Complex question on NPV help please

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  • #3063330
    some_tear
    Participant

    I'm trying to to understand the fundamental concept of this question. I understand the concept of NPV and and how annuity calculation comes into play of calculating NPV but I cannot wrap my head around UNDERSTANDING this question as a whole, even after looking at the solution.

    Para Co. is reviewing the following data relating to an energy saving investment proposal:

    Cost $50,000
    Residual at the end of 5 years $10,000
    Present ‘value of an annuity of 1 at 12% for 5 years 3.60
    Present ‘.value of 1 due in 5 years at 12% 0.57

    What would be the annual sayings needed to make the investment realize a 12% yield?

    a, $8,189
    b, $12,306
    c, $13,889
    d, $11,111

    Answer is B and this is their explanation:

    PV cash savings/inflows = PV net cash outflows
    Annual savings x 3.60 = $50,000 – $10,000(0.57)
    Annual savings = ($50,000 – $5,700)/3.60
    Annual savings = $12,306

    #3063405
    Guest
    Guest

    You will be spending $50,000 now. So, to realize a 12% investment yield, you want to make sure that the present value of the residual value (at a 12% rate) plus the present value of whatever the annual savings will be (at a 12% rate) will equal the initial $50,000 cost.

    Therefore $50,000 = Present Value of Residual Value + Present Value of Annual Savings

    Present Value of Residual Value = Residual Value * PV Factor
    Present Value of Residual Value = $10,000 * 0.57
    Present Value of Residual Value = $5,700

    $50,000 = $5,700 + Present Value of Annual Savings

    Present Value of Annual Savings = 50,000 – 5,700 = $44,300

    Now that we know what the present value of the annual savings is, we need to determine what the annual savings actually is:

    Present Value of Annual Savings = Annual Savings * PV Annuity Factor
    $44,300 = Annual Savings * 3.6

    Annual Savings = $44,300 / 3.6 = $12,305.56

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