Time Value of money questions that have me stumped

hangin1

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May 9, 2010
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Hello all, first I wanna say thanks in advance to anyone here that takes the time to help me. I currently have a few time value of money problems that have me stumped and I dont know which formulas to use to figure them out so I figured I would post them here and maybe someone could help me out. the questions I am currently having trouble with are as follows:

1. Assume you have just inherited $600,000. Because of this, you have decided to quit your job and live off this inheritance. To make the money last, you have decided to invest it at 12% and withdraw it in 20 equal amounts over the next 20 years. Your first withdrawal will be one year from today. How much will you be able to withdraw each year?

2. Your boss has given you the responsibility for furnishing the soon-to-be-completed headquarters building. The furniture you have picked out at Cape Furniture Company can be purchased for $125,000 and then sold at the end of its 10 year useful life for $10,000. Cape has also given you the option of leasing the furniture for $18,000 per year for 10 years. Your first payment will be made when you sign the lease and receive the furniture. Under the lease agreement, you will have to return the furniture to Cape at the end of ten years (with no compensation). Assuming the annual interest rate of 9%, which option (buying or leasing) is better and by how much?

3. Assume your company just sold a mainframe computer. The computer originally cost $300,000 and had accumulated depreciation of $100,000 on the date of the sale. Instead of the buyer paying cash, she gave you a $400,000 noninterest-bearing note due and payable in 3 years. There is no established exchange price for the computer, and the note has no ready market. The prevailing rate of interest for a note of this type is 8%. What should your company record as a gain from the sale of this computer?

I look forward to your help and I will once again say I do appreciate the help greatly as I have been pounding my head against the wall on these questions now for some time today.
 
hangin1 said:
1. Assume you have just inherited $600,000. Because of this, you have decided to quit your job and live off this inheritance. To make the money last, you have decided to invest it at 12% and withdraw it in 20 equal amounts over the next 20 years. Your first withdrawal will be one year from today. How much will you be able to withdraw each year?
Code:
0                                                  600000.00
1                - w              72000.00         600000.00 - w + 72000.00 (12% of 600000.00)
....
20               - w                   ?                 .00
If w = withdrawal, above represents "kwickly(!)" what happens; follow that?

You can look at this as you lending a bank $600,000 at 12% annual interest, repayable over 20 years.
The formula to determine the payment/withdrawal is:
W = Ai / (1 - v) where v = 1 / (1 + i)^n
W = Withdrawal (?)
A = Amount (600,000)
i = interest rate (.12)
n = number of withdrawals (20)

W = (600000 * .12) / (1 - 1 / 1.12^20) = 80327.268.....; so $80,327.27 rounded

Clear?
I'm kinda surprised this formula was not given to you in class...
 
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