Sunk Costs in Capital Budgeting

Why Sunk Costs Must Not Drive a Current Decision

A project proposal often arrives with a history: management may already have paid for market research, a prototype, or preliminary design work. Those expenditures matter to an accurate record of what has been spent. But if the money is irrecoverably gone, deciding whether to proceed cannot change that past cash flow. A sound capital-budgeting decision therefore focuses on the future cash flows that differ between the available choices.

This distinction is important when a project has disappointing results or when decision-makers feel pressure to justify prior spending. The question is not whether the project has already cost money. The question is whether accepting it, rather than rejecting it, changes the cash flows from this point forward. This tutorial develops that rule and applies it to project net present value (NPV), using the time-value-of-money methods covered in the earlier material on uneven cash flows. The treatment is aligned with the SOA VEE Accounting and Finance syllabus.

Definition: A sunk cost is a cost already incurred that cannot be recovered and cannot be changed by the current decision. Because it is the same under every choice now available, it is excluded from the incremental cash flows used to compare those choices.

Classifying Costs at the Decision Date

Classification depends on the decision being made and the timing of the cash flow. An expense may be important in a project’s history without being relevant to whether the project should proceed now. Conversely, a large future expenditure is not sunk merely because earlier project work led to it: if the firm can avoid that expenditure by rejecting the proposal, it is part of the decision.

For example, suppose a firm paid for completed market research last month. The amount is already spent, cannot be refunded, and will not change whether the firm launches the product. It is sunk. If launching requires a new payment today, that payment is not sunk: it occurs in the future and can be avoided by not launching. The test is not whether a cost is associated with an old project. The test is whether the current choice changes the cash flow.

Decision rule: Include a cash flow in the current project comparison only if its amount or timing differs between the choices being compared. Exclude an irrecoverable past expenditure that is identical under all choices.

The rule applies to both accept-or-reject decisions and comparisons among alternative projects. In an accept-or-reject decision, compare proceeding with rejecting. In a choice among projects, compare each project’s future cash flows with the other available choices. A past expenditure common to all of them does not favor one current choice over another.

Why the Sunk Cost Cancels

The cancellation follows directly from comparing the value of the alternatives at the decision date. Let $C$ be a cost incurred before that date, and suppose it cannot be recovered under either choice. Let $PV_A$ be the present value of future cash flows if the project is accepted and $PV_R$ the present value of future cash flows if it is rejected. If one is measuring the full history from before $C$ was spent, that expenditure appears in both alternatives. The difference between the alternatives is therefore:

$$ (-C+PV_A)-(-C+PV_R)=PV_A-PV_R $$

The term $-C$ cancels. At the current decision date, the expenditure has already occurred, so it is not a new cash flow to include in either alternative’s current NPV. This is why adding a past payment to a current project NPV can produce a misleading answer: it mixes the historical performance of the project with the current decision.

For a single project with future cash flows $CF_t$ at times $t=0,1,\ldots,n$, valued at an effective annual discount rate $i$, the relevant NPV at the decision date is:

\operatorname{NPV}=\sum_{t=0}^{n}\frac{CF_t}{(1+i)^t}

This formula includes future inflows and outflows that occur because the project is undertaken, including an outlay at $t=0$. It does not include a past sunk cost. The formula assumes the stated cash flows occur at the specified times and that $i$ is the appropriate effective annual discount rate for those periods. It does not, by itself, determine whether the cash-flow forecasts or discount rate are appropriate.

Set the decision date.
Identify when the accept, reject, or project-choice decision is being made.

List the alternatives.
For each alternative, identify cash flows that occur from the decision date onward.

Test each item.
Ask whether choosing one alternative rather than another changes the cash flow. A past, irrecoverable amount that does not change is sunk.

Discount and compare.
Calculate the present value or NPV using the relevant future cash flows, then compare the alternatives.

