• Profile photo of 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).

    • Profile photo of 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.

      • Profile photo of BrianH says


        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?

      • Profile photo of 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.

    • Profile photo of 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.

  1. avatar 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?

    • Profile photo of 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.)

  2. avatar 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).

    • Profile photo of 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 :-)

  3. avatar 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

    • Profile photo of 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 :-)

      • Profile photo of 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.

      • avatar 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?

      • Profile photo of 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.

      • Profile photo of 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)?

  4. Profile photo of 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.

  5. avatar 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!

    • Profile photo of 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.

  6. avatar 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…

  7. avatar 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

  8. avatar 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?

    • Profile photo of 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)

  9. avatar 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.

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