However, I’m still confused with examiner’s answer re: Q4 June 2011 MMC, option to delay. The call option=$9.53m=full value of project with option to delay. because NPV is negative -2.98m =value of the project without option is -2.98m, so the value added by option should be 9.53-(-2.98)=12.51.

I don’t understand the examiner’s answer below:
Overall value of the project = $9·53m – $2·98m = $6·55m.
I thought overall value is $9.53m??

I get confused with the full value of project. The value of the call option to delay is 3.92m, does it mean the company has to pay 3.92m to buy this option to delay the project? id it is the case, then NPV=2m, the full value of the project will be 2-3.92=-1.92. the company made a loss?

Thanks. by looking at the answer in notes, I realise that 3.92m is full value of the project with the option, so without option is NPV 2m, the value of option is 1.92m which is different from the lecture. Is it right?

The difference is that the option in the lecture notes is an option to delay the existing project, but the March/June question was the option to expand – effectively to do the project as it is but to have the option to invest more and get more (almost like the option to do an extra project).

I’m a bit confused, in the lecture and comments below you have explained that 3,92 makes the value of the whole project greater than it would have been without the option to delay and the full value of the project is 5.92. However in this comment and in lecture notes the full value is 3,92.

In the example we take Pa as 12m as the value of the project. Shouldn’t we be taking Pa as 2m ie the NPV as that can also be denoted as the value of the project?

I don’t really understand why that makes it less confusing. You must have a scientific calculator in the exam and it should have a button for e^x, and using that button is a bit faster than typing out e to 5 decimal places 🙂

Maybe i did not understand his problem but from the way i understood it i think it has to do with him using his scientific calculator cause nothing can be confusing about that e .

Hi,
I find the most confusing part to define Pa and Pe. in this case maybe these variables are more straightforward, but in other cases like adandon, redeploy or expand they are less clear. Could you please provide guidelines how to define these variables.

Because you have the option to invest at a fixed cost on a future date (just like a call option for shares gives you the right to buy at a fixed price on a future date).

in the question 3 (DIGUNDER) of Dec 07 past question., how was the current price /PV of the project arrived at to be $28m? PV given in the question was $4m.

No – the $4m given in the question is the NET present value.
Since the cost is $24M, it therefore means that the PV of the returns is $28M

(PS If you want me to answer a question then please post it in the Ask the Tutor F5 Forum – it is not possible for me always to read all the comments under lectures 🙂 )

Hi John, I’m sorry but the question below confused me, could you please clear it out? thanks much appreciated 🙂

June 2012 Q1 part iii)

In the Model Answers the examiner answers it in the following way:
Price of asset (PV of future positive cash flows) = $2,434,000
Exercise price (initial cost of project, not discounted) = $2,500,000
Time to expiry of option = 2 years
Risk free rate (estimate) = 3·2%
Volatility = 42%
d1 = [ln(2,434/2,500) + (0·032 + 0·5 x 0·422) x 2]/(0·42 x 21/2) = 0·359 (in normal distribution tables is = .1368)
d2 = 0·359 – (0·42 x 21/2) = –0·235 (in normal distribution tables is = .0910)

N(d1) = 0·5 + (0·1368 + 0·9 x (0·1406 – 0·1368)) = 0·6402 ***What is the + 0·9 x (0·1406 – 0·1368 part??
N(d2) = 0·5 – (0·0910 + 0·5 x (0·0948 – 0·0910)) = 0·4071 **What is the + 0·5 x (0·0948 – 0·0910)) part??

***Shouldn’t it just be N(d1)= 0.5 + 0.1368 = 0.6368
**Shouldn’t it just be N(d2) = 0·5 – 0·0910 = .409
:/

It is because the tables only have two decimal places when you are looking up. So for 0.359 he has taken 90% of the way between 0.35 and 0.36.
Similarly, for 0.235 he has taken half way between 0.23 and 0.24.

I don’t think you would lose any marks for not doing that (and therefore just going to the nearest) even though your final answer would be slightly different.

Sir in this example u have added the value to delay the option to the NPV. BUT there is a question of past paper DIGUNDER of Dec 07. kaplan in its previous answer have added the value of option (i.e 7.48) with projects npv (i.e. 4). When they have amended in new edition they just write as 7.48 which incldes 4m intrinsic value and rest is time value. please resolve my query whether the value of project would taken after addition or the value got from the formula is the eltimate answer?

