First of all, thank you @John Moffat for all your videos and support it has truly helped me through my studies.
I just want to make sure my understanding is correct, with WACC we calculated Ke and Kd, due to the tax savings of debt the WACC is reduced as gearing increases, therefore the NPV increases.
The effect of the above is similar to APV in that although we do not use Kd to discount the C.F. to obtain the NPV, we do incorporate the tax shield element in the second step and the sum of NPV and financing effects gives the APV.
The result of using WACC or APV (given we have all necessary information in the question) should therefore result in more or less the same answer as each other because the decrease in WACC comes from the tax savings adjusted in Kd and the tax savings is what we are adding when calculating APV.

Yes, except for two things. Using M&M to get a cost of equity for the project and then using this to get a WACC assumes that the debt is irredeemable, whereas with APV we can deal with redeemable debt. Secondly, when using the WACC the NPV will be the gain to shareholders which changes the gearing and hence the WACC and so we go round in circles a bit 🙂
Whenever there is a significant change in the gearing, APV is the better approach.

Sorry to dip my little fly in your ointment, but if we are taking the saving of the tax on the debt into consideration, why are we not taking into account the interest charge?

NPV of the project gain = $19.64
Tax shield = $9
Interest charge on debt = $?

If you remember from M&M, without tax it would be irrelevant whether we used debt finance or not – the NPV would be the same.
With tax, the only difference is due to the tax saving on the debt interest.

Hi Sir, i refer to you example 2 and the question from BPP text book as below:

(A company is considering a project that would cost $100,000 to be financed 50% by equity (cost 21.6%) and 50% by debt (pre-tax cost 12%). The financing method would maintain the company’s WACC unchanged. The cash flows from the project would be $36,000 a year in perpetuity, before interest charges. Tax is at 30%.

Appraise the project using APV method.)

I have no idea how to apply your example 2b techique to solve this BPP question as in this question no risk free rate figure was given

I’ve tried Question 34 Strayer Inc. It says that the company is considering to invest $25m, which willbe financed by internal funds-6m, rights issue-10m and loans-9m.

There is no note whether these are quoted net of issue costs or not.

So, when calculating the isuue costs don’t we need to gross them up?

In the answer to this question issue costs are calculated on 10m and 9m respectively without grossing up.

If you are not required to calculate the APV then we just calculate the NPV by discounting the cash flows at the WACC. (You will probably need to use CAPM to calculate the cost of equity, which is obviously needed to get the WACC).

Hi John the lecture is very nice and you have made it very simple but what about issue cost of debts and equity and things like government grants
thanks

The purpose of the lecture is to explain the M&M equations and to explain the reasoning and method of APV.

In a full exam question there are lots of extra things involved (for example, arriving at the cash flows int he first place in order to be able to then calculate the APV will be a lot more complicated). However, they are not ‘technical’ or ‘theoretical’ issues that I am trying to explain in the lecture.

On courses, after explaining APV etc. the students then practice past exam questions and it is then that we sort out problems with the cash flows, the issue costs etc.. None of them are theoretical problems and it is impossible to teach every little ‘trick’ that can be in a question – that can only be got from practicing lots of questions.

when the debt is redeemable, would this not mean that there is an extra cash flow to consider (cash flow being the principal being repaid) at the end of the project?

Yes there will be the repayment, but this will not be tax allowable – for APV we are calculating the tax saving due to debt, which only applies to the interest.

I have tried to rework example 2b using the Beta and always get back to a wacc of 18.2 (1.5=Xx70/91=new beta of 1.95x(15-5)+5=24.5% x.7=17.15 + (3.5x.3=1.05) total 18.2 Annuity = 3.113x40M=124.52.) To get to 128.64 the annuity needs to be 3.214 = 16.8!) where am I going wrong?
Thanks

The problem is that although the finance is being raised 70% equity and 30% debt (so 70M from equity and 30M from debt), there will be a gain from doing the project, and the gain will all go to the shareholders.

That will mean that the value of the equity in the project will be higher than 70M (because of the gain) but the debt in the project will stay at 30M.

So the gearing will be a bit different, and so it is not valid to use 70%/30% in the asset beta formula, or when calculating the WACC.

(You could do it this way by using algebra, but it gets very messy and I really would not waste your time on it – trust me, it will work! But in the exam you would be specifically asked for the APV and so doing it any other way would be wrong anyway.)

