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What formula do I need to calculate the comparative value of these investments?
Hi all,
Law student here, knowing nothing about economics. I need to come up with a formula that will let me demonstrate the difference between different multipliers in costs awards. (I'm not asking you to do my homework! I can make my point just by saying that 2.5 is greater than 1.5, but I'd really like some real numbers for emotional effect.)
The question:
Suppose there is a law firm that does $100,000 worth of work on a case every year for ten years. At the end of that ten years, there is a 75% chance that they will win the case. If they win, they will have those costs reimbursed (suppose a 3% annual interest rate). Furthermore, the judge might order that that reimbursement be multiplied by 1.5, 2.0, or 2.5. (Jackpot!)
What I'm looking for is the net present value of that ten-year investment of $100,000 annually if the judge:
a) does not make any multiplier order
b) orders a 1.5x multiplier
c) orders a 2.0x multiplier
d) orders a 2.5x multiplier
If you can just provide me with the appropriate formula, I'm happy to do this myself --- it's just that having to base the value of these orders on an investment that is itself compounding over ten years is well beyond my capacity to figure out!
Thanks in advance!
3 Answers
- SuzanneLv 51 decade agoFavorite Answer
There is not really a single formula. To calculate the NPV you need to calculate the present value of the cash flows in each year and then add them together.
The easiest way (imo) to do this is to set up a cash flow table in Excel and then use the NPV function to calculate the NPV of the cash flows, years 1-10 Other people may prefer a financial calculator. The excel NPV formula format is =NPV(rate,cf1, cf2, cf3,,,,cfx)
Year 1 - 9 would each have a negative cash flow of (100,000).
Year 10 would have a cash inflow of $1,000,000 times your multiplier less the year 10 outflow of (100,00)
This assumes the 100,000 outflow occurs at the end of the year.
Your cost of capital is 3% (I am assuming this what you mean and not simply inflation)
Given this information, I show the NPV of each possibility is:
a. A loss of ($130,599)
b. A gain of $266,732
c. A gain of $664,064
d. A gain of $1,061,396
Also these are the NPV if you actually win the case. In order to find the Expected Value, which accounts for the possibility you might receieve nothing, you need to multiply each by .75
- 1 decade ago
Assumes the 100,000 is incurred at the end of year 1.
= (100,000 / 1.03^1) + (100,000 / 1.03^2) + (100,000 / 1.03^3) + (100,000 / 1.03^4) .... All the way up to ^10 for 10 years.
This should equal 853,020.28 * 75% (chance winning) = 639,765.21
Multiply this number by the multiplier.
