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    Computing The Value of A Growing Finite Annuity

    Uploaded by

    Mahmood Ahmad
    The document provides information to calculate the present value of a growing finite annuity, including the periodic payment amount, growth rate, number of periods, and discount rate. It then shows the present value calculated using the formula and using an NPV function. It also includes an example of calculating the internal rate of return for a series of cash flows using the IRR function, loan table, and goal seek.

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    Computing The Value of A Growing Finite Annuity

    Uploaded by

    Mahmood Ahmad
    24 views10 pages
    The document provides information to calculate the present value of a growing finite annuity, including the periodic payment amount, growth rate, number of periods, and discount rate. It then shows the present value calculated using the formula and using an NPV function. It also includes an example of calculating the internal rate of return for a series of cash flows using the IRR function, loan table, and goal seek.

    Original Title

    Lecture 3 (25-09-2020) 2-40 to 4

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    The document provides information to calculate the present value of a growing finite annuity, including the periodic payment amount, growth rate, number of periods, and discount rate. It then shows the present value calculated using the formula and using an NPV function. It also includes an example of calculating the internal rate of return for a series of cash flows using the IRR function, loan table, and goal seek.

    Copyright:

    © All Rights Reserved
    Download as XLSX, PDF, TXT or read online from Scribd
    Download as xlsx, pdf, or txt
    24 views10 pages

    Computing The Value of A Growing Finite Annuity

    Uploaded by

    Mahmood Ahmad
    The document provides information to calculate the present value of a growing finite annuity, including the periodic payment amount, growth rate, number of periods, and discount rate. It then shows the present value calculated using the formula and using an NPV function. It also includes an example of calculating the internal rate of return for a series of cash flows using the IRR function, loan table, and goal seek.

    Copyright:

    © All Rights Reserved
    Download as XLSX, PDF, TXT or read online from Scribd
    Download as xlsx, pdf, or txt
    of 10

    COMPUTING THE VALUE OF A GROWING FINITE ANNU

    First Payment, C 1000


    Growth Rate of Payments, g 6%
    No. of Future Periods paid, n 5
    Discount Rate, r 12%

    Present Value of Annuity


    Using Formula 4010.91 PV=>C*(1-((1+g)/(1+r))^n)/(r-g)

    Period Annuity Payment


    1 1000
    2 1060.00
    3 1123.60
    4 1191.02
    5 1262.48
    943.40
    Present Value of Annuity Using NPV Function 4010.91
    ING FINITE ANNUITY
    Periodic payment, C 1,000
    Growth rate of payments, g 6%
    Discount rate, r 12%
    Present value of infiniteannuity 16,666.67 C/(r-g)

    ))^n)/(r-g)
    INTERNAL RATE OF RETURN
    Year CashFlow
    0 -800
    1 200
    2 250
    3 300
    4 350
    5 400

    Internal rate of Return 22%

    Using the IRR in Loan Table


    Cash Flow at
    Investment at the End of the
    Year Beginning of the year year Income Return of Principle
    1 800.00 200.00 177.28 22.72
    2 777.28 250.00 172.25 77.75
    3 699.53 300.00 155.02 144.98
    4 554.55 350.00 122.89 227.11
    5 327.44 400.00 72.56 327.44
    6 0.00
    USING LOAN TABLE TO FIND IRR

    IRR? 15.00%

    Cash Flow
    Investment at at the End
    Year Beginning of the year of the year Income Principle
    1 1000.00 300.00 150.00 150.00
    2 850.00 200.00 127.50 72.50
    3 777.50 150.00 116.63 33.38
    4 744.13 600.00 111.62 488.38
    5 255.74 900.00 38.36 861.64
    6 -605.89

    DIRECT CALCULATION OF IRR


    Year Cash Flow
    0 -1000
    1 300
    2 200
    3 150
    4 600
    5 900
    IRR 24%
    USING GOAL SEEK
    IRR? 24.44%

    Investment
    at
    Beginning Cash Flow at the
    Year of the year End of the year Income Principle
    1 1000.00 300.00 244.36 55.64
    2 944.36 200.00 230.76 -30.76
    3 975.13 150.00 238.28 -88.28
    4 1063.41 600.00 259.86 340.14
    5 723.26 900.00 176.74 723.26
    6 0.00

    OF IRR
    USING EXCEL'S RATE FUNCTION TO COMPUTE THE
    IRR

    Initial Investment 1000


    Periodic Cash Flow 100
    Number Of Payments 30
    IRR 9.307%
    Multiple Internal Rates of Return
    Discount Rate 6% Discount NPV 12
    NPV ($3.99) ($3.99)
    Year Cashflows 0% 10
    0 -145 3%
    1 100 6% 8
    2 100 9%
    3 100 12% 6
    4 100 15%
    5 -275 18% 4
    21%
    24% 2
    27%
    30% 0
    0% 5% 10% 15% 20% 25% 30% 35% 40
    33%
    36%
    39%
    Column F

    5% 20% 25% 30% 35% 40% 45%


    FLAT PAYMENT SCHEDULE
    Loan Principle 10000
    Interest Rate 7% Effective Interest Rate = (1+(Inom/m)^m)
    Loan Term 6 Effective Interest Rate = (1+(Inom/m)^m)
    Annual Payment 2097.96

    Principal at
    the Beginning Payment at the End
    Year of the Year of Year Interest
    1 10000 2097.96 700
    2 8602.04 2097.96 602.1429
    3 7106.23 2097.96 497.4359
    4 5505.70 2097.96 385.3993
    5 3793.15 2097.96 265.5202
    6 1960.71 2097.96 137.2496
    7 0.00
    ate = (1+(Inom/m)^m)-1
    ate = (1+(Inom/m)^m)-1

    (1+(Inom/m))^m)-1 7%

    Return of
    Principal ((1+(Inom/m))^m) 107%
    1397.96 (1+(Inom/m) 101%
    1495.82 (Inom/m) 0.56541% Monthly Interest Rate
    1600.52
    1712.56
    1832.44
    1960.71

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