Dear Sir,
is one expected to switch between discrete and continuos rates within such tasks (e.g., if the same risk-free rate given for project appraisal is expected to be used also for pricing of a real option)?
The difference isn’t likely to exceed a couple of bps, so my concern is mostly methodology.
Thank you very much for support,

Thank you very much for your answer. Could you please comment in a little bit more detail on the following:
when I’m calculating the NPV, the rates given are assumed to be discrete, so the P1=P0(1+R1), etc, but when I calculate the value of a real option, I apply the Black Scholes formula, which in general case assumes continuous compounding . So my question was, in fact, whether I am supposed to convert the risk-free rate to continuous setting before pricing the option, or whether this can be ignored.

We do not have lectures on all topics – more will be added as time permits.
Mergers and acquisitions are an important area – they are covered in the course notes (and most of the techniques involved are covered in other lectures).

Hi John, you know some of us rely on these your lectures to understand some of these topics because most are new to us: i know your services are free and on behalf of all those using this site i would like to say thank you: but leaving some topics at this level of the course will mean making things difficult: it will prefereable the topics that were covered in an earlier course be left out than leaving out something new at this level
thank you

Firstly, we do not pretend to offer a distance learning course. We provide everything on the site voluntarily in our spare time to try and help people. We make it clear that we are not trying to replace study texts.

Secondly, mergers and acquisitions are best not regarded as a separate topic for learning. As with so much of P4 it draws upon existing knowledge (there is not so much extra to learn at P4 than what has already been learned at F9) but expects more depth. This is not a topic that I actually lecture much on during courses I teach – instead we look at past exam questions and sort it out from there. Again, we make it clear on this website that it is so important to practice questions – at the very least past exam questions, but preferably using an exam/revision kit from one of the approved publishers.

Hello,
Thank you very much for a brilliant lecture.
I have a question. In share option lecture you expressed that the value of the option is what we pay for the option now. Is it same for the real option? Does it mean, as in example 1, we pay now $3.90m to buy option to delay – call option?
Can you please also clarify what is behind of the full value of project of $5.9m
Thanks

It does not mean that we pay 3.90 now – it means that the option is worth that much to us. It makes the value of the whole project greater than it would have been without the option to delay.

Sir, just some clarification please. In June 2012 exam Q1 (iii) which dealt with delaying the project I noticed they used a different method to calculate N(d1) & N(d2), does that mean I can use EITHER method in the exam? Which is the preferred option?
Thank you –

The examiner has not used a different method. It is simply that the tables only have 2 decimal places for d and so he has made it slightly more accurate by approximating to a third decimal place.
Although it does make it a little more accurate, you do not really need to do this in the exam – just take d to the nearest 2 decimal places.

It is certain that i will pass P4 now, brilliant lecture. Please can we have videos for the other options as well? and for (The valuation of acquisitions and mergers)?. This will be helpful a lot.

Thanks alot for the great lecture! May I ask where I could find the lecture for chapter 16(The valuation of acquisitions and mergers)? Are there any vedios are for example 1 (calculate the economic value added)?

Sir..kindly late me know, in making decision of delay or proceed..i am going to compare present npv with value of call option???? that is $2m with $3.92

Thank you for the lecture.it was easy and straight forward but please could you tell me what the full value of the project will be compared to,as the video cut the decision aspect out.

@achalaand, sorry – there is a mistake (the synergistic benefit is 7 p.a. after tax, but the answer has it as 5 p.a.). The updated course notes have corrected this mistake.

I was also looking for part 2 of this video. The video ends before the lecturer finishes with his explanations and when you read technical article on real options it seems like there are still more matters that the videos could discuss concerning around this matter….

helensqq says

Thanks John,

However, I’m still confused with examiner’s answer re: Q4 June 2011 MMC, option to delay. The call option=$9.53m=full value of project with option to delay. because NPV is negative -2.98m =value of the project without option is -2.98m, so the value added by option should be 9.53-(-2.98)=12.51.

I don’t understand the examiner’s answer below:

Overall value of the project = $9·53m – $2·98m = $6·55m.

I thought overall value is $9.53m??

John Moffat says

The examiners answer was wrong (and he has since accepted this).

What you have written is correct 🙂

helensqq says

hi John,

I get confused with the full value of project. The value of the call option to delay is 3.92m, does it mean the company has to pay 3.92m to buy this option to delay the project? id it is the case, then NPV=2m, the full value of the project will be 2-3.92=-1.92. the company made a loss?

