Present & Future Value | Interactive Finance Math

Evaluate the project

Initial project cost ($) Future project payoff ($) Required return (%) Project life (years)

Initial cost today—

PV of future payoff—

PV surplus / shortfall—

Required FV of today's cost—

Future-value surplus / shortfall—

Project decision—

Evaluation viewpoint	Project value	Required value	Difference
Present-value test (today)
Future-value test (year n)

Why both tests give the same decision: Present Value and Future Value are simply values measured at different points in time. If the project's future payoff discounts back to more than its cost today, then the same payoff must also be greater than the amount that the initial cost would need to grow to at the required rate. Change the interest rate or project life and watch the break-even payoff move.

Present and Future Value Project Model

Use the required rate of return to compare money occurring at different times. The project can be evaluated either at time 0 using present value or at the end of the project using future value.

The two methods should always produce the same accept/reject decision when the same interest rate and time period are used.

# Project Evaluation using
# Present Value and Future Value

initial_cost = 10000
future_payoff = 15000
required_return = 0.08
years = 5

# ---------------------------------
# Method 1: Present Value
# ---------------------------------

present_value = future_payoff / (
    1 + required_return
) ** years

pv_surplus = (
    present_value - initial_cost
)

# ---------------------------------
# Method 2: Future Value
# ---------------------------------

required_future_value = (
    initial_cost
    * (1 + required_return) ** years
)

fv_surplus = (
    future_payoff
    - required_future_value
)

print(
    "Initial project cost:",
    round(initial_cost, 2)
)

print(
    "Future project payoff:",
    round(future_payoff, 2)
)

print(
    "PV of future payoff:",
    round(present_value, 2)
)

print(
    "PV surplus:",
    round(pv_surplus, 2)
)

print(
    "Required future value:",
    round(required_future_value, 2)
)

print(
    "FV surplus:",
    round(fv_surplus, 2)
)

# Both methods give the
# same project decision.

if present_value > initial_cost:
    print("Decision: ACCEPT project")

elif present_value < initial_cost:
    print("Decision: REJECT project")

else:
    print("Decision: BREAK EVEN")

# Break-even future payoff
break_even_payoff = (
    initial_cost
    * (1 + required_return) ** years
)

print(
    "Break-even payoff:",
    round(break_even_payoff, 2)
)

Project Evaluation Python Model

Change the initial cost, future payoff, required return and project life. Compare the project's value today with its cost, then check the same decision by moving the cost forward to the project's final year.