far more confusing !! pls help !!! tks

hi i’m new to this and i need some advise on how many sub to do this time.. I’m doing f8 and p2… and i had to fill my form for f9 as well in order to do my p2…I dont know shall i do f9 or shall i leave it for next term..

@dayah, In my opinion, we are currently getting a NPV of +5329, in order to result in a NPV of zero(Breakeven analysis), we can let the sales volume to drop by that percentage. And hence, it is negative. Similarly, we can let the cont. p.u. to drop by 2.21%, it’s also negative. That’s the conclusion I came to and I hope it will help,

loukasierides says

dear Sir,

thank you for another great lecture. Shouldn’t the volume sensitivity be the NPV / 15000u*sales price?

John Moffat says

No, because if the volume changes then both the revenue and the variable costs will change.

loukasierides says

thank you very much. So. just to be clear, if the question asks for sales volume sensitivity , would that be different from selling price sensitivity?

John Moffat says

Yes – because changes in sales volume change both the revenue and the variable costs. Changes in the selling price only affects the revenue.

Simone Azzopardi says

Dear John, thank you for your lectures, they are great 🙂

I have a question with regards to the units of production. Your example above is 15,000 per year, but what if i have different numbers of units per year, do i add the total and continue following the rest of the equation?

Thank you

John Moffat says

Thank you for the comment.

The approach remains exactly the same 🙂

Simone Azzopardi says

Thank you for your reply. My scenario is for 5 years with different units per year, i add the total of all units and use the cumulative pv table at 12% for 5 years, is this correct?

Thank you once again

John Moffat says

No – you can only use the annuity tables if there is an equal cash flow each year. If the units change each year then you discount using the present value tables for each year separately.

ABC says

sir you said that the rule to obtain sensitivity is npv/ pv of flows affected. what would happen if say more than one flows get affected ? will pv of of both the flows be added up and substituted in the formula you mentioned to get sensitivity?

John Moffat says

We can only calculate the sensitivity of one flow at a time (unless two or more flows are directly connected, in which case we would add them up).

May says

Dear Sir,

I used Discount factor at 17% and NPV is -2231, IRR is 16.41 (15%+(5329/7560 x 2%)

So Sensitivity of capital= (16.41-15) / 15 x 100% = 9.4%

Am I right? Thanks sir.

John Moffat says

There is an answer at the back of the lecture notes.

Salman says

Dear sir,

If there are more than one critical factors, hence the investment has high uncertainty. Can we decide after sensitivity analysis that we should not go ahead with this investment as we may most probably lose money?

To further confirm our decision, should we perform some of the below analysis:?

1. Probability analysis – Expected values

2. Using risk-adjusted discount RATE

3. Adjusted payback PERIOD

4. Simulation

So before accepting an investment from the proposed investments/projects, we do the above analysis to assess its risk and then decide to accept it or not.

Please see if I need correction. Thanks.

John Moffat says

You are correct, except that you will not automatically decide not to do a project – it is just that the more uncertainty there is the more you might decide not to risk going ahead.

It is not a problem in the exam – you accept or reject based on whether the NPV is positive or negative. But for written parts you must be able to discuss the relevance of uncertainty.

pejz says

dear John

my question about the scrap value is why was the value of 15000 discounted and not taken as 15000. thank you for your valued response

John Moffat says

Because the project is scrapped at the end of its life, and so the 15,000 is received in 15 years time.

Candy says

Mr Moffat,

But why in previous example such as Lease vs Buy did we not discount the Scrap?

John Moffat says

But it was discounted – it is always discounted. Obviously not when the asset is leased because then there are no scrap proceeds.

Candy says

I take from this that we have to be extremely careful with reading the question and determining what is being stated.

In Lease buy example it states “will have a scrap value after 4 years of $10,000.”

Whereas in this example it states “final scrap value of $15000”.

I do find this tricky, because if someone tells me there will be a final value of£xxxx. I take that to mean that is the amount that will be available.

John Moffat says

You certainly have to read the question carefully.

In the lease buy question it is made very clear that the scrap value is only relevant if the machine is purchased.

In the sensitivity question is says that the final scrap value is 15,000, and scrapping can obviously only occur at the end of the projects life!

maria says

Hello, Mr. Moffat!