Thanks.

John Moffat says

It is not that they are paying for the option.

If the option exists then the project is more beneficial than if it does not exist.

helensqq says

Thanks. by looking at the answer in notes, I realise that 3.92m is full value of the project with the option, so without option is NPV 2m, the value of option is 1.92m which is different from the lecture. Is it right?

John Moffat says

That is correct

cyh says

Hi Sir,

i refer to the March/June 2016 SAMPLE Question 4, real option.

The NPV of the project is -1.01M, the call option is 1.36M, so the overall value is 1.36-1.01=0.35.

This is different from what u reply on 28 November 2016, so i am confused now.

John Moffat says

The difference is that the option in the lecture notes is an option to delay the existing project, but the March/June question was the option to expand – effectively to do the project as it is but to have the option to invest more and get more (almost like the option to do an extra project).

cyh says

so for the delay/abandon option, total value of project would be the value of the option

for the expand option, the total value of project would be the value of the option + original NPV.

am i correct?

John Moffat says

That is correct 🙂

cyh says

c=3.92m. how do we interpret this amount ? NPV is 2M, so the total NPV + delay option is 2+3.92= 5.92M?

or total NPV + delay option is 3.92m, and the delay option is worth 3.92-2=1.92M?

John Moffat says

The second line.

cyh says

how about the put option? if p = $3m, NPV is 2m, so the abandon option is worth 3-2m=1m?

John Moffat says

Correct.

Pavel says

I’m a bit confused, in the lecture and comments below you have explained that 3,92 makes the value of the whole project greater than it would have been without the option to delay and the full value of the project is 5.92. However in this comment and in lecture notes the full value is 3,92.

Can you please explain it in more details.

Thanks a lot!

John Moffat says

The comment above and the answer in the lecture notes are correct, and I must re-record the lecture – thank you for reminding me.

My excuse is that I did in the lecture what the examiner did in his answer the first time calculations on real options were asked.

More recently the examiner realised he was wrong! I will re-record the lecture. (All the other figures will obviously remain unchanged)

Pavel says

Thank you so much!

John Moffat says

You are welcome 🙂

Arun says

Hi John,

In the example we take Pa as 12m as the value of the project. Shouldn’t we be taking Pa as 2m ie the NPV as that can also be denoted as the value of the project?

Thanks.

John Moffat says

The value of the project is the PV of the future flows – not the NPV. The NPV is the value of the returns less the investment.

zee says

Dear Sir,

I’m struggling to perform the calculation on the last part of the call option formula, that is with the “e”. Can you please clarify one by one.

John Moffat says

Have you watched the lectures on normal option pricing, because I go through the steps slowly in that lecture?

tich2010 says

Instead of using e use 2.71828 that will make the calculation not confusing.

John Moffat says

I don’t really understand why that makes it less confusing. You must have a scientific calculator in the exam and it should have a button for e^x, and using that button is a bit faster than typing out e to 5 decimal places 🙂

tich2010 says

Maybe i did not understand his problem but from the way i understood it i think it has to do with him using his scientific calculator cause nothing can be confusing about that e .

Rst says

Hi,

I find the most confusing part to define Pa and Pe. in this case maybe these variables are more straightforward, but in other cases like adandon, redeploy or expand they are less clear. Could you please provide guidelines how to define these variables.

Darren says

d2 was .8727, why did we round to .88 and not .87 when looking for N(d2)?

John Moffat says

My mistake – I should have used 0.87 (or even better apportioned between 0.87 and 0.88, but there is no real need to do that).

sogan0 says

Hi Lecture how do you arrive to 0,.3888 I understand how to get to 1,2 in the table but not how to get to 0.3888

John Moffat says

You look to the row for 1.2 and the column for 0.02

I don’t know if you have watched the previous lectures on share options, but I spend time in that lecture showing how to use the tables.

badmus4u says

Why and how is the option in the example a call option? I did not really get the justification.

Thanks

John Moffat says

Because you have the option to invest at a fixed cost on a future date (just like a call option for shares gives you the right to buy at a fixed price on a future date).

badmus4u says

Oh I get. Thanks a lot.

sogan0 says

Thank You

Fabregas says

Sir,

Can you please add an option to adjust the speed of the video? Although it is very informative, I find it hard to concentrate at a low pace.

