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Learn through experiments

Compare benefits at the same date

Can a project repay its cost yet have negative discounted value?

Entering midway? Revisit What does the reward encourage? for the preceding worked example, or start here and use the explanation below.

1 · Try

Start with a concrete question

A fictional equipment project costs money now and returns equal year-end benefits. Discounting converts future credits to comparable present credits.

Try the initial inputs, then write a prediction before changing one setting. All calculations run locally on your CPU.

Go directly to the experiment · Review basic mathematics

2 · Predict

What do you expect?

Predict whether a higher discount rate makes delayed benefits worth more or less today.

3 · Experiment

Change one thing. Inspect what happens.

  1. Set discount rate zero and reconcile present value with ordinary addition.
  2. Raise the discount rate and inspect each year separately.
  3. Find a case with positive undiscounted net but negative net present value; write the assumptions behind a decision.
Experiment inputs
Inputs
Your settingsMechanism
Calculation belowEvidence
Compare outcomes
Present benefits198.948 credits
Net present value-1.0518 credits
Undiscounted net40 credits

Compare the current results

Every bar starts at zero and uses the same numeric scale in this chart. The upper bound automatically adjusts to the largest current value (at least 1), so compare the numbers when changing inputs. Units and quantities come from each label; different kinds of quantity are not interchangeable. Displayed values are rounded to at most six significant digits.
072.7273
  • Year 1 discounted benefit72.7273
    Year 1 discounted benefit: 72.7273Horizontal bar from zero to 72.7273, on the shared zero to 72.7273 numeric axis.
  • Year 2 discounted benefit66.1157
    Year 2 discounted benefit: 66.1157Horizontal bar from zero to 66.1157, on the shared zero to 72.7273 numeric axis.
  • Year 3 discounted benefit60.1052
    Year 3 discounted benefit: 60.1052Horizontal bar from zero to 60.1052, on the shared zero to 72.7273 numeric axis.

Follow the calculation

  1. Year 1: 80/(1 + 0.1)^1 = 72.7273 present credits.
  2. Year 2: 80/(1 + 0.1)^2 = 66.1157 present credits.
  3. Year 3: 80/(1 + 0.1)^3 = 60.1052 present credits.
  4. Subtract upfront 200: net present value -1.0518.

Compare benefits at a common date. Positive modeled value depends on assumed cash flows and discount rate; it does not guarantee a real investment return.

Captures keep your inputs, prediction and observation. Results are recalculated from those inputs. Resetting inputs keeps your captures and challenge history.

4 · Understand

Explain the mechanism

Compare benefits at the same date

A fictional equipment project costs money now and returns equal year-end benefits. Discounting converts future credits to comparable present credits.

Predict before changing inputs

Predict whether a higher discount rate makes delayed benefits worth more or less today.

Understand the mechanism

Receiving a credit later is not identical to receiving one now when time and alternative uses matter. A discount rate encodes the chosen comparison assumption.

A benefit of 100 one year away at 10% is 100/1.1 ≈ 90.91 today. Two years away it is 100/1.1² ≈ 82.64.

Net present value adds discounted benefits and subtracts cost now. It is a model-based comparison, not a promise of returns.

Calculate it yourself

Present benefit in year t = benefit/(1 + discount rate)^t; NPV = sum of present benefits − upfront cost.

Guided investigation

  1. Set discount rate zero and reconcile present value with ordinary addition.

  2. Raise the discount rate and inspect each year separately.

  3. Find a case with positive undiscounted net but negative net present value; write the assumptions behind a decision.

Assumptions and limitations

  • Deterministic benefits, no taxes, inflation split, salvage value or probability-weighted risk.

  • Fictional project arithmetic is not investment advice.

Further investigations

High school: Compare receiving fictional credits now and later under an explicit rule.

College: Build a sensitivity table and distinguish nominal and real discounting.

Working professionals: Write a project decision brief with downside scenarios and nonfinancial constraints.

5 · Apply

Try a fresh case

A project costs 100 now and returns 121 at the end of year two. At 10% annual discount, what is net present value?

This is a public practice check. Retries support learning; matching a number does not certify independent proficiency.

Take the investigation further

Choose any extension. These are project prompts for you to carry out; they are not automatically assessed.

School investigation

Compare receiving fictional credits now and later under an explicit rule.

College investigation

Build a sensitivity table and distinguish nominal and real discounting.

Workplace investigation

Write a project decision brief with downside scenarios and nonfinancial constraints.

6 · Continue

Keep the evidence, choose your next step

Completion records your own decision that you have worked through this investigation. Practice checks and independent project evidence are separate.