I got the overall idea, but confused with sensitivity for sales volume. Can we use PV of revenue instead of contribution? Follow the same logics: if sales volume fall by 10%, revenue fall by 10% and PV fall by 10%. Same as for contribution.

Why don’t we have the same answer as for contribution, if everthing else remain constant?

(The question appeared while practicing specimen exam for Sept.2016, question 2).

Thank you in advance!

Moloantoa says

hallo JOHN!!

i did not get the meaning of -/+ sings on the percentages when deriving the sensitivity

regards

John Moffat says

It depends whether increasing the flow is what will cause problems (in which case it is + ) or whether the flow decreasing will cause problems ( in which case it is – )

Auret says

Mr. Moffat, am I correct in saying that when calculating the PV for Cash inflow in Question 1 (a) only using contribution and not price can only be done if price (and variable cost) remain constant?

John Moffat says

Yes – you are correct 🙂

Arun says

Hi John,

Something that worries me is that I understood the whole lecture but I got parts iv and v wrong because in both cases I divided the NPV by the fixed costs (15,000) in part iv and by the scrap value (15,000) in part v and consequently got the wrong answer.

But my understanding was that I wanted to know the percentage change in fixed costs or scrap value because that would ultimately bring the present value of that particular flow down by the same percentage resulting in a NPV of zero and that’s what we are doing, aren’t we. Where am I wrong then?

Thanks in advance!

John Moffat says

For the NPV to end up at zero, the PV of the relevant flow has to change by the amount of the current NPV.

So, for example, if the NPV is 100, and the PV of the fixed costs is 1,000. Then for the NPV to fall by 100 to zero, the PV of the fixed costs will have to increase by 100.

In percentage terms this is 100/100 = 10%

It is always the NPV divided by the PV of the flows that change (expressed as a %).

Kelvin says

Mr John nice to know you

I greatly need your help on sensitivity analysis

It on the fact that how to calculate sensitivity of selling price

John Moffat says

You take exactly the same approach as for the others.

Calculate the present value of the revenue flows (because they are the flows that will change if the selling price changes).

The sensitivity is then the NPV as a percentage of the PV just calculated.

aliimranacca007 says

Dear sir in example in solution for senstivity of cost of capital

by using IRR rate 15.84% and given rate is 15%

in calculation of senstivity of cost of capital you do.

0.84÷15 why you do like this bcoz by formola as you told it will be NPV ÷ pv of variables

John Moffat says

It should be clear that it would be silly to divide a % by a PV. For cost of capital we have to go back to the basis logic and divide the change needed (0.84) by the current value (15)

questforknowledge says

thank you sir John

questforknowledge says

Hi John, permit me ask you this question. how do you go about calculating the sensitivity of the price. I mean the percentage of the price change that will lead to the NPV falling to zero

thank you

John Moffat says

For this particular example we can not, because we do not know the estimated selling price.

In general terms you would take the same approach as the others i.e. express the NPV as a % of the present value of those cash flows that would change (which in the same of the price would be the sales revenue flows).

questforknowledge says

you mean NPV/ present value of sales revenue? this will give me the percentage change in sales revenue. I am preparing for P4 and there is this question Dec 2012 question that asked for this. when i tried going through the solution i didnt understand how it was solved. If use this your approach i will get the percentage change in sales revenue but the question asked for sales price

John Moffat says

But surely, if the sales price changes by 10% then the revenue changes by 10% as well!

(I know it could be affected by other things, but with sensitivity we can only consider one item at a time)

One other thing is that if there is tax in the question, then the flows that will change if the selling price changes will be the revenue and the tax on the revenue. So you need the net PV of these two. Then express the NPV of the project as a % of it.

brenda1 says

Thanks John,

an issue here,when we are calculating the sensitivity of change on for example part (iii) which is contribution p.u, why do we put that negative sign yet in our table the final value was a positive??

John Moffat says

To show that we are only worried about the contribution falling. (If the contribution increased then there would be no problem at all)

cartea says

Now the F9 carries a MCQ do I need to read the text book from cover to cover, or your notes, lectures and the kit will be sufficient to help me pass the exam.

