The cost of debt is not 11.67% (think about it – if the risk free rate is only 5% (and is before tax) then the cost of debt could not possibly be 11.67% 馃檪 ). The cost of debt (assuming it to be risk free – here there is no choice but to assume that) is 5(1-0.3) = 3.5%.

From your calculations you did not factor in the effect of change in capital structure unless you are supposing M and M the world with no taxes. Our gain will be mistated by igonoring that effect.

Either

Using CAPM, we have to adjust Ke to come up with geared Ke. By adjusting B.

Ba=(Ve/Ve+Vd(1-T))Be i.e. 1.5=(70/70+(30*0.7))Be, then Be=1.95

Then Ke=Rm+Be(Rm-Rf) i.e. 0.05+1.95(0.15-0.05), then Ke=24.5%

Or

lever Ke using M&M proposition formulae

Ke = Kie + (1-T)*(Kie-Kd)*Vd/Ve

Ke = 24.5%

Lets calculate wacc, the discount rate for revised NPV, geared financing WACC=(24.5*70/100)+(5* 0.70* 30/100)=18.2% YEAR 0 – 100m Year 1-5 – 40m Disc rate – 18.2% NPV = 25m

Benefit of debt as calculated 1.95m APV = 34m irred debt (25+9) APV = 26.95m redemable debt (25m +1.95)

Good day, in the last part of the video it was on the rate to be used to calculate the tax benefit and also discounting factor. To calculate tax benefit i need to take the amount to be raised by debt financing * the interest rate to pay back to debt provider(coupon rate is preferable but if it is not given then we can choose risk free rate) * tax rate. For example, if the question is given the coupon rate(5%) and also the risk free rate(3%), then we have to choose the coupon rate(5%) to calculate the tax benefit. Whereas for discounting, i can choose any of the rate to discount it(5% or 3%). Even though it gives different value but it is still acceptable, is my understanding correct?

For question part b) is it okay to calculate the debt financing effect as the tax rate * 30% * 100m = 9m which is the same answer as if you were to discount with perpetuity using the risk-free rate 0.45/0.05 = 9m.

For question part b) if it okay to calculate the debt financing effect as the tax rate * 30% * 100m = 9m which is the same answer as if you were to discount with perpetuity using the risk free rate.

Hi John, thank you for the lecture. Could you please give an example of how to adjust for Subsided loans, just like you did for Issue Cost. That is, the 3% (8-5) is it deducted from Base NPV directly or is it multiplied with the Debt, discounted and deducted ?

If the loan is $100,000 for 5 years and the subsidy is 3% and the tax rate is 30% then the benefit added to the base case NPV is 3% x $100,000 x 0.7 x the 5 year annuity factor.

Sir, just regarding the cash flow in perpetuity – I see you didn’t have to discount CF * annuity rate. Is this because we don’t have a penultimate year (would be n=0) that we’re starting in year 1?

Hi John, Thank you very much for your lecture. I read an example in BPP text book related to APV which requires to appraise project using both NPV and APV with gearing of 50% debt: 50% equity. The project cost $100,000.

After calculating, NPV of project is $68 million. And they said that debt capital should be 84,200 (=50% (NPV + cost of project) I did not understand why debt capital comes out that way, because the company should only finance $100,000 to commence the project and so debt capital should be $50,000. Is it correct?

In future please ask this kind of question in the Ask the Tutor Forum, not as a comment on a lecture 馃檪

It depends on the exact wording of the question. Taking the project will increase the MV of the company by the PV of the future flows which is $168M and so that is why they have written that debt will need to be $84M. However all exam APV questions have been worded such as the debt raised is given as a fixed amount (which in this case would be $50M)

Hello, Thank you very much for uploading the thoroughly conducted and capturing lecture. Super helpful ;o) To enquire about part b when calculating tax shield on the irredeemable debt. Why “1/0.05” was used to arrive to $9m present value of tax saving?And what this fracture represents?

I do understand that irredeemable debt can bring interest forever but if we calculate APV of a project I would assume we should only calculate tax saving over the time of said project so 5 years. Tax saving after 5 years would not be part of that project and I don’t feel adding further tax saving is correct. Could you please advise?

Raiding debt finance will indeed increase the cost of equity. However, according to Modigliani Miller (which is where the APV ‘rules’ come from), as explained in earlier chapters, if there was no tax then it would be irrelevant how finance were to be raised (whether all equity or part equity / part debt and the NPV would stay the same regardless. When there is tax, the WACC falls and therefore the value increases, for no other reason than the tax benefit on debt.

