Diminishing cash flows
Remember how compounded returns grow rapidly over time? Well, it works in the reverse, too. Compounded discount factors over time will quickly shrink a number towards zero.
For example, $100 at a 3% annual discount for 1 year is still worth roughly $97.08:
\( \frac{\text{Value}}{(1 + \text{Discount Rate} )^{\text{# of Discount Periods}}} = \frac{\text{\$100}}{(1 + 0.03)^1} = \text{ \$97.08 } \)
But this number shrinks quite rapidly as the number of discounting periods increases:
\( \frac{\text{\$100}}{(1 + 0.03)^5} = \text{ \$86.26 } \)
\( \frac{\text{\$100}}{(1 + 0.03)^{10}} = \text{ \$74.41 } \)
This means that the longer in the future your cash flows will be received (or paid), the close to 0 that number will be.
This exercise is part of the course
Introduction to Financial Concepts in Python
Exercise instructions
- Calculate the present value of a single $100 payment received 30 years from now with an annual inflation rate of 3%, and assign it to
investment_1. - Calculate the present value of the same payment, but if it was received 50 and 100 years from now, and assign it to
investment_2andinvestment_3respectively.
Hands-on interactive exercise
Have a go at this exercise by completing this sample code.
import numpy as np
# Calculate investment_1
investment_1 = np.pv(rate=____, nper=____, pmt=____, fv=____)
print("Investment 1 is worth $" + str(round(-investment_1, 2)) + " in today's dollars")
# Calculate investment_2
investment_2 = np.pv(rate=____, nper=____, pmt=____, fv=____)
print("Investment 2 is worth $" + str(round(-investment_2, 2)) + " in today's dollars")
# Calculate investment_3
investment_3 = ____
print("Investment 3 is worth $" + str(round(-investment_3, 2)) + " in today's dollars")