Business, 25.01.2020 07:31 hardwick744

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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Answer from: kat6282

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

Answer from: Quest

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Answer from: Quest

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