Question regarding example 2 in chapter 12. Do i understand it correctly that we will have the same results when calculating the APV as shown in Chapter 12 example 2 for question b and if we would solve the queston at the same why as earlier in chapter 10 (by finding the new equity beta and new cost of equity using CAPM and the WACC).

You would, but it would be complicated because the problem is that any gain from the project would increase the market value of the equity, which in turn would change the gearing. It therefore requires a lot of algebra!

Don’t waste your time – the question will make it clear if it wants APV and if it does then you do APV 🙂

Sir in example2 partB shareholder’s required return should change due to gearing as before it was all equity financed now it is 70% equity and 30% debt ????
should we regerar beta and than calculate shareholders return

Best is to use an APV approach (as in the answer at the back of the notes) in which case you discount the project at the return required were there no gearing and then add on the tax benefit of the debt.

An alternative would be to calculate a new cost of equity for the project (by regearing the beta) and then a WACC for the project, and then discount at that rate. The problem is that any gain from the project would go to the equity and so the gearing would end up different from 70%/30% which would change things. That would either mean keep redoing the exercise with the new gearing (an interative approach) or else use lots of algebra 🙂

We calculate the NPV as though it was all equity financed and then calculate the tax benefit separately (whereas appraising at the WACC effectively deals with both things at the same time).

APV is a better approach if there are significant changes in the gearing.

“The problem is that any gain from the project would go to the equity and so the gearing would end up different from 70%/30% which would change things.”
What do u mean by this?

As you will know from this chapter (and previous ones), we measure gearing using the total market values of equity and debt.

If we invest in a project with a positive NPV, then it means it is giving more than the required return, and the benefit of this will go to equity (debt get fixed interest and so they are not affected). This will mean that the market value of the equity will change, which will change the gearing ratio.

I have not checked your arithmetic (the WACC is not relevant in this question) but it is not surprising that it is lower than the WACC if it was all equity financed. M&M prove that with tax the WACC will fall with higher gearing.

PS When you did calculate the WACC, I assume you took the cost of debt to be 3.5% (5% less tax)?

The APV cuts a lot of hussle! i think Moffat you trully handled this one well. the APV i almost overlooked it when studying now this question made me re read it a bit. Nicely done. it had given me head aches just think about how complex it can be the minute debt is said to be reedemable to get IRR rate.

John I agree with yenuar, I have calculated using the alternative method and the NPV is not 28.64 for part b! Please could you post the alternative solution steps in narrative as i understand posting a new video maybe cumbersome, but just a brief narrative so I can understand possibly I am missing something in the calculations I am doing!

I do need to change the lecture because it will not come to exactly the same result. The reason is that that the project is only lasting 5 years – if it lasted for perpetuity then it would be the same.

However, it will be clear in the question if they want you to take and APV approach.

John, if it’s possible, could you please post the alternative solutions to parts b) and c). I’ve tried to work them out but my answers are different from those calculated using the APV…

In Part C of Example 2, why is the tax saving 0.45m for year 1-5 if it is redeemable debt. If redeemable, surely the outstanding balance of debt after 1 year will not be $30m any more, but only $24.5m and interest in the second year will be only $1.2m with tax saving of $0.36m. The outstanding amount of debt reduces each year, thus interest paid and the tax saving will become less as the debt are repaid each year.
I get a total NPV tax saving on interest over 5 to be 1.23m

With redeemable debt, only interest is paid each year and the full amount of the principal is repaid at the end of the period (in this case after 5 years).

This is standard for traded debt (and remember we are talking about traded debt)!

@johnmoffat – the lecturer also states that the new WACC is approx 18% (actual is 18.2%), which is what andypandy, garlyliu and I calculated. However, this discount rate gives an NPV of $24.52.
Any idea of where we went wrong?
Anyone to help pls?

I tried part B using WACC and NPV = $24.52M (?equity=1.95 and WACC=18.2%). Has anybody else tried to do part B using WACC? If yes, what is your result?
Thanks

@andypandy, The problem is this……although the finance for the project is being raised in the ratio 70%/30%, any gain from the project will go to the shareholders and will therefore increase the market value of the equity.
As a result, the gearing will end up being different that 70%/30% (and also the cost of equity will change because of the gearing).
To be able to use WACC you would need to know what the gearing ratio ended up at, and what the cost of equity ended up being.
(You can check is because we have calculated the gain using APV and you can use the M&M formula to get to the new cost of equity)

Thanks very much. I have got a better understanding. When I read the question first time, I thought we will work out a NPV and then use WACC to discount on solution b and c.