John Moffat says

Our notes and lectures (together with lots of practice using a Revision Kit) are enough to be able to pass the exam.

cartea says

Thank you very much. I understand your lectures more than the text book and and my lecturer. I hope you keep on lecturing we need you.

arman90fy says

Hello Sir,

why lower the sensitivity—> the more worried about item.? how about the higher sensitivity, is the higher sensitivity more optimal? could u plz explain it again. thanks

John Moffat says

Its not really a question of calling it the optimum.

The problem is that we are making a decision on forecasts of cash flows, and therefore the actual cash flows may turn out to be different – if they are different then the NPV might turn out to be negative and then we will have made the wrong decision.

The higher the sensitivity the less the chance is of that flow changing enough to affect the decision. However if the sensitivity is low, then it means that even just a small change in the flow will affect the decision. Therefore the lower the sensitivity the more risk we are taking and therefore the more we will try to estimate the flow accurately (or else maybe decide not to take the risk).

arman90fy says

great explanation dear sir

thanks alot

May says

Sorry! My Apologist! I still did not get what you mean by lower sensitivity = more”worried” about item.

izhar says

Sir if calculation of tax given then how we calculate present value of relevant cash flow ?

jay0v says

Thank you sir! 😀

jay0v says

Sir, will the requirements be given in exam asking us which sensitivity to calculate, the initial investment, sales volume, selling price, etc.?

John Moffat says

Yes certainly:-)

If the question wants the sensitivity then it will specify of what.

DIANA says

Can someone explain about he -289 in scrap…

John Moffat says

The PV of the scrap is 1845.

This would have to fall by 5329 to end up with a NPV of zero.

So in percentage terms this is a fall of 5329/1845 x 100% = 289%

However (as I do state in the lecture) this is ridiculous because it would mean that the scrap value would have to be negative! Usually, obviously the most it can fall is 100% down to zero. So you would state that the scrap is not sensitive at all.

(The only time it could possibly be relevant is if there were a possibility of us having to pay money to scrap the machine, which is very unlikely)

DIANA says

Understand…thx u sir!

John Moffat says

You are welcome, Diana 🙂

Demmypet says

Hi Mr John,

I still dont understand how you arrived in the postive and negative sign from question i to v.

can you please explain how you derive at the figures being -tve or +ve.

many thanks

John Moffat says

What you have to ask yourself is will it make the NPV worse if it gets higher or lower.

So, for example, as far as the revenue is concerned, we are only worried if it should fall – so the sensitivy is negative (it measures the percentage fall that we can afford).

But as far as the cost of capital is concerned, we are only worried if it should increase – so the sensitivity is positive (it measures the percentage increase that we can afford).

Demmypet says

Wow, Now i understand. Many thanks for your quick response.

Your lectures has been great!

John Moffat says

Thank you 🙂

acca2050 says

Hey John, Why u didn’t do cost of captial sensitivity? However I done it by my self and the IRR comes = 15.842%. I took 20% as another npv that resulted in ($26306).

Now as per your formulae: NPV/PV of changes x 100% = 15%/15.842% x 100% = ~95%

BUT I think its wrong?

John Moffat says

Errrr….yes you are wrong 🙂

The change is 15.842-15 = 0.842.

So the percentage change from the actual cost of capital is 0.824/15 x 100% = 5.5%

(The answers to all of the examples are at the back of the Course Notes 🙂 )

acca2050 says

ok cool 🙂

George says

Hi John,

I had a go at part VI to test that I remembered IRR. heres the thing- I chose 16% as my comparative rate of interest and therefore got an NPV of -2036

therefore my calculation for IRR was (5329/7365)+15% = 15.72%

Surely IRR cannot be tested in the MCQ because there is no set rule for the comparative rate of interest?

I trust the examiner will have thought about this 🙂

Thanks for the lectures- they have been great so far albeit that i’m a little behind schedule for the March exam

John Moffat says

The examiner certainly can (and has) asked MCQ’s calculating the IRR.

He can do this either by specifying which ‘guesses’ to use in the calculation, or by asking for it to the nearest %’age.

Oboro says

Pls sir I still do not understand why sales volume is -2.2%

John Moffat says

At present the NPV is 5329, and we need to know the % fall in sales volume that will give NPV of zero.

