Robertson Inc. wishes to set aside lump sum money to withdraw from and invest in

Question

Robertson Inc. wishes to set aside lump sum money to withdraw from and invest in automating parts of its business over the next 5 years. This money is expected to earn compound interest at the rate of 10% per year. The following are the expected dates of withdrawals:
Year 1: $40,000
Year 2: No withdrawal
Year 3: $25,000
Year 4: $50,000
Year 5: $10,000.
How much money should Robertson Inc. deposit today to be able to withdraw the increments listed above? Also, make a table to show, on a year by year basis, if your calculated amount is correct. The table should show the interest earned, the withdrawals made and the balance left in the account.

Explanation / Answer

Y = 5 years
i = 10% per year
Year 1 = 40,000
Year 2 = 0
Year 3 = 25,000
Year 4 = 50,000
Year 5 = 10,000
P = ?

NPV = - P + 40,000 (P/F,i=10%,N=1) + 25,000 (P/F,i=10%,N=3) + 50,000 (P/F,i=10%,N=4) + 10,000 (P/F,i=10%,N=5)

0 = - P + 40,000 (1+10%)-1 + 25,000 (1+10%)-3 + 50,000 (1+10%)-4 + 10,000 (1+10%)-5
P = 36,363.64 + 18,782.87 + 34,150.67 + 6,209.21
P = 95,506.39

Year Balance Interest Earned Withdraw Balance Left 0                   -                         -                       -   95,506.39 1    95,506.39          9,550.64 (40,000.00) 65,057.03 2    65,057.03          6,505.70                     -   71,562.73 3    71,562.73          7,156.27 (25,000.00) 53,719.01 4    53,719.01          5,371.90 (50,000.00)      9,090.91 5      9,090.91             909.09 (10,000.00) (0.00)

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