Adjusted Present Value approach is much easier to use in this case.

I think I’m comfortable with gearing and identifying APV versus WACC questions. The problem is the scenarios given and how the information is presented.

Amer says

Why did we ignore 70% of equity during the calculation of gain?

Thank You

John Moffat says

It is the equity who get all of the gain.

Mishaal says

First of all, thank you @John Moffat for all your videos and support it has truly helped me through my studies.

I just want to make sure my understanding is correct, with WACC we calculated Ke and Kd, due to the tax savings of debt the WACC is reduced as gearing increases, therefore the NPV increases.

The effect of the above is similar to APV in that although we do not use Kd to discount the C.F. to obtain the NPV, we do incorporate the tax shield element in the second step and the sum of NPV and financing effects gives the APV.

The result of using WACC or APV (given we have all necessary information in the question) should therefore result in more or less the same answer as each other because the decrease in WACC comes from the tax savings adjusted in Kd and the tax savings is what we are adding when calculating APV.

John Moffat says

Yes, except for two things. Using M&M to get a cost of equity for the project and then using this to get a WACC assumes that the debt is irredeemable, whereas with APV we can deal with redeemable debt. Secondly, when using the WACC the NPV will be the gain to shareholders which changes the gearing and hence the WACC and so we go round in circles a bit 🙂

Whenever there is a significant change in the gearing, APV is the better approach.

Daniel says

Sorry to dip my little fly in your ointment, but if we are taking the saving of the tax on the debt into consideration, why are we not taking into account the interest charge?

NPV of the project gain = $19.64

Tax shield = $9

Interest charge on debt = $?

John Moffat says

If you remember from M&M, without tax it would be irrelevant whether we used debt finance or not – the NPV would be the same.

With tax, the only difference is due to the tax saving on the debt interest.

himanipatel says

Hy Sir,

In example 2 it says the Beta of the company is 1.5. How do we know whether this is asset or equity beta?

John Moffat says

In example 2 it says that the beta of the project is 1.5 (not the beta of the company).

Betas of projects are always asset betas.

himanipatel says

Oh thank you. It’s always a pleasure learning from your lectures.

John Moffat says

Thanks for the comment 🙂

cyh says

Hi Sir, i refer to you example 2 and the question from BPP text book as below:

(A company is considering a project that would cost $100,000 to be financed 50% by equity (cost 21.6%) and 50% by debt (pre-tax cost 12%). The financing method would maintain the company’s WACC unchanged. The cash flows from the project would be $36,000 a year in perpetuity, before interest charges. Tax is at 30%.

Appraise the project using APV method.)

I have no idea how to apply your example 2b techique to solve this BPP question as in this question no risk free rate figure was given

John Moffat says

You should ask questions like this in the Ask the Tutor Forum and not as a comment on a lecture.

You can calculate the ungeared cost of equity using the first formula on the formula sheet (M&M Proposition 2).

I do not have the BPP Study Text (only the Revision Kit) but surely they have an answer in the book?

mansoor says

the “beta of the project” means its asset beta?

John Moffat says

Yes.

zee says

Thanks 🙂 Its always a pleasure to hear your voice!

John Moffat says

Thank you 🙂

Sangria9 says

I absolutely agree, so much enjoy from studying with you, sir!

P.S. I have a feeling like I’m somewhere in your class, as my name is Ekaterina and you often refer to Ekaterina in your class 🙂

John Moffat says

Thank you 🙂

Hermine says

Dear Sir,

Also I have asked two questions to the tutor a few days ago, but have no answer yet.

When will I receive the reply?

John Moffat says

You have asked two question – one about payback period and one about Black Scholes.

Both of them were answered within 15 minutes of you asking the question.

Hermine says

I’m sorry, I didn’t receive a notification on my e-mail, that’s why I thought they had not been answered.

Thank you very much.

John Moffat says

No problem 🙂

Hermine says

Dear John Moffat,

I’ve tried Question 34 Strayer Inc. It says that the company is considering to invest $25m, which willbe financed by internal funds-6m, rights issue-10m and loans-9m.

There is no note whether these are quoted net of issue costs or not.

So, when calculating the isuue costs don’t we need to gross them up?

In the answer to this question issue costs are calculated on 10m and 9m respectively without grossing up.

Thank you in advance!