If the sales volume per year falls, then the contribution per year falls, and therefore so too will be present value of the contribution flows. At present the present value of the contribution flows is 241189 – we need this to fall by 5329, which is a 2.2% fall.

kaish says

and what about section c answer?

John Moffat says

You can find the answer at the back of the course notes.

Mohieddin says

I wish you taught all papers sir ! 🙂

fergalfavier says

I can see all the comments but not the online lecture…?

fergalfavier says

Downloaded Chrome, worked thank God!

eadinnu says

It happened to me. What I did was to delete the cookies on the the browser and I started seeing the lectures.

I also installed another browser. this option also worked.

Yando says

Wow, couldn’t be better. Nevertheless, if a question asked us to evaluate sensitivity for sales volume, sales price and variable cost it appears we would have the same change in the variables (for all of them) if we only calculated the PV for contribution only and not the independent variables i.e. separate PV for sales price and variable cost respectively. What I want to know is that wont such an approach limit us on the marks awarded?

John Moffat says

They would not be the same.

Sales price will have a different effect (and therefore a different sensitivity) than sales volume (with sales volume the contribution per unit remains the same, but if sales proie changes then the contribution per unit changes). So too will the variable costs.

Yando says

Thanks a lot. I get it.

adeel15 says

i am confused about the last part cost of capital sensitivity?? please can anyone tell me in detail the whole working including IRR please help me out….

Yando says

@adeel15, you can easily understand this if you went back to the video on the IRR. I have found it to be easy actually. Remember that the IRR gives you the cost of capital that will result into NPV of Zero. Compare that IRR (which you must calculate with the information in the question) with the cost of capital (we have been given). The difference in percentage terms is the sensitivity on cost of capital.

efyamav says

better

nisi11 says

cant we download this

?

admin says

No, you can watch lectures on line only

danielglover says

P.g 147 The answer for example 1 (vi) IRR (middle page).

Is the D.F wrong for (15,000 fixed costs)

Should the D.F be the same for (41,250 Contribution) ie. 4.675

tiffanytoon says

How to get the sensitivity of cost of capital =+5.6%

why using 0.84/15 x 100%,can anyone help?Thanks.

John Moffat says

@tiffanytoon, The cost of capital is 15%. For a NPV of 0, the cost of capital would have to be 15.84% (the IRR). So we can afford the cost of capital to change by 0.84 (15.84 – 15) from an existing 15.

In percentage terms, this is a change of 0.84/15 x 100 = 5.6%

tiffanytoon says

@johnmoffat, thanks & like your clear explanation.

amytan says

The screen is too small, I couldn’t view, can someone tell me what to do!!

John Moffat says

@amytan, On the right hand side of the bar at the bottom of the screen is a symbol with 4 little arrows. If you click on it, then the video should be full screen.

eyal says

Does anyone have the answer for IRR% for this question???

admin says

Look in the course notes

Answer should be there

sunflowerdragon says

hi. i used the same approach for sensitivity for qn dec 01 tower railways inc. i got 2003/10771 X 100% = 18.6% 🙁 no where near their ans. of 20.87% or fall in px of $2.50. Moreover their explanations n calculations are far more confusing !! pls help !!! tks

gracetsiga1 says

why is the contribution and the scrap a negative %?

John Moffat says

@gracetsiga1, This has already been answered below. The negative indicates that we only have a problem if the contribution falls.

manjeet12345 says

hi i’m new to this and i need some advise on how many sub to do this time.. I’m doing f8 and p2… and i had to fill my form for f9 as well in order to do my p2…I dont know shall i do f9 or shall i leave it for next term..

dayah says

i cannot understand why the sensitivity to change of sales volume is negative

chapter 10 1b)

help

louis06111 says

@dayah,

In my opinion, we are currently getting a NPV of +5329, in order to result in a NPV of zero(Breakeven analysis), we can let the sales volume to drop by that percentage.

And hence, it is negative.

Similarly, we can let the cont. p.u. to drop by 2.21%, it’s also negative.

That’s the conclusion I came to and I hope it will help,

chandandabs says

quality of F9 lectures is much much higher than that of F7 🙂 🙁