Thank You So much John For these great lectures! I have got something on my mind that is puzzling me a lot, you see in part (b) How can NPV stay at $19.64 when we expect the cost of equity to change as a result of raising 30m (30% of 100M) finance through debt? In other words haven’t we missed out on the effect of gearing on the investment, i.e. the cost of equity should increase – perhaps by re-gearing the asset beta of 1.5 and calculating new cost of equity to calculate a new NPV. I did that before watching you solve that example and I got really confused when I witnessed otherwise 馃檨

Or maybe Let me say what is actually bothering me. We need 100M funds, if we raise new equity its cost will be 20% and which will give an NPV of $19.64. But by raising 30M by debt finance surely will tempt the equity holders to demand a higher return but we haven’t accounted for it anywhere. I have no problem with tax saving though. I am lost I guess, I would really appreciate if you could guide me on this. Cheers

Because the first part always assumes all equity finance! Regardless the financing arrangement, when solving for APV, the first step is to calculate the PV assuming all equity finance. therefore the answer to first step will stay the same regardless the change in gearing level.

yashponda says

Hello, just a doubt. As per M&M with tax, if the company is geared then though the Ke will increase but the WACC as a whole falls.

In example 2, i tried computing Ke Kd and WACC as follows :-

Ba=(Ve/Ve+Vd(1-T))Be i.e. 1.5=(70/70+(30*0.7))Be, then Be=1.95

Further, Ke=Rm+Be(Rm-Rf) i.e. 0.05+1.95(0.15-0.05), then Ke=24.5% and Kd=5(1-0.3)/30 i.e. 11.67%.

WACC=(24.5*70/100)+(11.67*30/100)=20.65%

Where, WACC=Ke (without gearing) = 20%.

So here, infact the WACC has also gone up.

Please help, let me know if there’s a mistake.

John Moffat says

The cost of debt is not 11.67% (think about it – if the risk free rate is only 5% (and is before tax) then the cost of debt could not possibly be 11.67% 馃檪 ). The cost of debt (assuming it to be risk free – here there is no choice but to assume that) is 5(1-0.3) = 3.5%.

yashponda says

Understood, my bad. Thanks for taking the time to explain.

yashponda says

Hope the computation of Ke is correctly done?

John Moffat says

Yes it is 馃檪

mzeeobey says

I tend to be corrected

From your calculations you did not factor in the effect of change in capital structure unless you are supposing M and M the world with no taxes. Our gain will be mistated by igonoring that effect.

Either

Using CAPM, we have to adjust Ke to come up with geared Ke. By adjusting B.

Ba=(Ve/Ve+Vd(1-T))Be i.e. 1.5=(70/70+(30*0.7))Be, then Be=1.95

Then Ke=Rm+Be(Rm-Rf) i.e. 0.05+1.95(0.15-0.05), then Ke=24.5%

Or

lever Ke using M&M proposition formulae

Ke = Kie + (1-T)*(Kie-Kd)*Vd/Ve

Ke = 24.5%

Lets calculate wacc, the discount rate for revised NPV, geared financing

WACC=(24.5*70/100)+(5* 0.70* 30/100)=18.2%

YEAR 0 – 100m

Year 1-5 – 40m

Disc rate – 18.2%

NPV = 25m

Benefit of debt as calculated 1.95m

APV = 34m irred debt (25+9)

APV = 26.95m redemable debt (25m +1.95)

thaarsini says

Good day, in the last part of the video it was on the rate to be used to calculate the tax benefit and also discounting factor. To calculate tax benefit i need to take the amount to be raised by debt financing * the interest rate to pay back to debt provider(coupon rate is preferable but if it is not given then we can choose risk free rate) * tax rate.

For example, if the question is given the coupon rate(5%) and also the risk free rate(3%), then we have to choose the coupon rate(5%) to calculate the tax benefit. Whereas for discounting, i can choose any of the rate to discount it(5% or 3%). Even though it gives different value but it is still acceptable, is my understanding correct?

lasid says

Hi,

For question part b) is it okay to calculate the debt financing effect as the tax rate * 30% * 100m = 9m which is the same answer as if you were to discount with perpetuity using the risk-free rate 0.45/0.05 = 9m.

Many thanks.

lasid says

For question part b) if it okay to calculate the debt financing effect as the tax rate * 30% * 100m = 9m which is the same answer as if you were to discount with perpetuity using the risk free rate.

Many thanks.

John Moffat says

Yes it is OK 馃檪

Acca1290 says

Since the tax benefit on debt is kind of a saving for us, which is why we are adding it to the NPV right?

