from random import randint
year = range(0,6)
interestRate = .082
predictions = [ randint(0, 300) for _ in range(5)]
cashFlow = [-500] + predictions
cashFlow[-500, 195, 127, 44, 42, 196]Among the list of formulas I learned in the Financial Analyst coures, this is valuation is the one I instintively distrusted. Discounted Cash Flows is a way to evaluate the future returns on an investement based on: 1. The initial Investment. 2. The Expected Cashflow per each year.
The problem I have here is that the Expected Cashflows are purely guesses about what we belive the numbers to be in the future. While the example in the class picked - as far as I can tell - random numbers to fill them in, I would hope that the numbers provided here would be based on research of other similar projects. At least, I would hope in the real world this is was happens.
Discounting Cash Flows
The formula for this is: > \(DCF= (CF_1)/(1 + r)^1 + (CF_2)/(1 + r)^2 + .. + (CF_n)/(1 + r)^n\)
… where:
- CF stands for Cash Flow
- r is the interest rate
- n is the period of discount.
This all follows from the simple idea that money now is more valuble than money in the future. If given the choice between $100 now and $100 in a year then you’d obviously take the $100 now. This also applies to money we earn in the future: $60 now is better than the $60 we’d earn in the future. So, example time.
We’re going to use a similar example to the class: Imagine that we’re considering inveseting money into a venture. We’re going to do something a bit more modern and say we’re investing in a growing Online Streamer with the expectation that we’ll get some of the money in turn. A deal is worked out and you’ll be getting some kind of slice of the money they make in exchange. They’re going to ask for $500 in investment. For the interest rate, we’ll use the Inflation Rate since this is not a loan. Right now, it’s 8.2% so we’ll use that as our Interest Rate; Sometimes this also called the Discount Rate and Inflation certainly applies.
We’ll use random numbers over the span of 6 years and then calculate if this was a good idea.
We’ll need a function to calculate the Present Value for each term in the formula. For this, we’ll just write up a quick lambda function in python.
PV = (lambda f,i,n: f/(1+i)**n)
PV(30, interestRate, 1)27.726432532347502We’ll usually see this in a table so we’ll add all this to a Data frame.
data = pd.DataFrame(
{"Year":year,
"Cash":cashFlow,
'Pv':repeat(0,len(year))
})
data| Year | Cash | Pv | |
|---|---|---|---|
| 0 | 0 | -500 | 0 |
| 1 | 1 | 195 | 0 |
| 2 | 2 | 127 | 0 |
| 3 | 3 | 44 | 0 |
| 4 | 4 | 42 | 0 |
| 5 | 5 | 196 | 0 |
… and now we can iterate through the rows and fill in the Present Value per year.
for _,r in data.iterrows():
data.loc[r.Year, 'PV'] = round(PV(r.Cash, interestRate, r.Year), 2 )Lastly, we’ll take the sum to see if it was worth it.
data.PV.sum()-13.749999999999972Looks like we lost about $14 which is not that surprising since making money in Streaming can be quite challenging.