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?

Question

Business

Davon Harmon

1 June, 04:44

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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Answers (1)

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Monique Atkinson · Answer 1

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