CFA CFA Level 1 Capital Budgeting

Capital Budgeting

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    • Avatar of fmccrayfmccray
        • CFA Level 1

        Hi, I have two questions on the bolded parts. would anyone happen to know why it is not C01=100 , F01=5. the other part is that i would have put C02=50. i would hate to loose on this question as it is relatively easy. Thank you so much for you help.

        Question 1:

        C01 = 100, F01 = 4, C02 = 150, F02 = 1

        Digital Design Corporation is considering an investment of £400 million with expected after-tax cash inflows of £100 million per year for five years and an additional after-tax salvage value of £50 million in Year 5. The required rate of return is 7.5 percent. What is the investment’s PI?



        C is correct. The Profitability Index scales the NPV according to the size of the initial investment. It is calculated as the present value of a project’s future cash flows divided by the initial investment:

        Profitability Index PI = PV of future cash flows/ initial investment = 1 + NPV/initial investment

        Using the calculator: CF0 = – 400, C01 = 100, F01 = 4, C02 = 150, F02 = 1, I = 7.5, CPT NPV. NPV = 39.41.

        PI = 1 + (39.41/400) = 1.098 = 1.1 approx.

        Question 2:

        The questions did not say if $60 in year 1 is negative. How can i tell from the question? CF2 = -60.

        A project investment of $100 generates after-tax cash flows of $50 in Year 1, $60 in Year 2, $120 in Year 3 and $150 in Year 4. The required rate of return is 15 percent. The net present value is closest to:


        Your answer was Wrong.


        A is correct. Net present value is the present value of the future after-tax cash flows minus the investment outlay.

        NPV = -100 + (50/1.15) + (60/(1.15)^2) + (120/(1.15)^3) + (150/(1.15)^4) = 153.51.

        Using a financial calculator, enter the cash flows.

        CF0 = – 100, CF1 = 50, CF2 = -60, CF3 = 120, CF4 = 150, I = 15, CPT NPV. NPV = 153.51.

      • Avatar of rahul12rahul12
          • CFA Level 3

          sorry I don’t follow your question Answer. does this relate to a particular question that you can share?

        • Avatar of fmccrayfmccray
            • CFA Level 1

            Thank you so much Sophie. yes, you are right. i was not thinking about the question correctly.

          • Avatar of AnswerAnswer
              • Undecided

              Rahul12, let me post the whole question

            • Avatar of rahul12rahul12
                • CFA Level 3

                whoa, it’s indeed a long one. not sure if i’m right, but will take a stab at this:

                Answer said:

                How do I go about it in terms of adjusting for inflation?

                for NPV, if you use nominal cashflows then you must discounted at nominal discount rates and if you use real cashflows, then you must discount in real discount rates. both should get the same answer.

                so in this case, say for machine 1:

                • you would need to adjust the sales, variable cost and fixed cost per year with 6% inflation. For example just for the sales figures:
                • year 1 = 3,500 * (1.06)
                • year 2 = 3,500 * (1.06)^2
                • year 3 = 3,500 * (1.06)^3
                • year 4 = 3,500 * (1.06)^4
                • year 5 = 3,500 * (1.06)^5

                does that help?

              • Avatar of AnswerAnswer
                  • Undecided

                  Cotton Pty(Ltd) is has to replace a machine that is used to make a pulp out of grain fibres which is used in their main product, cereals. The current machine is not acceptable in terms of industry good practice anymore and needs to be replaced. The management of the firm has identified two new possible machines that can be used, but are unsure of the financial implications of acquiring any one of the two machines. You have been tasked with determining the acceptability of the two respective machines in terms of financing costs. This will assist the management of the firm, as they need information regarding which of the machines to investigate further and to discuss further with possible suppliers. You have been given permission to ask for any information from other employees at the firm.

                  Some general information was e-mailed to you by the bookkeeper: 

                   The current machine has been written off but there is already a committed buyer who has agreed to pay R5000 for the old machine, which he wants to sell as scrap metal. 
                   The company is taxed at 28%.
                   The machines are always depreciated on a straight- line basis over the usable life of the project. 
                   Quotes from an installer have already been obtained. It will cost R2 000 000 to install either machine. 
                   The company has always had such machines on their books and they need to be replaced at the end of their life. One can say that they are continually renewable projects.