Thank you

gabby11 says

in the question 3 (DIGUNDER) of Dec 07 past question., how was the current price /PV of the project arrived at to be $28m? PV given in the question was $4m.

John Moffat says

No – the $4m given in the question is the NET present value.

Since the cost is $24M, it therefore means that the PV of the returns is $28M

(PS If you want me to answer a question then please post it in the Ask the Tutor F5 Forum – it is not possible for me always to read all the comments under lectures 🙂 )

yohanxtech says

Hi John, I’m sorry but the question below confused me, could you please clear it out? thanks much appreciated 🙂

June 2012 Q1 part iii)

In the Model Answers the examiner answers it in the following way:

Price of asset (PV of future positive cash flows) = $2,434,000

Exercise price (initial cost of project, not discounted) = $2,500,000

Time to expiry of option = 2 years

Risk free rate (estimate) = 3·2%

Volatility = 42%

d1 = [ln(2,434/2,500) + (0·032 + 0·5 x 0·422) x 2]/(0·42 x 21/2) = 0·359 (in normal distribution tables is = .1368)

d2 = 0·359 – (0·42 x 21/2) = –0·235 (in normal distribution tables is = .0910)

N(d1) = 0·5 + (0·1368 + 0·9 x (0·1406 – 0·1368)) = 0·6402 ***What is the + 0·9 x (0·1406 – 0·1368 part??

N(d2) = 0·5 – (0·0910 + 0·5 x (0·0948 – 0·0910)) = 0·4071 **What is the + 0·5 x (0·0948 – 0·0910)) part??

***Shouldn’t it just be N(d1)= 0.5 + 0.1368 = 0.6368

**Shouldn’t it just be N(d2) = 0·5 – 0·0910 = .409

:/

John Moffat says

It is because the tables only have two decimal places when you are looking up. So for 0.359 he has taken 90% of the way between 0.35 and 0.36.

Similarly, for 0.235 he has taken half way between 0.23 and 0.24.

I don’t think you would lose any marks for not doing that (and therefore just going to the nearest) even though your final answer would be slightly different.

minhajh says

But I want to ask Mr tutor how the examiner estimated the risk free rate of 3.2%. Please can you calculate me this?

John Moffat says

The question says that Nente pays interest of 7% which is 380 basis points above government base rate.

7% – 3.8% = 3.2% !

minhajh says

Where in the normal distribution table the amount of 0.359 and 0.235 shows?

John Moffat says

I have answered this in my answer two above.

NEENA says

Sir in this example u have added the value to delay the option to the NPV. BUT there is a question of past paper DIGUNDER of Dec 07. kaplan in its previous answer have added the value of option (i.e 7.48) with projects npv (i.e. 4). When they have amended in new edition they just write as 7.48 which incldes 4m intrinsic value and rest is time value. please resolve my query whether the value of project would taken after addition or the value got from the formula is the eltimate answer?

John Moffat says

Without the option, the value of the project is simply the NPV.

If we do have the option, then the option itself has a value.

So…..the value of the project together with the option is higher. It is the NPV plus the value of the option.

ibarats says

Dear Sir,

is one expected to switch between discrete and continuos rates within such tasks (e.g., if the same risk-free rate given for project appraisal is expected to be used also for pricing of a real option)?

The difference isn’t likely to exceed a couple of bps, so my concern is mostly methodology.

Thank you very much for support,

John Moffat says

Within the same question, yes – assume rates are the same for all parts unless, obviously, you are told differently.

ibarats says

Thank you very much for your answer. Could you please comment in a little bit more detail on the following:

when I’m calculating the NPV, the rates given are assumed to be discrete, so the P1=P0(1+R1), etc, but when I calculate the value of a real option, I apply the Black Scholes formula, which in general case assumes continuous compounding . So my question was, in fact, whether I am supposed to convert the risk-free rate to continuous setting before pricing the option, or whether this can be ignored.

Thank you once again,

John Moffat says

No – the formula does the continuous compounding. (That’s what the ‘e’ part of the formula is doing)

questforknowledge says

hello sir, if i may ask, why dont’t we have lectures on mergers and acquisitions? is it not an important area of the syllabus for the exam?

John Moffat says

We do not have lectures on all topics – more will be added as time permits.

