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?

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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