John Moffat says

You must ask this in the Ask the Tutor Forum and not as a comment on a lecture.

Gaurav says

In part B of the solution, the risk free rate of 5% that we have used to discount tax saving on interest, Is it pre-tax or post tax?

John Moffat says

Pre-tax (the risk free rate is always pre-tax).

sogan0 says

Hi Sir What is the alternative formula if the question does not ask for APV? CAPM and WACC?

John Moffat says

If you are not required to calculate the APV then we just calculate the NPV by discounting the cash flows at the WACC. (You will probably need to use CAPM to calculate the cost of equity, which is obviously needed to get the WACC).

questforknowledge says

Hi John the lecture is very nice and you have made it very simple but what about issue cost of debts and equity and things like government grants

thanks

John Moffat says

The purpose of the lecture is to explain the M&M equations and to explain the reasoning and method of APV.

In a full exam question there are lots of extra things involved (for example, arriving at the cash flows int he first place in order to be able to then calculate the APV will be a lot more complicated). However, they are not ‘technical’ or ‘theoretical’ issues that I am trying to explain in the lecture.

On courses, after explaining APV etc. the students then practice past exam questions and it is then that we sort out problems with the cash flows, the issue costs etc.. None of them are theoretical problems and it is impossible to teach every little ‘trick’ that can be in a question – that can only be got from practicing lots of questions.

BrianH says

Sir

when the debt is redeemable, would this not mean that there is an extra cash flow to consider (cash flow being the principal being repaid) at the end of the project?

John Moffat says

Yes there will be the repayment, but this will not be tax allowable – for APV we are calculating the tax saving due to debt, which only applies to the interest.

ramya says

Sir,

why we took 5% as Discounting factor? Debt interest should always be after tax, therefore we would have taken 3.5% (5%x0.7)

John Moffat says

After tax interest is used when we are calculating the cost of debt.

Here we are not calculating the cost of debt – we are calculating the benefit of the tax saving by discount at the risk-free rate.

grungyhorn says

I have tried to rework example 2b using the Beta and always get back to a wacc of 18.2 (1.5=Xx70/91=new beta of 1.95x(15-5)+5=24.5% x.7=17.15 + (3.5x.3=1.05) total 18.2 Annuity = 3.113x40M=124.52.) To get to 128.64 the annuity needs to be 3.214 = 16.8!) where am I going wrong?

Thanks

John Moffat says

The problem is that although the finance is being raised 70% equity and 30% debt (so 70M from equity and 30M from debt), there will be a gain from doing the project, and the gain will all go to the shareholders.

That will mean that the value of the equity in the project will be higher than 70M (because of the gain) but the debt in the project will stay at 30M.

So the gearing will be a bit different, and so it is not valid to use 70%/30% in the asset beta formula, or when calculating the WACC.

(You could do it this way by using algebra, but it gets very messy and I really would not waste your time on it – trust me, it will work! But in the exam you would be specifically asked for the APV and so doing it any other way would be wrong anyway.)

pillekesekene says

Question regarding example 2 in chapter 12. Do i understand it correctly that we will have the same results when calculating the APV as shown in Chapter 12 example 2 for question b and if we would solve the queston at the same why as earlier in chapter 10 (by finding the new equity beta and new cost of equity using CAPM and the WACC).

John Moffat says

You would, but it would be complicated because the problem is that any gain from the project would increase the market value of the equity, which in turn would change the gearing. It therefore requires a lot of algebra!

Don’t waste your time – the question will make it clear if it wants APV and if it does then you do APV 🙂

rmracca says

Thanks for a well explained lecture:)

zee90 says

Sir in example2 partB shareholder’s required return should change due to gearing as before it was all equity financed now it is 70% equity and 30% debt ????

should we regerar beta and than calculate shareholders return

John Moffat says

Best is to use an APV approach (as in the answer at the back of the notes) in which case you discount the project at the return required were there no gearing and then add on the tax benefit of the debt.

An alternative would be to calculate a new cost of equity for the project (by regearing the beta) and then a WACC for the project, and then discount at that rate. The problem is that any gain from the project would go to the equity and so the gearing would end up different from 70%/30% which would change things. That would either mean keep redoing the exercise with the new gearing (an interative approach) or else use lots of algebra 🙂

zee90 says

in APV approach we assume npv is all equity financed so gearing will not effect the cost of equity ????

John Moffat says

Not quite.

