Corbin Consulting Cash Flow

SPFV Future Value of $1 paid now = (1+x)^n
SPPV Present Value of $1 paid in future = 1/(1+x)^n
USFV Future Value of uniform future payments of $1 = ((1+x)^n)-1)/x
SFFV Payment required each period to achieve Future Value of $1 = x/((1+x)^n)-1)
CRPV Payment required each period to achieve Present Value of $1 = (x*(1+x)^n)/((1+x)^n)-1)
USPV Present Value of uniform future payments of $1 = ((1+x)^n)-1)/(x*(1+x)^n)
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Definitions: n=number of periods, x=interest rate for a period.

SPFV example: (Future value of $100 in 7 years at 10% interest = $194.87)
SPPV example: (Present value of $500 received six years from now at 8% interest = $315)
USFV example: (Future value of $1,000 each year for 7 years at 9% interest = $9,200)
SFFV example: (Deposit required each month for 10 years at 15% interest to accumulate $200,000 = $603)
CRPV example: (Monthly payment on $300,000 mortgage for 20 years at 6% interest = $2,149)
USPV example: (Present value of $50,000 per year for 20 years at 7% interest = $529,700)

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Most often, cash flow problems are multi-part. Cash flows must be broken down into components and brought to same point in time. More than one iteration may be required.

Example Problem: At 8.2% interest, what is the present value of this cash flow? [$Y] = Uniform payments of $1500 each year for 5 years but the payments start 3 years from now. Also, [$Z] a final payment of $25000 will be made in the tenth year.
Solution:
Part A: Three years from now, [$Y] present value:
USPV = 3.972 factor; $1500, 5 periods at 8.2% per period = $5957
but today, present value $5958
SPPV = 0.789 factor; $5958, 3 periods at 8.2% per period = $4703 (answer part A)
Part B: Present value of [$Z] ten years from now:
SPPV = 0.455 factor; $25000, 10 periods at 8.2% per period = $11367 (answer part B)
Answer: (add the two results) $4703 + $11367 = $16,070 Present Value.

Solutions to problems may be subjective based on the assumptions used. Interest rate must be established by the evaluator. Risk and taxes are other considerations. 'What ifs' and 'trial and error' calculations may be required.
Caveat Emptor: How interest rates are stated by lenders can be tricky, leading one to believe the rate is lower than it is. That problem and other considerations are left to the evaluator.