Investment Appraisal Under Uncertainty – Sensitivity Analysis (example 1)

ACCA F9 lectures ACCA F9 notes


    • Profile photo of John Moffat says

      You take exactly the same approach as for the others.

      Calculate the present value of the revenue flows (because they are the flows that will change if the selling price changes).

      The sensitivity is then the NPV as a percentage of the PV just calculated.

    • Profile photo of John Moffat says

      For this particular example we can not, because we do not know the estimated selling price.
      In general terms you would take the same approach as the others i.e. express the NPV as a % of the present value of those cash flows that would change (which in the same of the price would be the sales revenue flows).

      • Profile photo of questforknowledge says

        you mean NPV/ present value of sales revenue? this will give me the percentage change in sales revenue. I am preparing for P4 and there is this question Dec 2012 question that asked for this. when i tried going through the solution i didnt understand how it was solved. If use this your approach i will get the percentage change in sales revenue but the question asked for sales price

      • Profile photo of John Moffat says

        But surely, if the sales price changes by 10% then the revenue changes by 10% as well!
        (I know it could be affected by other things, but with sensitivity we can only consider one item at a time)

        One other thing is that if there is tax in the question, then the flows that will change if the selling price changes will be the revenue and the tax on the revenue. So you need the net PV of these two. Then express the NPV of the project as a % of it.

  1. avatar says

    Thanks John,
    an issue here,when we are calculating the sensitivity of change on for example part (iii) which is contribution p.u, why do we put that negative sign yet in our table the final value was a positive??

    • Profile photo of John Moffat says

      Its not really a question of calling it the optimum.

      The problem is that we are making a decision on forecasts of cash flows, and therefore the actual cash flows may turn out to be different – if they are different then the NPV might turn out to be negative and then we will have made the wrong decision.

      The higher the sensitivity the less the chance is of that flow changing enough to affect the decision. However if the sensitivity is low, then it means that even just a small change in the flow will affect the decision. Therefore the lower the sensitivity the more risk we are taking and therefore the more we will try to estimate the flow accurately (or else maybe decide not to take the risk).

    • Profile photo of John Moffat says

      The PV of the scrap is 1845.
      This would have to fall by 5329 to end up with a NPV of zero.

      So in percentage terms this is a fall of 5329/1845 x 100% = 289%

      However (as I do state in the lecture) this is ridiculous because it would mean that the scrap value would have to be negative! Usually, obviously the most it can fall is 100% down to zero. So you would state that the scrap is not sensitive at all.

      (The only time it could possibly be relevant is if there were a possibility of us having to pay money to scrap the machine, which is very unlikely)

  2. avatar says

    Hi Mr John,

    I still dont understand how you arrived in the postive and negative sign from question i to v.

    can you please explain how you derive at the figures being -tve or +ve.

    many thanks

    • Profile photo of John Moffat says

      What you have to ask yourself is will it make the NPV worse if it gets higher or lower.

      So, for example, as far as the revenue is concerned, we are only worried if it should fall – so the sensitivy is negative (it measures the percentage fall that we can afford).
      But as far as the cost of capital is concerned, we are only worried if it should increase – so the sensitivity is positive (it measures the percentage increase that we can afford).

  3. avatar says

    Hey John, Why u didn’t do cost of captial sensitivity? However I done it by my self and the IRR comes = 15.842%. I took 20% as another npv that resulted in ($26306).

    Now as per your formulae: NPV/PV of changes x 100% = 15%/15.842% x 100% = ~95%

    BUT I think its wrong?

    • Profile photo of John Moffat says

      At present the NPV is 5329, and we need to know the % fall in sales volume that will give NPV of zero.

      If the sales volume per year falls, then the contribution per year falls, and therefore so too will be present value of the contribution flows. At present the present value of the contribution flows is 241189 – we need this to fall by 5329, which is a 2.2% fall.

  4. avatar says

    Wow, couldn’t be better. Nevertheless, if a question asked us to evaluate sensitivity for sales volume, sales price and variable cost it appears we would have the same change in the variables (for all of them) if we only calculated the PV for contribution only and not the independent variables i.e. separate PV for sales price and variable cost respectively. What I want to know is that wont such an approach limit us on the marks awarded?

    • Profile photo of John Moffat says

      They would not be the same.

      Sales price will have a different effect (and therefore a different sensitivity) than sales volume (with sales volume the contribution per unit remains the same, but if sales proie changes then the contribution per unit changes). So too will the variable costs.

    • avatar says

      @adeel15, you can easily understand this if you went back to the video on the IRR. I have found it to be easy actually. Remember that the IRR gives you the cost of capital that will result into NPV of Zero. Compare that IRR (which you must calculate with the information in the question) with the cost of capital (we have been given). The difference in percentage terms is the sensitivity on cost of capital.

  5. avatar says

    hi. i used the same approach for sensitivity for qn dec 01 tower railways inc. i got 2003/10771 X 100% = 18.6% :( no where near their ans. of 20.87% or fall in px of $2.50. Moreover their explanations n calculations are far more confusing !! pls help !!! tks

  6. avatar says

    hi i’m new to this and i need some advise on how many sub to do this time.. I’m doing f8 and p2… and i had to fill my form for f9 as well in order to do my p2…I dont know shall i do f9 or shall i leave it for next term..

    • Profile photo of louis06111 says

      In my opinion, we are currently getting a NPV of +5329, in order to result in a NPV of zero(Breakeven analysis), we can let the sales volume to drop by that percentage.
      And hence, it is negative.
      Similarly, we can let the cont. p.u. to drop by 2.21%, it’s also negative.
      That’s the conclusion I came to and I hope it will help,

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