Answer:
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