We calculate the NPV as though it was all equity financed and then calculate the tax benefit separately (whereas appraising at the WACC effectively deals with both things at the same time).

APV is a better approach if there are significant changes in the gearing.

zee90 says

thank you very much sir

toobaalvi says

“The problem is that any gain from the project would go to the equity and so the gearing would end up different from 70%/30% which would change things.”

What do u mean by this?

John Moffat says

As you will know from this chapter (and previous ones), we measure gearing using the total market values of equity and debt.

If we invest in a project with a positive NPV, then it means it is giving more than the required return, and the benefit of this will go to equity (debt get fixed interest and so they are not affected). This will mean that the market value of the equity will change, which will change the gearing ratio.

toobaalvi says

my WACC ends up to be 19% if i regear the beta. Can you please tell why does this happen?

John Moffat says

I have not checked your arithmetic (the WACC is not relevant in this question) but it is not surprising that it is lower than the WACC if it was all equity financed. M&M prove that with tax the WACC will fall with higher gearing.

PS When you did calculate the WACC, I assume you took the cost of debt to be 3.5% (5% less tax)?

tinashe says

The APV cuts a lot of hussle! i think Moffat you trully handled this one well. the APV i almost overlooked it when studying now this question made me re read it a bit. Nicely done. it had given me head aches just think about how complex it can be the minute debt is said to be reedemable to get IRR rate.

bmparadzi says

John I agree with yenuar, I have calculated using the alternative method and the NPV is not 28.64 for part b! Please could you post the alternative solution steps in narrative as i understand posting a new video maybe cumbersome, but just a brief narrative so I can understand possibly I am missing something in the calculations I am doing!

John Moffat says

I do need to change the lecture because it will not come to exactly the same result. The reason is that that the project is only lasting 5 years – if it lasted for perpetuity then it would be the same.

However, it will be clear in the question if they want you to take and APV approach.

yenuar says

John, if it’s possible, could you please post the alternative solutions to parts b) and c). I’ve tried to work them out but my answers are different from those calculated using the APV…

yenuar says

Or should we just use the APV approach whenever possible?

John Moffat says

The question will make it clear if they want APV and if so then you should obviously use that approach.

jurgenshniek says

In Part C of Example 2, why is the tax saving 0.45m for year 1-5 if it is redeemable debt. If redeemable, surely the outstanding balance of debt after 1 year will not be $30m any more, but only $24.5m and interest in the second year will be only $1.2m with tax saving of $0.36m. The outstanding amount of debt reduces each year, thus interest paid and the tax saving will become less as the debt are repaid each year.

I get a total NPV tax saving on interest over 5 to be 1.23m

jurgenshniek says

@jurgenshniek, the $30m is paid back at the end of 5 years. I have never seen this in real practice.

John Moffat says

With redeemable debt, only interest is paid each year and the full amount of the principal is repaid at the end of the period (in this case after 5 years).

This is standard for traded debt (and remember we are talking about traded debt)!

sahil107 says

@johnmoffat – the lecturer also states that the new WACC is approx 18% (actual is 18.2%), which is what andypandy, garlyliu and I calculated. However, this discount rate gives an NPV of $24.52.

Any idea of where we went wrong?

Anyone to help pls?

andypandy says

I tried part B using WACC and NPV = $24.52M (?equity=1.95 and WACC=18.2%). Has anybody else tried to do part B using WACC? If yes, what is your result?

Thanks

garlyliu says

@andypandy, i tried and got the same answer as yours. anybody knows which part goes wrong?

Thanks!

John Moffat says

@andypandy, The problem is this……although the finance for the project is being raised in the ratio 70%/30%, any gain from the project will go to the shareholders and will therefore increase the market value of the equity.

As a result, the gearing will end up being different that 70%/30% (and also the cost of equity will change because of the gearing).

To be able to use WACC you would need to know what the gearing ratio ended up at, and what the cost of equity ended up being.

(You can check is because we have calculated the gain using APV and you can use the M&M formula to get to the new cost of equity)

jjchiwasa says

i get lost failed to follow from e.g 1, bcz it cuts whn we started part b.

mwachilale says

Thanks very much. I have got a better understanding. When I read the question first time, I thought we will work out a NPV and then use WACC to discount on solution b and c.

Adjusted Present Value approach is much easier to use in this case.

kerr says

I think I’m comfortable with gearing and identifying APV versus WACC questions. The problem is the scenarios given and how the information is presented.