Discounted Cash Flow | Interactive Finance Math

Interactive DCF model

Initial investment ($) Year 1 cash flow ($) Cash-flow growth (%) Discount rate (%) Forecast years

Future cash flow Present value

Total future cash flows—

Present value of cash flows—

Initial investment—

Net present value (NPV)—

Value lost to discounting—

Investment indication—

Year	Cash Flow ($)	Discount Factor	Present Value ($)

Interpretation: A positive NPV means the discounted value of the forecast cash inflows is greater than the initial investment under these assumptions. A negative NPV means the forecast inflows do not recover the investment after allowing for the required discount rate. Try increasing the discount rate and observe how present value falls.

Explore Discounted Cash Flow

Change the assumptions and observe how the discount rate and time affect the present value of future money. Compare the undiscounted cash flows with their values today.

DCF is widely used to connect exponential mathematics with investment and business decisions.

import numpy as np
import matplotlib.pyplot as plt

# Discounted Cash Flow assumptions
initial_investment = 10000
cash_flow_1 = 2500
growth_rate = 0.05
discount_rate = 0.08
years = 5

year = np.arange(1, years + 1)

# Forecast cash flows
cash_flows = cash_flow_1 * (
    1 + growth_rate
) ** (year - 1)

# Discount each future cash flow
discount_factors = 1 / (
    1 + discount_rate
) ** year

present_values = (
    cash_flows * discount_factors
)

# Total present value of future cash flows
total_pv = present_values.sum()

# Net Present Value
npv = total_pv - initial_investment

print("Year   Cash Flow   Present Value")

for t, cf, pv in zip(
    year, cash_flows, present_values
):
    print(
        f"{t:4d} "
        f"{cf:11.2f} "
        f"{pv:14.2f}"
    )

print()
print(
    "Total future cash flows:",
    round(cash_flows.sum(), 2)
)
print(
    "Present value:",
    round(total_pv, 2)
)
print(
    "Initial investment:",
    initial_investment
)
print(
    "NPV:",
    round(npv, 2)
)

# Plot future cash flow and
# its discounted present value
plt.plot(
    year,
    cash_flows,
    marker="o",
    label="Future cash flow"
)

plt.plot(
    year,
    present_values,
    marker="o",
    label="Present value"
)

plt.xlabel("Year")
plt.ylabel("Money ($)")
plt.title("Discounted Cash Flow")
plt.grid()
plt.legend()
plt.show()

DCF Python Model

This Python model forecasts a growing series of cash flows and discounts each one back to today. Change the assumptions and compare the Python result with the interactive explorer.