Worked Applications

Worked Example: A Completed Market Survey

A firm has already paid a nonrefundable $6,000 survey fee. It can invest $25,000 now in a proposed service that will produce a single cash inflow of $29,000 at the end of year 1. The effective annual discount rate is 8%. Calculate the current project NPV and state whether the survey fee is included.

Method. Calculate NPV at the current decision date using the new investment and the year-1 cash inflow. The survey fee was paid already and cannot be recovered, so it is sunk.

Step 1: Discount the year-1 inflow. At an 8% effective annual rate, the present value of $29,000 due in one year is:

\frac{\$29{,}000}{1.08}=\$26{,}851.85185\ldots

Step 2: Subtract the investment made now.

\operatorname{NPV}=-\$25{,}000+\$26{,}851.85185\ldots =\$1{,}851.85185\ldots

Rounded to the nearest cent, the current NPV is $1,851.85. The NPV is positive, so this cash-flow forecast supports accepting the project, subject to the assumptions in the analysis. The $6,000 survey fee is excluded.

Check. The discounted inflow exceeds the current investment by $26,851.85 − $25,000 = $1,851.85, consistent with the NPV. The common mistake is to subtract the $6,000 survey fee again, which would give $-\$6{,}000-\$25{,}000+\$29{,}000/1.08=-\$4{,}148.15$. That calculation combines a past expense with the current investment decision; it does not measure the incremental value of proceeding now.

Worked Example: A Prior Feasibility Study and a Future Launch Cost

A hypothetical insurer paid $7,500 for a feasibility study that is complete and nonrefundable. The insurer must decide whether to launch a new administrative service. Launching requires an outlay of $12,000 now and is forecast to generate $5,000 at the end of each of the next three years. Use an effective annual discount rate of 8%. Should the firm launch based on NPV?

Method. Exclude the completed study fee and discount each of the three future annual inflows. Include the $12,000 launch outlay because it is paid now only if the firm launches.

Step 1: Discount each inflow.

\begin{aligned} PV_1&=\frac{\$5{,}000}{1.08}=\$4{,}629.63,\\ PV_2&=\frac{\$5{,}000}{1.08^2} =\frac{\$5{,}000}{1.1664}=\$4{,}286.69,\\ PV_3&=\frac{\$5{,}000}{1.08^3} =\frac{\$5{,}000}{1.259712}=\$3{,}969.16. \end{aligned}

Step 2: Add the present values and subtract the launch outlay. The total present value of inflows is $4,629.63 + $4,286.69 + $3,969.16 = $12,885.48. Therefore:

\operatorname{NPV}=-\$12{,}000+\$12{,}885.48=\$885.48

The NPV is positive, so the forecast supports launching. The $7,500 study fee is not part of this current NPV. Including it would yield a historical-plus-current total of $885.48 − $7,500 = −$6,614.52, but that amount does not answer whether launching now adds value relative to not launching.

Check. The discounted inflows exceed the future launch outlay by $885.48. The study fee is unchanged by the launch decision, so it cannot reverse the comparison.

Worked Example: Deciding Whether to Continue After Development Spending

A hypothetical firm has spent $120,000 developing a data-processing tool. That amount cannot be recovered. Before the tool can be used, the firm must spend another $50,000 now. If it proceeds, the tool is forecast to generate $30,000 at the end of each of the next three years. The firm uses an effective annual discount rate of 9%. Compare continuing with stopping now, assuming stopping creates no further cash flow.

Method. Compare the future cash flows from continuing with zero future project cash flows from stopping. The prior $120,000 is sunk; the $50,000 is a future outlay that can be avoided by stopping.

