Opportunity Costs of Project Resources

Why Existing Resources Have a Project Cost

A project may use a company-owned site, machine, facility, or employee without requiring a new payment to obtain it. That does not make the resource free. If the resource could instead be sold, leased, or put to another productive use, choosing the project means giving up the value of that alternative. Capital budgeting includes this sacrifice when assessing the project’s incremental cash flows.

The relevant amount is not automatically the resource’s original purchase price, its accounting book value, or an internal department’s charge. The question is what the company could gain from the best feasible alternative use now, given the project’s timing and the cash flows each alternative would produce. The examples below use pre-tax cash flows and assume the stated discount rate is appropriate for valuing the alternatives. Tax effects are excluded.

Definition: An opportunity cost is the value of the best alternative forgone when a resource is committed to a particular choice. For a project resource, it is the value of the most valuable feasible alternative use that the project prevents. When alternatives produce cash flows at different dates, value each alternative at a common date using the stated discount rate before comparing them.

Valuing Alternatives at a Common Date

A current sale offer is a value at time 0. A series of future lease receipts is not directly comparable with that offer until the receipts have been discounted to time 0. With an effective annual discount rate $i$, a cash flow $C_t$ received at the end of year $t$ has present value $C_t/(1+i)^t$. This comparison assumes the cash flows occur at the stated dates and that the same stated rate is used to value each alternative.

For an alternative with dated net cash flows $C_1,\ldots,C_n$, its time-0 value is:

V_0=\sum_{t=1}^{n}\frac{C_t}{(1+i)^t}.

If an alternative includes both operating receipts and later sale proceeds, include each cash flow once at its own date. Compare the resulting present value with the values of the other feasible uses. The highest value is the opportunity cost of committing the resource elsewhere.

Worked Example: Sell a Facility or Lease It Before Selling

A company owns a small facility. It can sell it now for $100,000, or lease it and then sell it at the end of Year 3. The lease alternative produces net receipts of $37,000 at the end of each of Years 1, 2, and 3, followed by sale proceeds of $30,000 at the end of Year 3. The effective annual discount rate is 10%. Which is the best alternative, and what time-0 value is forgone if a project uses the facility?

Method. Discount all alternative cash flows to time 0, then compare the lease-and-sale value with the immediate sale proceeds. The stated lease receipts are net of the direct costs specified in the problem.

The immediate sale is worth $100,000 at time 0. For the lease alternative, the Year 1 receipt has present value:

\frac{\$37{,}000}{1.10}=\$33{,}636.36.

The Year 2 receipt has present value:

\frac{\$37{,}000}{(1.10)^2} =\frac{\$37{,}000}{1.21} =\$30{,}578.51.

Both the Year 3 lease receipt and the sale proceeds occur at the end of Year 3. Their present values are:

\frac{\$37{,}000}{(1.10)^3} =\frac{\$37{,}000}{1.331} =\$27{,}798.65, \qquad \frac{\$30{,}000}{(1.10)^3} =\frac{\$30{,}000}{1.331} =\$22{,}539.44.

Using unrounded amounts, the lease-and-sale alternative is worth:

\$37{,}000(2.486851991)+\$30{,}000(0.751314801) =\$114{,}552.97.

The lease-and-sale alternative is worth more than the $100,000 immediate sale, so it is the best alternative. The project’s opportunity cost for using the facility is $114,552.97 at time 0. The displayed individual present values add to $114,552.96 because each is rounded to cents; the total is calculated from unrounded amounts and then rounded to cents.

Check and trap avoided. The Year 3 discount factor is $(1.10)^3=1.331$, not a Year 2 factor. Dividing by 1.331 gives $27,798.65 for the lease receipt and $22,539.44 for the sale proceeds. Using incorrect Year 3 present values can materially distort the comparison.

Why the Best Forgone Use Is the Relevant Cost

The opportunity cost follows from comparing choices, not from assigning a price to a resource merely because it appears in the project. Suppose a resource has several feasible alternatives with time-0 values $V_{1,0}, V_{2,0},\ldots,V_{m,0}$. The value sacrificed by committing it to the project is the value of the best one:

OC_0=\max_{1\leq j\leq m} V_{j,0}.

The reason is direct: by choosing the project, the company gives up every competing use, including the most valuable. Giving up a lower-value use does not capture the full economic sacrifice when a better use was also available.

More generally, compare the project with the best alternative using cash flows at the same dates. Let $C_{P,t}$ be the project’s net cash flow attributable to the resource and $C_{B,t}$ the cash flow from the best alternative. The value added by choosing the project rather than that alternative is:

\sum_{t=1}^{n}\frac{C_{P,t}-C_{B,t}}{(1+i)^t}.

This expression is the present value of the differences because discounting and subtraction are both linear: discounting each project cash flow and subtracting the discounted alternative is equivalent to discounting the period-by-period difference. It also shows why timing matters: a dollar of foregone cash flow in Year 2 is not the same time-0 amount as a dollar foregone today.

For a project cash-flow estimate that does not yet reflect the resource’s alternative use, one consistent approach is to subtract the present value of the best alternative from that estimate. Another is to subtract the alternative’s foregone cash flow in each period from the project cash flow for that period. These approaches give the same present value when they use the same dates and discount rate. Do not use both approaches at once, since that would count the same sacrifice twice.

List feasible uses.
Identify the actual alternatives available for the resource over the project’s relevant period, such as selling, leasing, or using it elsewhere.

Write each alternative’s cash flows and dates.
Include receipts and costs that differ between alternatives, and distinguish cash flows received now from those received later.

Value the alternatives consistently.
Discount their net cash flows to a common date using the stated rate and assumptions.

Select the best alternative and reflect it once.
Use its value as the opportunity cost, or include its foregone cash flows period by period, but not both.

