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FM Chapter 7 Questions – Investment appraisal – methods

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  1. excuse me sir, could you please explain why is number 4’s answer of “the graphical approach to IRR is only an estimate; linear interpolation is required for a precise answer?” Does this mean that calculating the IRR using the linear interpolation would only give estimates as well? So, which method would give IRR a precise answer Sir? Or is there none?

    • Linear interpolation only gives an estimate. To get a precise answer we would need to draw a graph. So that is why both statements in this option are false. I do explain this in my free lectures – have you not watched them? 🙂

      Best of all to get a precise answer is to use the IRR function in a spreadsheet such as excel, but this is not relevant until Paper AFM.

    • 1/r is the discount factor for a perpetuity starting in 1 years time. Here the first receipt is immediate and so the PV of that receipt is 12,000 which needs to be added on to the PV of the perpetuity.

      So the total PV is 12,000 + (12,000/0.11)

  3. I dont know if you still reply to comments but for question 4 I did the graph and it is negatively sloped, showing that as interest increases the npv decreases or does the interest not mean Cost of capital in this situation?

      • Yes thanks, I realized the questions didn’t ask about irr. Thanks for the lectures, just did my exam today. Only thing I didn’t like were section a and b questions they should take in to consider calculations or give u part marks because some were confusing.

      • The graph is ploted npv against against interest rates i think it is indeed negatively sloped… NPV on y-axis and intetest rates on x-axis…
        Please Sir advise whre iam getting it wrong?

  4. Dear Sir,
    I’m really sorry bother you. I have tried to understand the last question, but i can’t. Iam confused about last answer.
    The question : what is the present value of 48.000( fist receivale in 3 years time) + 48.000 (receive 7 times from 4th year – 10th year).
    So, the total = we’ll receive total = 8 times for 48.000 (ignore cost captial).
    But the answer just give present value of 7 times for 48.000.
    Amount 10%
    0-2 48000 ———–

    3 48000 36,063.11
    4 48000 32,784.65
    5 48000 29,804.22
    6 48000 27,094.75
    7 48000 24,631.59
    8 48000 22,392.35
    9 48000 20,356.69
    Sum 193,127.36 .
    Why don’t we caculate Present value for the fist receivabe?

    • at the end of 3rd year we will receive 48000 and thereafter we will receive it for 7 years more. The amount which we received in 3rd year is return for the 3rd year as we assume that we receive the cash flow at the end of the year therefor we are not receiving the 48000 for first 2 years.
      remaining 7 years we will count from 3, 4 , 5 till 9th year
      annuity for 9 years is 5.759 we will deduct first 2 years annuity in which we are not generating income.
      Therefore 5.759-1.736 which is annuity for 2 years
      we get 4.023*48000 which is 193104.
      I hope you understood.

    • Here the first receipt is received in 3 years time ie at the end of 3rd year(t3).
      And continues for a period total of 7 years( t3,t4,t5,t6,t7,t8,t9).
      This case is delayed annuity so the answer can be arrived by using the formula Pv= Annuity cf * annuity factor* Discounting factor
      so 48000*4.868*0.826
      Here the annuity factor means , annuity factor of number of years the payment is received ie 7yr
      And discounting factor of previous year when the first payment is received ie (t2)

  6. I got 3 out the 5 questions right but I found the mistakes I was making were not technical but where I hadn’t taken the time to read the question and rushed to answer it. For example in the last question I added up the periods wrong calculated from year 3 to 10 instead of 3 to 9 because I read 7 as being 7 more years rather then a total of 7 years which in the exam would cost me 2 marks. It pays to take your time even if you think you know the how to answer it!

  7. i have a tiny little problem with regards to counting the number of periods.

    When we say ‘in three years’ time , shouldnt it be any period which falls within the third period???rather than what i am seeing within the examples ‘in three years time = time period 2’

    Example

    What is the present value of $48000 first receivable *in three years time* and thereafter each year for a total period of seven years?
    Cost of capital is 10%

  8. Im in dilemma! normally when you discount a cash flow at suppose 11%, should not it be 0.901 multiply by 12000 = 10812 like we do for the other PV calculation then why it used PV= CF (1+1/r), this perplexes me with the Future CF

    • The discount factor for a perpetuity is 1/r, where r is the rate of interest. However that applies for a perpetuity that starts in 1 years time. In this question (and I assume you are referring to question 1, but you have not said!), then the first receipt is immediate rather than in 1 years time, and the PV of a flow receive immediately is the amount of the flow.

