Homework help!

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Please help me on how to compute for the following problem and what formula to use. I am confused. Should this be treated as FV? If so, what would be my PV? And where should I place the cash inflows per year? Thanks!!

You are thinking of starting a new product line that initially costs $32,000. Your annual projected cash inflows are as follow:

Year 1 -- $10,000
Year 2 -- $20,000
Year 3 -- $5,000

If you earn an interest of 10%, would you undertake this investment? Why?
 
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Unless stated otherwise, problems of this sort assume that the cash flows all occur on the last day of each year in question. Hence the three cash inflows as given occur on the last day of years 1, 2, and 3, respectively.

The basic idea is to...
  1. Determine the present value (PV) of each of the cash flows individually;
  2. Add up these three PVs; and then
  3. Compare this sum of the three PVs with the project's initial investment.

To calc the PV of any one cash inflow, use the formula

C / (1 + r)^n

Where C, r, and n denote, respectively,
  • The Cash flow amount itself
  • The applicable investment rate, interest rate, or discount rate
  • The number of periods (years, in this case) between today and the occurence of the cash flow

As an example, if I expect a cash flow of 15,000 to be received 4 years from now, and I can earn a rate of 7% on my investments generally, then this cash flow has a PV today of

15,000 / 1.07^4 = 11,443.43.

To answer the question, you'd accept the project if and only if the sum of the three PVs exceeds the original cost of the investment.

That gets you out of the starting gate; I'll let you bring it across the finish line.
 

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