Money already spent

Paper packet. Every task here also exists on screen, where it is checked automatically; answers written on paper are not assessed by Nydus. When you are back at a device, enter your answers there.

1. What you will learn

You will identify the irrecoverable portion of past expenditure and compare the future benefits, additional costs and available recoveries of current alternatives. Explain why a refund can matter even after an earlier payment, why sunk cost alone supports neither continuation nor abandonment, and why historical accounting and current choice answer different questions.

2. Starting point

Use the stated alternatives, quantities and units. Separate a model's assumptions from the conclusion derived from them.

3. Terms to use precisely

4. Irrecoverable past costs do not change with today's choice

A sunk cost is a cost already incurred that cannot be recovered under the alternatives currently being compared. A nonrefundable ticket payment can be sunk when deciding whether to attend an event today. Attending does not get the payment back, and staying home does not get it back either. The payment is the same in both forward-looking comparisons, so it does not by itself favor attendance.

Both parts of the definition matter. A payment made earlier is not automatically sunk in full. If it can be refunded, resold, or recovered through a feasible alternative, the recoverable amount can affect today's decision. Likewise, a cost scheduled for later is not sunk merely because someone has promised or planned to pay it. We need to know what changes under the alternatives, not just whether the amount appears in an old receipt.

The useful question is: which benefits, costs, and recoveries still differ depending on what we choose now? These may include enjoyment, additional travel, future fees, refund rights, resale possibilities, and alternative uses of time. The lesson's numerical models give comparable future values so that the arithmetic can be checked. They do not assume that every real experience can be measured precisely in money.

Ignoring a sunk amount in an incremental comparison does not mean pretending that the earlier expenditure never happened. It may matter to accounting, learning from decisions, remaining wealth, or responsibility for past actions. The narrower claim is that an unchanged irrecoverable cost should not be added as a reason to select one current option over another when their future consequences are otherwise being compared.

Term	What it means
Sunk cost	A cost already incurred that cannot be recovered under the current alternatives.
Avoidable cost	A future cost that can be avoided by selecting another feasible option.
Recovery	Value returned through an available refund, resale, or similar alternative.
Incremental comparison	A comparison of the future consequences that differ between current options.
Historical account	A record that includes past expenditure even when it does not affect today's ranking.

Another way: Compare future net results from the same starting point

Imagine that a group paid thirty dollars for nonrefundable tickets. Going now brings a supplied benefit of eighteen teaching units but requires six units of additional travel cost. Staying brings a benefit of ten units with no extra cost. From today's starting point, the net results are twelve for going and ten for staying. Going is better by two under this supplied model, but the reason is the future difference, not the old thirty-dollar payment.

Now suppose the expected benefit of going falls to nine while the additional travel cost remains six. Its future net becomes three, while staying still gives ten. Staying is better by seven. The sunk ticket price has not changed, yet the recommendation changes because a relevant future condition changed. This is exactly what a forward-looking comparison should allow.

If the task asks for total historical profit or total expenditure, include the old payment in that separate accounting question. If it asks which option is better from now on, compare the consequences that differ from now on. Mixing those two questions creates apparent contradictions. A project can have lost money overall while continuing it is the better current option, or have been profitable so far while stopping it is now better.

Check the arithmetic by calculating each option's future net separately before comparing. Benefits plus recoveries minus additional avoidable costs gives the result under the simple model. The same already-irrecoverable amount should not appear as a penalty only on the option of stopping. That asymmetric treatment is the mistake in the claim that staying home uniquely throws away a nonrefundable ticket payment.

Another way: Refunds and resale are relevant alternatives

Suppose staying home permits a refund of twelve dollars while attending gives up that refund. The twelve-dollar recovery is relevant because it changes with today's choice. It is not erased merely because the original payment occurred last week. A comparison can record twelve as a benefit of canceling or as a forgone recovery when attending, but should not count it twice.

A partially refundable payment illustrates why the original total and the recoverable portion must be separated. If a forty-dollar ticket allows a ten-dollar refund, thirty dollars is unrecoverable under those alternatives. The ten dollars can still affect today's decision. The task may use comparable teaching units rather than actual money, but the logical distinction is the same: an amount shared across alternatives cancels, while an amount that differs can matter.

Resale can play a similar role if it is genuinely feasible. A machine bought years ago may now have a resale value. Keeping it for a project forgoes that available recovery, so the old purchase price is not the only relevant figure. Whether the resale can actually occur, what transaction costs apply, and when the money is received are factual conditions that the model must state. Do not invent a resale market simply to make every old expense recoverable.

The principle also applies to deposits, reservations, and prepaid materials. Read the cancellation conditions rather than deciding from the word 'deposit'. Some deposits are refundable, some partly refundable, and some irrecoverable. The economic classification follows those conditions. A learner should be able to explain why two equal past payments can play different roles in a current decision when their recovery possibilities differ.

Another way: Past information can still matter without the sunk amount deciding

A failed earlier attempt may reveal that completing a project will be harder than expected. That information can change a forecast of future costs. Using the new forecast is not a sunk-cost error. The error would be insisting on continuation solely because much has already been spent, without a favorable comparison of what continuing and stopping now would bring.

Likewise, past spending may reduce the resources currently available. A household or club with less remaining money faces a different budget constraint. The future options must be feasible under that current constraint. Recognizing the constraint does not mean counting the old payment again as an extra future charge. Separate the current resource position produced by history from the claim that a previous irrecoverable expenditure must be justified by further spending.