Mergers and acquisitions are an important area – they are covered in the course notes (and most of the techniques involved are covered in other lectures).

questforknowledge says

Hi John, you know some of us rely on these your lectures to understand some of these topics because most are new to us: i know your services are free and on behalf of all those using this site i would like to say thank you: but leaving some topics at this level of the course will mean making things difficult: it will prefereable the topics that were covered in an earlier course be left out than leaving out something new at this level

thank you

John Moffat says

Two things:

Firstly, we do not pretend to offer a distance learning course. We provide everything on the site voluntarily in our spare time to try and help people. We make it clear that we are not trying to replace study texts.

Secondly, mergers and acquisitions are best not regarded as a separate topic for learning. As with so much of P4 it draws upon existing knowledge (there is not so much extra to learn at P4 than what has already been learned at F9) but expects more depth. This is not a topic that I actually lecture much on during courses I teach – instead we look at past exam questions and sort it out from there. Again, we make it clear on this website that it is so important to practice questions – at the very least past exam questions, but preferably using an exam/revision kit from one of the approved publishers.

questforknowledge says

thank you John for taking your time to explain things. may God bless youi

tuenli says

Hello,

Thank you very much for a brilliant lecture.

I have a question. In share option lecture you expressed that the value of the option is what we pay for the option now. Is it same for the real option? Does it mean, as in example 1, we pay now $3.90m to buy option to delay – call option?

Can you please also clarify what is behind of the full value of project of $5.9m

Thanks

John Moffat says

It does not mean that we pay 3.90 now – it means that the option is worth that much to us. It makes the value of the whole project greater than it would have been without the option to delay.

edu1care says

Sir, just some clarification please. In June 2012 exam Q1 (iii) which dealt with delaying the project I noticed they used a different method to calculate N(d1) & N(d2), does that mean I can use EITHER method in the exam? Which is the preferred option?

Thank you –

John Moffat says

The examiner has not used a different method. It is simply that the tables only have 2 decimal places for d and so he has made it slightly more accurate by approximating to a third decimal place.

Although it does make it a little more accurate, you do not really need to do this in the exam – just take d to the nearest 2 decimal places.

lakeside says

It is certain that i will pass P4 now, brilliant lecture. Please can we have videos for the other options as well? and for (The valuation of acquisitions and mergers)?. This will be helpful a lot.

Thanks

constanceqin says

Thanks alot for the great lecture! May I ask where I could find the lecture for chapter 16(The valuation of acquisitions and mergers)? Are there any vedios are for example 1 (calculate the economic value added)?

syedwaqar says

HELLO!

Sir..kindly late me know, in making decision of delay or proceed..i am going to compare present npv with value of call option???? that is $2m with $3.92

Regards

John Moffat says

@syedwaqar, You don’t compare them. The option makes the project worth more than if the option did not exist.

oreomolabake says

Thank you for the lecture.it was easy and straight forward but please could you tell me what the full value of the project will be compared to,as the video cut the decision aspect out.

achalaand says

Can you please explain me that how cash flows have been arrived in the given answer of Example 02 in Chapter 16…???

John Moffat says

@achalaand, sorry – there is a mistake (the synergistic benefit is 7 p.a. after tax, but the answer has it as 5 p.a.). The updated course notes have corrected this mistake.

y.prananv says

This lecture was awesomeeee!!!…..However, can you please upload a video on option to abandon/redeploy please?:)

nkechiokoro says

thank you so much for the lecture, but i want to find out if all real options will always be a call option?

utn9 says

@nkechiokoro,

Delay and Expand are Call Options

Redeploy and Abandon are Put Options

sheda100 says

Sir, pls was the conclusion/decision to delay the project based on the fact that it has a positive value. Thnx

accaforall says

thank you very much:)

this was very helpful

yengibaryan says

I could watch only part of the video:( There was some problem in the middle

abiose says

thank you, this was brief but clear

pissukade says

N(d2) rounding off error? answers in the back of course notes has the right answer.

Sam says

Yeah, it should be 0.87 which translates to 0.3078 on the SND table

viviankyc82 says

hi is there suppose to be a part 2 for this video? thanks

admin says

there is not part 2, if it was mentioned in the lecture, it was a mistake

Adelino says

I was also looking for part 2 of this video. The video ends before the lecturer finishes with his explanations and when you read technical article on real options it seems like there are still more matters that the videos could discuss concerning around this matter….

John Moffat says

There is no part 2. The free lecture notes discuss other matters.