Worked Example: Compare a Machine’s Sale Value With Another Job

A machine could be sold now for $55,000. If retained for a different job, it would produce net cash flows of $30,000 at the end of Year 1 and $32,000 at the end of Year 2, with no residual value after Year 2. The effective annual discount rate is 10%. Determine the best alternative and its time-0 value.

Method. Compare the immediate sale value with the present value of the other job’s net cash flows. The job’s Year 1 cash flow is worth:

\frac{\$30{,}000}{1.10}=\$27{,}272.73.

The Year 2 cash flow is worth:

\frac{\$32{,}000}{(1.10)^2} =\frac{\$32{,}000}{1.21} =\$26{,}446.28.

Therefore, the other job’s present value is:

\$27{,}272.73+\$26{,}446.28=\$53{,}719.01.

The $55,000 sale value exceeds $53,719.01, so selling is the better alternative. The opportunity cost of using the machine for the project is $55,000 at time 0, not the value of the other job.

Check and trap avoided. A tempting error is to select the job because it produces $30,000+$32,000=$62,000, which exceeds $55,000. That compares cash flows at different dates without discounting them. At 10%, the job’s present value is only $53,719.01, so the correct choice is the sale.

Resources Used Over Several Periods

Sometimes an existing resource has a recurring alternative use rather than a single sale value. For example, a company might be able to sublease unused space. In that case, the cash flows forgone are the net sublease receipts the company would have collected. The fact that the project already owns the space does not remove this sacrifice.

A resource does not need a separate cash payment in the project budget for its alternative use to have value. Conversely, a book charge or internal allocation is not, by itself, an opportunity cost. A charge is economically relevant only to the extent that using the resource actually prevents cash flows or another valuable use. This is the same incremental perspective used in capital budgeting: count the financial consequences that change when the company chooses the project.

Worked Example: Include Foregone Sublease Receipts Once

A company has a storage bay that it could sublease for net receipts of $12,000 at the end of each of the next two years. Instead, a proposed project will occupy the bay for both years. Before accounting for the space, the project is forecast to produce net cash flows of $30,000 at the end of Year 1 and $40,000 at the end of Year 2. The effective annual discount rate is 9%. Find the present value of the space’s opportunity cost and the project cash flows after accounting for the space.

Method. The project gives up the $12,000 sublease receipt in each year. First discount those foregone receipts to time 0; then show the equivalent period-by-period adjustment to the project cash flows.

The present value of the Year 1 receipt is:

\frac{\$12{,}000}{1.09}=\$11{,}009.17.

The present value of the Year 2 receipt is:

\frac{\$12{,}000}{(1.09)^2} =\frac{\$12{,}000}{1.1881} =\$10{,}100.16.

Thus, the time-0 opportunity cost is $11,009.17+$10,100.16=$21,109.33, rounded to cents from the unrounded amounts. Alternatively, subtract $12,000 from the project’s cash flow in each year:

Year 1: $30,000-$12,000=$18,000.
Year 2: $40,000-$12,000=$28,000.

These adjusted cash flows reflect the foregone sublease receipts in the years they would have been earned. If the analysis instead subtracts the $21,109.33 present value as a time-0 opportunity cost, it must not also subtract $12,000 in each year. Doing both would count the same use of the storage bay twice.

Common Errors in Identifying Opportunity Costs

The central exam skill is to identify what actually changes when the resource is committed. A useful check is to write down the alternatives and ask which cash flows each one produces that the project would prevent. Then verify that all alternatives are valued at the same date.

Using historical purchase cost. The amount originally paid for an asset does not measure the value of its best use today. Focus on the current feasible alternatives.
Choosing the largest undiscounted total. Cash flows at different dates are not directly comparable as totals. Discount them to a common date before selecting the best alternative.
Assuming an owned resource is free. A resource can have an opportunity cost even if the project requires no new purchase payment.
Treating every internal charge as a cash cost. An allocation matters only if it represents cash flows or an alternative use that the project actually displaces.
Counting the sacrifice twice. Do not both subtract the present value of an alternative and subtract its foregone cash flows in each period.

Key takeaway: The opportunity cost of a project resource is the value of the best feasible alternative that the project prevents. Compare alternatives at a common date, use the appropriate discounting, and reflect the chosen alternative’s sacrifice exactly once in the project cash flows.

Check Your Understanding

For each problem, compare alternatives at the stated effective annual rate and round money to the nearest cent.

A machine can be sold now for $48,000. Alternatively, it can support another job with net cash flows of $18,000 at the end of Year 1 and $20,000 at the end of Year 2. At 10%, which alternative is best, and what is its time-0 value? (Answer: Sell the machine now; $48,000. The job’s present value is $32,892.56.)
A company can sell a kiosk now for $72,000 or lease it for net receipts of $28,000 at each year-end for three years, with no residual value. At 8%, which alternative is best and what is its value? (Answer: Lease it; $72,158.72.)
A project will use a storage room that could instead be subleased for net receipts of $11,000 at the end of each of the next two years. At 10%, what is the present value of the opportunity cost? (Answer: $19,090.91.)
A facility can be sold now for $60,000. Alternatively, it can be leased for net receipts of $25,000 at the end of each of Years 1 and 2, then sold for $40,000 at the end of Year 2. At 10%, which alternative is better and what is its present value? (Answer: Lease and then sell; $76,446.28.)
A project’s cash flows before accounting for its use of a facility are $50,000 at the end of Year 1 and $60,000 at the end of Year 2. The facility could be subleased for net receipts of $8,000 at each year-end. At 10%, state the project cash flows after accounting for this opportunity cost, and calculate their present value. (Answer: $42,000 in Year 1 and $52,000 in Year 2; present value $81,157.02.)

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