Step 1: Calculate the present value of the three inflows.

\begin{aligned} PV_1&=\frac{\$30{,}000}{1.09}=\$27{,}522.94,\\ PV_2&=\frac{\$30{,}000}{1.09^2} =\frac{\$30{,}000}{1.1881}=\$25{,}250.40,\\ PV_3&=\frac{\$30{,}000}{1.09^3} =\frac{\$30{,}000}{1.295029}=\$23{,}165.50. \end{aligned}

The inflows have a total present value of $27,522.94 + $25,250.40 + $23,165.50 = $75,938.84. Subtract the required outlay now:

\operatorname{NPV}_{\text{continue}}=-\$50{,}000+\$75{,}938.84 =\$25{,}938.84

Stopping has zero future project cash flow under the stated assumption, so continuing has an incremental NPV of $25,938.84 relative to stopping. Continuing is supported by these forecasts. The $120,000 already spent is excluded.

Check. The present value of the three future inflows exceeds the avoidable outlay by $25,938.84. The method avoids the sunk-cost fallacy in either direction: the $120,000 is not a reason to continue, and its size is not a reason to stop.

Common Mistakes and Practical Checks

A common exam trap is to treat every amount listed in a project description as part of the NPV calculation. The relevant question is not whether the amount is mentioned, nor whether it is large. It is whether the current decision changes the cash flow. Read for timing, recoverability, and whether the amount occurs under the alternatives being compared.

Counting a past payment again. A completed, nonrefundable study is not a new outflow at the current decision date. Do not subtract it again in the project NPV.
Ignoring an avoidable future outlay. A required payment due now or later is relevant if rejecting the project avoids it. It is not sunk simply because prior work has been done.
Using sunk spending to justify continuation. “We have already spent so much that we must finish” is not an incremental cash-flow argument. The past amount is common to both choices.
Confusing project history with the current decision. A cumulative record of spending can be useful for reporting, but it is not the same calculation as the NPV of proceeding from today.

A useful final check is to write the alternatives side by side and cross out any past, irrecoverable cash flow that appears identically in each. Then verify that each remaining cash flow is assigned to the correct date and discounted using the stated annual rate and time unit. This keeps the analysis focused on the value changed by the decision.

Key takeaway: A sunk cost is past, irrecoverable, and unchanged by the current choice. Exclude it from incremental project cash flows; evaluate the decision using future cash flows that differ between the alternatives.

Check Your Understanding

For each problem, identify the sunk cost, calculate the relevant NPV or comparison, and use the stated effective annual discount rate.

A firm paid a nonrefundable $2,400 survey fee last month. A project requires $10,000 now and pays $11,500 at the end of year 1. The effective annual rate is 5%. What is the current NPV, and should the survey fee be included? (Answer: NPV = $952.38; exclude the $2,400 fee.)
A completed design study cost $9,000 and cannot be recovered. A proposed system costs $20,000 now and generates $8,000 at each year-end for three years. At an effective annual rate of 10%, calculate NPV and state whether the design cost is included. (Answer: NPV = −$105.18; exclude the $9,000 design cost.)
A pilot program has already cost $30,000, with no refund available. Continuing requires $7,000 now and generates $4,000 at the end of each of the next two years. At an effective annual rate of 8%, calculate the incremental NPV of continuing versus stopping. (Answer: NPV = $133.06; exclude the $30,000 already spent.)
A firm has already paid $5,000 for a preliminary pilot. It must choose between two mutually exclusive projects, with no further project cash flows if it rejects both. Project A costs $18,000 now and pays $10,000 at each of the next two year-ends. Project B costs $15,000 now and pays $8,500 at each of the next two year-ends. At an effective annual rate of 10%, which alternative has the highest NPV, and should either project be accepted? (Answer: A NPV = −$644.63; B NPV = −$247.93; reject both, and exclude the $5,000 pilot cost.)
A firm has spent $90,000 developing a tool, and that amount is irrecoverable. Completing it requires $40,000 now and produces $15,000 at each of the next three year-ends. At an effective annual rate of 8%, should the firm continue rather than stop, assuming stopping has no future cash flows? (Answer: NPV of continuing = −$1,343.55; stop, and exclude the $90,000 development cost.)

What You'll Learn