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18 December, 16:10

You just won the TVM Lottery. You will receive $1 million today plus another 10 annual payments that increase by $375,000 per year. Thus, in one year, you receive $1.375 million. In two years, you get $1.75 million, and so on. If the appropriate interest rate is 6.5 percent, what is the value of your winnings today?

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  1. 18 December, 19:37
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    Total Present value (Sum of all PVs $21,624,467.720

    Explanation:

    The question is asking for the calculation or computation of the total PV of all the payments. This can be derived by summing up the Present Value (PV) of individual cash received.

    Step 1: Calculate the Present Value of each cash payment

    Formula = PV = C0 + C1 / (1+r) 1 + C2 / (1+r) 2 + ... + C n / (1+r) n

    C0, C1 ... Cn = Cash payments for each year for the 10 years

    r = The rate each period ... in the question this is 6.5%

    Step 2: Use the Formula to calculate annual cash payment

    Year Cash payment

    0 $1,000,000

    1 $1,000,000 + $ 375,000 = $1,375,000

    2 $1,375,000 + $ 375000 = $1,750,000

    3 $1,750,000 + $ 375000 = $2,125,000

    4 $2,125,000 + $ 375000 = $2,500,000

    5 $2,500,000 + $ 375000 = $2,875,000

    6 $2,875,000 + $ 375000 = $3,250,000

    7 3,250,000 + $ 375000 = $3,625,000

    8 $3,625,000 + $ 375000 = $4,000,000

    9 4,000,000 + $ 375000 = $4,375,000

    10 $4,375,000 + $ 375000 = $4,750,000

    Step 3: Use the calculated annual cash payments and the formula in step 1 to compute the Total Present Value

    Computation of PV:

    Yr Cash (C) PV Factor PV Factor @ 6.5 % (F) PV (C x F)

    0 1,000,000 1 / (1+0.065) ^0 1 1,000,000

    1 1,375,000 1 / (1+0.065) ^1 0.939 $1,291,079.812

    2 1,750,000 1 / (1+0.065) ^2 0.882 $1,542,903.745

    3 2,125,000 1 / (1+0.065) ^3 0.828 $1,759,179.320

    4 2,500,000 1 / (1+0.065) ^4 0.777 $1,943,307.727

    5 2,875,000 1 / (1+0.065) ^5 0.730 $2,098,407.405

    6 3,250,000 1 / (1+0.065) ^6 0.685 $2,227,335.886

    7 3,625,000 1 / (1+0.065) ^7 0.644 $2,332,710.029

    8 4,000,000 1 / (1+0.065) ^8 0.604 $2,416,924.751

    9 4,375,000 1 / (1+0.065) ^9 0.567 $2,482,170.372

    10 4,750,000 1 / (1+0.065) ^10 0.533 $2,530,448.669

    Total Present value (Sum of all PVs) $21,624,467.720
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Home » Business » You just won the TVM Lottery. You will receive $1 million today plus another 10 annual payments that increase by $375,000 per year. Thus, in one year, you receive $1.375 million. In two years, you get $1.75 million, and so on.
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