                  The financial manager of the firm e-mailed you the following: 

                  “All of our projects are evaluated to take inflation and risk into account. For inflation, we adjust by using nominal cash flows (we adjust any real cash flows using the inflation rate) and we adjust for risk by using a risk-adjusted discount rate (RADR) based on the coefficient of variation (CV) of the cash flows.   

                  A risk adjustment is always made as follows: 

                  If the CV is smaller than 0,5, the risk premium is multiplied by 0,8

                  If the CV is larger than 0,5 but smaller than 0,75, the risk premium is kept as is. 

                  If the CV is more than 0,75, the risk premium is multiplied by 1,5.

                  Where the risk premium refers to WACC minus the risk free rate 

                  The WACC of the company is 15%, the risk free rate is 8%, inflation is 6% and the market risk premium is 6%. Excess funds can be re-invested at 12%. The company is established and has a beta of 0,9 which it also uses in evaluating core projects.

                  When evaluating multiple projects, we compare net present value (NPV), internal rate of return (IRR), modified internal rate of return (MIRR) and equivalent annual annuities (EAA) as well as the payback period. All of this information is passed on to decision makers so that they can start evaluating all projects that will at least offer acceptable returns.” 

                  Cash flows of the respective machines have been estimated as follows: 
                  Cash flows
                                                         Machine 1 (R000’s) Purchase price                            4000                Sales generated per year .         3500.  Variable costs associated.        50% of sales Fixed costs associated              200
                  Increase in NOWC.                     500 
                  Economic lifespan                      5 years Residual value @end of life      1500

                  Machine 2 (R000’s)
                  Purchase price                            5000              Sales generated per year          4500
                  Variable costs associated        40% of sales Fixed costs associated             500 
                  Increase in NOWC                      1000 
                  Economic lifespan                     4 years Residual value @end of life      2000

                   The sales generated per year were determined as follows:
                   Hint: The values above should be used in the determination of relevant cash flows,

                  the values below are for the CV calculation and not for the NPV calculation. 

                  All values in R’000’s.
                   Machine 1
                  Cash flow                                   Probability 2000                                                    0.1        3500                                                    0.8
                  5000                                                    0.1

                  Machine 2
                  Cashflow                                    Probability
                  1000                                                    0.2
                  4500                                                    0.7
                  11500                                                  0.1

                  Determine the: 
                  1. Relevant cash flows          (12)
                  2. Discount rates to be used         (8)
                  3. NPV’s            (2)
                  4. IRR’s            (2)
                  5. MIRR’s           (4)
                  6. Payback periods          (2)
                  7. EAA’s;            (4)

                  and making use of the given information, evaluate the acceptability of the two projects.

                  Also write a brief report regarding which one of the two machines would financially be better than the other, taking into account the information at hand only. Refer to your calculations findings in your report.  (6)

                  Number your calculations as set out above and use the number to refer to your calculations in your report.    

                  Its a long one

                • Up

                  Hey @fmccray:

                  For question 1, there is just a slight error in your understanding here. For the last final year where t=5 (5th year), not only there is £100m after tax cash inflow, there is also the £50m after tax salvage value. The salvage value ALSO happens in the final year, i.e. t=5, NOT t=6.

                  If you put C01=100 , F01=5, and C02=50, you are assuming that the £50m salvage value is received in year 6, which is incorrect.

                  In year 5, the total cash inflow is £150m (£100m + £50m salvage value), hence C01 = 100, F01 = 4, C02 = 150, F02 = 1 is correct.

                  Does this make sense?

                  For question 2, the minus sign on CF2 is incorrect and a typo on the publisher’s part. If you compute this without minus sign on 60 you should get 153.51 as I did.

                  CF0 = – 100, CF1 = 50, CF2 = 60, CF3 = 120, CF4 = 150, I = 15, CPT NPV. NPV = 153.51.

                  Hope these helps!

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