#### Present Value

R
```"""
Reference: https://www.investopedia.com/terms/p/presentvalue.asp

An algorithm that calculates the present value of a stream of yearly cash flows given...
1. The discount rate (as a decimal, not a percent)
2. An array of cash flows, with the index of the cash flow being the associated year

Note: This algorithm assumes that cash flows are paid at the end of the specified year
"""

def present_value(discount_rate: float, cash_flows: list[float]) -> float:
"""
>>> present_value(0.13, [10, 20.70, -293, 297])
4.69
>>> present_value(0.07, [-109129.39, 30923.23, 15098.93, 29734,39])
-42739.63
>>> present_value(0.07, [109129.39, 30923.23, 15098.93, 29734,39])
175519.15
>>> present_value(-1, [109129.39, 30923.23, 15098.93, 29734,39])
Traceback (most recent call last):
...
ValueError: Discount rate cannot be negative
>>> present_value(0.03, [])
Traceback (most recent call last):
...
ValueError: Cash flows list cannot be empty
"""
if discount_rate < 0:
raise ValueError("Discount rate cannot be negative")
if not cash_flows:
raise ValueError("Cash flows list cannot be empty")
present_value = sum(
cash_flow / ((1 + discount_rate) ** i) for i, cash_flow in enumerate(cash_flows)
)
return round(present_value, ndigits=2)

if __name__ == "__main__":
import doctest

doctest.testmod()
```