Commitments to other people can also create future consequences of canceling, such as a stated cancellation fee or a broken promise whose consequences the decision maker values. Those considerations are not automatically sunk just because the arrangement was made earlier. The exercise must specify what remains avoidable and what effects differ. The slogan 'ignore the past' is too broad to perform that analysis responsibly.

A careful review can therefore say two things together: the past expenditure should inform accounting and lessons learned, while today's action should be evaluated using the relevant feasible future alternatives. This protects the distinction without suggesting that memory, trust, or responsibility disappear from economic reasoning. The model is about which consequences differ, not about declaring the past morally irrelevant.

Another way: Avoid both automatic continuation and automatic abandonment

Recognizing a sunk cost does not imply that the project should stop. If the future benefits of completing it exceed the relevant future costs and the best feasible alternative under the stated criterion, continuing may be the better option. A partially completed project can be worth finishing even if starting it originally was a mistake. The current decision and the original decision use different opportunity sets.

The opposite error is to believe that a large sunk cost creates a stronger reason to continue than a small one when all future options are identical. Suppose two groups face the same remaining benefits and avoidable costs but paid different nonrefundable amounts in the past. Under the simple forward-looking model, the comparison between continuing and stopping is the same for both. Their historical accounts differ, but the present incremental ranking does not.

Use a decision table with one row per current option. Put future benefits, additional costs, and feasible recoveries in separate columns. Exclude a wholly irrecoverable past amount from those changing columns. Then calculate each future net and compare the results. If there is a tie, the model alone does not select a unique option unless a tie rule is supplied. Our scored cases avoid ties so the final label is determinate.

Explain the result with its reason. 'Choose A because its future net is fourteen rather than nine' is a model-based comparison. 'Choose A because we already paid' is not. The distinction helps people reconsider plans without treating a change of mind as proof that the earlier resources can somehow be recovered by spending more. A transparent calculation names what can still be gained, avoided, or recovered.

5. Reconsidering tickets after the forecast changes

A fictional club has already paid forty-eight dollars for nonrefundable fair tickets. A message argues that the club must attend because staying home would throw away the payment. The payment is irrecoverable under both options, so that sentence gives the past amount a role it does not have in the current comparison. Attending cannot recover the forty-eight dollars either.

For a bounded exercise, suppose attending now offers twenty benefit units and requires eight additional travel units, while an indoor alternative offers fifteen benefit units and requires three additional cost units. Both future net values are twelve. The old ticket payment does not break this tie. More information or an explicitly supplied tie rule would be needed to choose one option within this model.

Now change the facts: the organizer offers a six-unit refund if the club cancels. The indoor alternative then yields fifteen plus six minus three, or eighteen units, while attendance remains twelve. Canceling is better by six under the supplied values. The refund matters because it is recoverable and changes with today's choice, even though the original payment is in the past.

A complete report distinguishes these two situations. In the first, the nonrefundable payment is sunk and future nets tie. In the second, a recoverable portion changes the future comparison. The example neither tells a real club what to do nor assumes that enjoyment is exactly measurable. It teaches why the words 'already paid' are insufficient: the reviewer must ask what is recoverable and which consequences still differ.

6. Check the tempting inference

A past payment is sunk only to the extent that it cannot be recovered. Do not charge an irrecoverable amount only to stopping. Refunds, resale, current budget constraints and new information about future costs can remain relevant. A sunk cost alone supports neither automatic continuation nor automatic abandonment.

7. Continuing can be the better option

8. A changed forecast supports stopping

9. A recovery changes today's comparison

10. Finish a forward-looking comparison

11. Guided practice

A past 30-unit payment is irrecoverable under both options. A now gives 18 and costs 5 more; B gives 11 and costs 1. No refunds. Calculate future nets and select A or B.

12. Guided practice

An old payment is irrecoverable. A offers 15 and costs 4 more; B offers 9 and costs 1, with no refund. Complete the comparison.

13. Guided practice

A past 60-unit payment cannot be recovered. A now gives 12 and costs 7 more; B gives 10 and costs 2. No refunds. Give future nets and higher-net label.

14. Practice

A prior payment has a 5-unit refund only under B; the rest is irrecoverable. A gives 20 and costs 6 more; B gives 13 and costs 2. Calculate future nets including the stated recovery once, then choose.

15. Practice

An old 90-unit payment is entirely irrecoverable. A now gives 24 and costs 8; B gives 13 and costs 1. No refunds. Give future nets and select the higher.

16. Somewhere new

A fictional club prepaid a workshop. Most of the payment cannot be recovered, but canceling under B returns 4 units. Attending A offers 19 benefit units and 7 extra cost units. Alternative B offers 14 and costs 3. Compute both future nets and select the higher; all values are stipulated comparable units.

17. Lesson test

Lesson test: one question per skill, one attempt each, no hints. Your answers are checked when you submit.

18. Test question

A new decision follows a past payment, with 3 units recoverable only under B and the rest sunk. A now gives 26 and costs 9; B gives 16 and costs 1. Give future nets and select the higher-net label.

19. What you can do now

Compare both options from today, counting a feasible recovery once. Explain which old amount is unchanged and which future difference supports the chosen option.

	Your result
Future net A
Future net B
Higher future-net option