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Time Value of Money: Mixed Streams

Fixed amounts were the first calculations discussed in Time Value of Money: Present & Future and we filled out that knowledge with Time Value of Money: Financial Tables. Then we moved into Time Value of Money: Ordinary Annuities and Time Value of Money: Annuities Due. The next step is to understand Mixed Streams of cash inflows and outflows in your business.

Future Value of Mixed Streams of Cash Flow

Unlike a regular periodic cash flow like an annuity, there are often cases where you need to be able to evaluate the Future Value and Present Value of a mixed stream of cash inflows / outflows.

To calculate the Future Value of a Mixed Stream of cash flows you can simply work out the individual values using Financial Tables and find their total. For example, you may expect to receive a series of cash flows over the next 4 years of $10,000, $12,000, $8,000 and $21,000 and you expect that a reasonable amount to earn on the investment is 7 per cent interest.

To follow those calculations through:

  • Future Value(1) = Present Value * (FVIFi,n)
  • Future Value(1) = $10,000 * (FVIF0.07,3)
  • Future Value(1) = $10,000 * 1.225
  • Future Value(1) = $12,250
  • Future Value(2) = Present Value * (FVIFi,n)
  • Future Value(2) = $12,000 * (FVIF0.07,2)
  • Future Value(2) = $12,000 * 1.145
  • Future Value(2) = $13,740
  • Future Value(3) = Present Value * (FVIFi,n)
  • Future Value(3) = $8,000 * (FVIF0.07,1)
  • Future Value(3) = $10,000 * 1.070
  • Future Value(3) = $8,560

The Future Value(4) of the $21,000 remains at $21,000 because it accumulates zero interest.

Adding the Future Value(1) + Future Value(2) + Future Value(3) + Future Value(4) gives us the Future Value of that Mixed Stream: $55,550.

Time line for a Mixed Stream of $10,000, $12,000, $8,000 & $21,000 cash outflow at 7% for 4 years

A tip: Draw the diagrams first and it will help you visualise when cash flows occur and the number of periods to apply interest.

Present Value of Mixed Streams of Cash Flow

To calculate the Present Value of a Mixed Stream of cash flows you can simply work out the individual values at a depreciated interest rate and add the totals.

To follow those calculations through:

  • Present Value(1) = Future Value * (PVIFi,n)
  • Present Value(1) = $10,000 * (PVIF0.07,1)
  • Present Value(1) = $10,000 * 0.935
  • Present Value(1) = $9,350
  • Present Value(2) = Future Valuye * (PVIFi,n)
  • Present Value(2) = $12,000 * (PVIF0.07,2)
  • Present Value(2) = $12,000 * 0.873
  • Present Value(2) = $10,476
  • Present Value(3) = Future Value * (PVIFi,n)
  • Present Value(3) = $8,000 * (PVIF0.07,3)
  • Present Value(3) = $10,000 * 0.816
  • Present Value(3) = $6,528
  • Present Value(4) = Future Value * (PVIFi,n)
  • Present Value(4) = $21,000 * (PVIF0.07,4)
  • Present Value(4) = $21,000 * 0.763
  • Present Value(4) = $16,023

Adding the Present Value(1) + Present Value(2) + Present Value(3) + Present Value(4) gives us the Future Value of that Mixed Stream: $42,337.

Time line for Mixed Stream of $10,000, $12,000, $8,000 & $21,000 cash outflow at 7% for 4 years

Whereas the Future Value of the same Mixed Stream was: $55,550.

The Next Step: Frequency of Compound Interest

In the next instalment in this Time Value of Money series we will discuss compounding of interest more frequent than once per year.

I would also advise you to pick up any decent copy of a managerial finance textbook to underpin these articles and to complete the exercises that will cement this understanding at the end of each chapter. The textbook will also provide more precise context important to your understanding.

Time Value of Money 101 Series

  1. Time Value of Money: Present & Future
  2. Time Value of Money: Financial Tables
  3. Time Value of Money: Ordinary Annuities
  4. Time Value of Money: Annuities Due
  5. Time Value of Money: Mixed Streams
  6. Time Value of Money: Compound Interest (redux)
  7. Time Value of Money: Nominal versus Effective Interest Rates
  8. Time Value of Money: Accumulation of a Target Sum & Loan Amortisation
  9. Time Value of Money: Time Periods to Reach a Sum & Growth Rates

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About the Author

Steven Clark Steven Clark - the stand up guy on this site

My name is Steven Clark (aka nortypig) and I live in Southern Tasmania. I have an MBA (Specialisation) and a Bachelor of Computing from the University of Tasmania. I'm a photographer making pictures with film. A web developer for money. A business consultant for fun. A journalist on paper. Dreams of owning the World. Idea champion. Paradox. Life partner to Megan.

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