      This basic discounting is revision from Paper MA (was F2) and I suggest that you watch the free Paper MA lectures on interest and on investment appraisal (as well as the Paper FM lectures).

    • I assume that you are referring to question 3. If you submit your answers and then click on ‘review quiz’ the answers and workings will appear.

      (I do assume that you watched the free lectures on investment appraisal before attempting the quiz?)

      • Sorry I did not mention the ques num. but in any way for the ques 3, I got it right but at 15%, NPV= +0.338 m when its 0.343m

        Also, using the formula of IRR, the nominator stands the lowest NPV but here, it is the +ve NPV

        My answer = 17.82%

      • If you are using the tables provided then the NPV at 15% is 0.343m as stated in the answer. If you are not using tables then the answer will be slightly different because the tables are rounded to 3 decimal places, but rounding is irrelevant in the exam (just as in real life).

        17.82% is not one of the answer choices available. Just as in the exam the question is expecting you to use the nearest answer.

        You should not be using a formula to calculate the IRR but should understand what we are doing, as I explain in my lectures. The examiner is always trying to set questions that check you understand and have not simply learned rules. You will see plenty of the sort of questions I mean in your Revision Kit.

  10. Sir.. I want to ask how can i get ready for april attempt… I dont know how to get prepare myself for Financial management paper..please help me out.. I m really nervous regarding thoery and all

    • In future please pose this kind of question in the Ask the Tutor Forum and not as a comment on a test.

      There is no exam session in April so I don’t know whether you are meaning March or June.

      You need to study by watching all of our free lectures, and then you need to practice by buying a Revision Kit from one of the ACCA Approved Publishers and attempting every question in it.

  11. Sir, I have a doubt pertaining to the 4th question.

    Why is the statement “A graph showing NPV on the Y axis and Interest rate on the X axis will have a negative slope,” not true? Please could you help me understand?

    (I agree that the statement “Two NPVs are required to estimate IRR using linear interpolation,” is true. I was just wondering if there were two true statements).

    Thank you!

    • The flows are from time 3 to 9.

      You can do it in either or two ways:

      The 9 year annuity factor less the 2 year annuity factor will leave us with the total factor for 3 to 9.

      Alternatively, you can take the 7 year annuity factor and then discount for 2 years because the annuity starts 2 years late.

      Both approaches give the same answer (any small difference is simply due to rounding in the tables).

      I do explain this in my free lectures.

      • I’m not sure why discount for 2 year instead of 3 year, sir?
        E.g, the second one, why not discount for 3 years as the title saying that the amount from 3 year but 2 years?

      • Multiplying by the 7 year annuity factor gives the PV ‘now’ for an annuity starting in 1 years time.
        The annuity starts in 3 years time, which is 2 years later than 1 years time. Therefore the annuity factor gives the PV two years later – i.e. time 2 instead of time zero and therefore we need to discount it for 2 years to get the PV ‘now’.

    • By definition, the IRR is the rate of interest at which the NPV is zero.

      The cost of capital is of no relevance in the calculation. It is only relevant if we are using an IRR approach to decide whether or not to invest – it the IRR is greater than the cost of capital the project is worthwhile. If the IRR is less than the cost of capital then the project should be rejected.

      Did you watch my free lectures before attempting this test? If you did and are still not clear then watch also my free Paper MA (was F2) lectures on the IRR because this is revision from Paper MA.

    • The difference between + 0.343 and – 0.2659 is the sum of the two (or if you want to be mathematical (although this is not a maths exam) subtract a negative number is the same as adding the number).

      I do suggest that you watch my free lectures on this and if necessary my Paper MA (was F2) lectures on discounting, because this is revision from Paper MA.

  17. This might be a silly question, but when I was calculating the NPV in Question 3 for 20%, I accidentally got a positive net present value which ofcourse, messed up my IRR. Fixed that, no worries.
    But would they ever ask us to use two discount rates which BOTH give a positive NPV to calculate the IRR? Or do you need the second discount rate to result in a negative NPV for IRR calculations…

  19. HI Sir,

    I have a question about the question n.5: I have tried to carry out the excercise using (for the 2 years) both the annuity for two years (1.736) and also calculating yearly with the annual discount (0.877and 0.756) but I arrive a two different results. In the first case with the annuity the amount is 83,328 (48,000 * 1.736), menawhile in the second case the amount is 83,280 (43,632+39,648). am I making a mistake? I was expecting the calculation to have the same result.

    Thanks in advance.

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