John Moffat says

Correct 馃檪

JMonye says

Hi John, thank you for the lecture. Could you please give an example of how to adjust for Subsided loans, just like you did for Issue Cost.

That is, the 3% (8-5) is it deducted from Base NPV directly or is it multiplied with the Debt, discounted and deducted ?

John Moffat says

The benefit of the subsidy (less the tax relief lost) is added to the base case NPV.

JMonye says

Thank you. Please could you use numbers.

John Moffat says

If the loan is $100,000 for 5 years and the subsidy is 3% and the tax rate is 30% then the benefit added to the base case NPV is 3% x $100,000 x 0.7 x the 5 year annuity factor.

JMonye says

thank you John. !!! This is understood.

John Moffat says

You are welcome 馃檪

SayuriFan15 says

Sir,

just regarding the cash flow in perpetuity – I see you didn’t have to discount CF * annuity rate. Is this because we don’t have a penultimate year (would be n=0) that we’re starting in year 1?

ngoquynh1224 says

Hi John,

Thank you very much for your lecture.

I read an example in BPP text book related to APV which requires to appraise project using both NPV and APV with gearing of 50% debt: 50% equity.

The project cost $100,000.

After calculating, NPV of project is $68 million. And they said that debt capital should be 84,200 (=50% (NPV + cost of project)

I did not understand why debt capital comes out that way, because the company should only finance $100,000 to commence the project and so debt capital should be $50,000. Is it correct?

Thank you!

John Moffat says

In future please ask this kind of question in the Ask the Tutor Forum, not as a comment on a lecture 馃檪

It depends on the exact wording of the question. Taking the project will increase the MV of the company by the PV of the future flows which is $168M and so that is why they have written that debt will need to be $84M. However all exam APV questions have been worded such as the debt raised is given as a fixed amount (which in this case would be $50M)

ngoquynh1224 says

Thank you for your help and kindness 馃檪

John Moffat says

You are welcome 馃檪

daivaa says

Hello,

Thank you very much for uploading the thoroughly conducted and capturing lecture. Super helpful ;o)

To enquire about part b when calculating tax shield on the irredeemable debt.

Why “1/0.05” was used to arrive to $9m present value of tax saving?And what this fracture represents?

Thank you very much for your response in advance.

John Moffat says

1/r is the discount factor for a perpetuity, where r is the discount rate.

If you are unsure about this then please do watch the Paper MA (was F2) lectures on discounting.

daivaa says

Thank you very much. I do recall this formulae now. Certainly, I’ll be looking into it.

Much appreciated for your help.

John Moffat says

You are welcome 馃檪

konrad79 says

Hi John,

I do understand that irredeemable debt can bring interest forever but if we calculate APV of a project I would assume we should only calculate tax saving over the time of said project so 5 years. Tax saving after 5 years would not be part of that project and I don’t feel adding further tax saving is correct. Could you please advise?

thanks

arjun585 says

Hi Sir, there is any formula to calculate Tax Shield on subsidised loan & Subsidy benefit from government loan. Thanks

John Moffat says

Raiding debt finance will indeed increase the cost of equity. However, according to Modigliani Miller (which is where the APV ‘rules’ come from), as explained in earlier chapters, if there was no tax then it would be irrelevant how finance were to be raised (whether all equity or part equity / part debt and the NPV would stay the same regardless. When there is tax, the WACC falls and therefore the value increases, for no other reason than the tax benefit on debt.

endless says

Thank You So much John For these great lectures!

I have got something on my mind that is puzzling me a lot, you see in part (b) How can NPV stay at $19.64 when we expect the cost of equity to change as a result of raising 30m (30% of 100M) finance through debt? In other words haven’t we missed out on the effect of gearing on the investment, i.e. the cost of equity should increase – perhaps by re-gearing the asset beta of 1.5 and calculating new cost of equity to calculate a new NPV. I did that before watching you solve that example and I got really confused when I witnessed otherwise 馃檨

Or maybe Let me say what is actually bothering me. We need 100M funds, if we raise new equity its cost will be 20% and which will give an NPV of $19.64. But by raising 30M by debt finance surely will tempt the equity holders to demand a higher return but we haven’t accounted for it anywhere. I have no problem with tax saving though. I am lost I guess, I would really appreciate if you could guide me on this. Cheers

badare says

Because the first part always assumes all equity finance!

Regardless the financing arrangement, when solving for APV, the first step is to calculate the PV assuming all equity finance.

therefore the answer to first step will stay the same regardless the change in gearing level.