Relevant costs for decision making

Managers make decisions every day that are not about the whole budget but about a single choice between alternatives. Should we accept a discounted order? Make a part ourselves or buy it? Keep a product line that appears to lose money? Which product should get the limited time on our busiest machine? Should we sell a product as it is or process it further? Replace an old machine? Each of these decisions has the same structure: compare the future costs and revenues that differ between the alternatives, and ignore everything else. This lesson develops that discipline, called relevant costing or differential analysis, and applies it to six common decisions at Cedar Ridge. Decisions whose effects span many years, such as buying major equipment, also need the time value of money, covered in FIN-201 lessons 7 to 9; here the focus is on short-term choices.

What makes a cost or revenue relevant

A cost or revenue is relevant to a decision if it meets two tests: it is a future amount, and it differs between the alternatives being considered. Costs already incurred (sunk costs) fail the first test; no decision can change them. Future costs that will be the same whatever is chosen fail the second; including them does no harm if they are included for every alternative, but leaving them out keeps the analysis focused. Opportunity costs, the benefits given up by choosing one alternative, are relevant even though they never appear in the ledger.

Two cautions follow. First, fixed costs are not automatically irrelevant: a fixed cost that would be avoided, such as a supervisor laid off if a line closes or a rental that ends, is relevant. Second, unit costs are dangerous. A unit cost that includes allocated fixed overhead looks like a variable cost but is not; multiplying it by extra units overstates the cost of additional output, as lesson 2 warned. Work with total costs and total revenues for each alternative whenever possible.

Decision 1: a special order

A hotel chain offers to buy 500 Classic chairs at $130 each, branded with its logo. The regular price is $180 and the absorption cost is $132, so at first glance the order loses money. But the plant can make 8,500 chairs a year and expects to make 7,200, so there is idle capacity. The hotel will collect the chairs itself, so there is no freight or commission. A logo stencil and set-up will cost $2,000.

# Special order: 500 branded chairs at $130 (illustrative)
qty, offer = 500, 130
variable_mfg = 102          # DM 60 + DL 30 + variable overhead 12
variable_selling = 0        # customer collects; no commission
one_time = 2_000            # logo stencil and set-up

revenue = qty * offer
relevant_cost = qty * (variable_mfg + variable_selling) + one_time
print(f"Incremental revenue  ${revenue:,}")
print(f"Incremental cost     ${relevant_cost:,}")
print(f"Effect on income     ${revenue - relevant_cost:+,}")
print(f"Lowest acceptable price per chair: ${(relevant_cost) / qty:.2f}")

Incremental revenue  $65,000
Incremental cost     $53,000
Effect on income     $+12,000
Lowest acceptable price per chair: $106.00

Accepting the order raises operating income by $12,000. Fixed overhead of $216,000 will be incurred anyway, so the $30 per chair of fixed overhead in the absorption cost is irrelevant. The minimum price that covers the incremental cost is $106 per chair. The analysis changes if the plant were at full capacity: accepting would then displace regular sales, and the contribution margin lost on those sales ($72 per chair) becomes an opportunity cost that the special price must also cover.

Qualitative factors matter too. Will regular customers learn of the discount and demand the same price? Do competition laws restrict price discrimination between competing buyers? Will the hotel become a repeat customer? Will the order strain staff or quality? A positive number is the start of the decision, not the end.

In the United States, the Robinson-Patman Act can prohibit price discrimination between competing purchasers of goods of like grade and quality where the effect may be to lessen competition, subject to defenses such as cost justification and meeting competition. A branded order for a hotel chain that does not compete with Cedar Ridge's furniture retailers is unlikely to raise an issue, but firms should take advice when discounting to some resellers and not others.

Decision 2: make or buy

Cedar Ridge makes the upholstered seat cushions for its chairs. A supplier offers to provide them for $13.50 each. The cost accountant's unit cost for making a cushion is $16, made up of direct materials $7, direct labor $4, variable overhead $1.50 and fixed overhead $3.50 allocated per cushion at 7,000 cushions a year. Of the fixed overhead, $9,800 a year is the salary of a part-time upholstery supervisor who would be let go if cushions were bought; the rest is allocated plant overhead that would continue. If cushions are bought, the upholstery area could be rented to a neighboring business for $6,000 a year.

# Make or buy seat cushions, 7,000 a year (illustrative)
units = 7_000
make_variable = 7 + 4 + 1.50          # DM, DL, variable overhead per cushion
avoidable_fixed = 9_800               # supervisor salary avoided if we buy
rent_forgone = 6_000                  # opportunity cost of making
buy_price = 13.50

make = units * make_variable + avoidable_fixed + rent_forgone
buy = units * buy_price
print(f"Relevant cost to make: ${make:,.0f}")
print(f"Relevant cost to buy:  ${buy:,.0f}")
print(("Buy" if buy < make else "Make") + f" saves ${abs(make - buy):,.0f} a year")

Relevant cost to make: $103,300
Relevant cost to buy:  $94,500
Buy saves $8,800 a year

The full unit cost of $16 is misleading: $2.10 of the $3.50 of fixed overhead per cushion would continue after outsourcing, so it is irrelevant. The relevant cost of making is the variable cost ($87,500), the avoidable supervisor salary ($9,800) and the rent forgone by using the space ($6,000), a total of $103,300, against $94,500 to buy. Buying saves $8,800 a year. Without the rental opportunity, buying would still save $2,800. Before deciding, managers should consider the supplier's quality and reliability, the risk of price increases once in-house capability is lost, the effect on employees, and whether cushions are a source of competitive advantage. Make-or-buy decisions are a form of outsourcing decision, and the same logic applies to services such as payroll, cleaning and IT.

Decision 3: keeping or dropping a product line

After its first year, the trestle bench appears to lose money on a segment report that allocates common fixed costs to products. The question is whether dropping it would raise Cedar Ridge's income. The answer depends on which costs would disappear with the bench: its contribution margin would be lost, its traceable fixed costs would be avoided, but the common fixed costs allocated to it would remain and be shifted onto the other products.

The conclusion could change if the space and equipment used for benches could earn more in another use, for example by expanding custom work, or if bench sales help sell chairs (complementary demand), in which case dropping benches would also cost some chair sales. A careful analysis includes those effects.

Decision 4: using a constrained resource

When a resource limits output, the product with the highest contribution margin per unit is not necessarily the most profitable to make. What matters is the contribution margin per unit of the constrained resource. Cedar Ridge's CNC router has 5,000 hours available next year. A chair needs 0.5 router hours and earns $72 of contribution margin; a bench needs 1.0 router hour and earns $105. Market demand is at most 8,000 chairs and 2,000 benches.

# Allocating 5,000 router hours between chairs and benches (illustrative)
hours_available = 5_000
products = {  # name: (CM per unit, router hours per unit, max demand)
    "chair": (72, 0.5, 8_000),
    "bench": (105, 1.0, 2_000),
}
ranked = sorted(products.items(), key=lambda kv: kv[1][0] / kv[1][1], reverse=True)
for name, (cm, hrs, demand) in ranked:
    print(f"{name}: CM per router hour ${cm / hrs:.0f}")

left, total_cm = hours_available, 0
for name, (cm, hrs, demand) in ranked:
    make = min(demand, left / hrs)
    left -= make * hrs
    total_cm += make * cm
    plural = {"chair": "chairs", "bench": "benches"}[name]
    print(f"Make {make:,.0f} {plural} using {make * hrs:,.0f} hours")
print(f"Total contribution margin ${total_cm:,.0f}")

chair: CM per router hour $144
bench: CM per router hour $105
Make 8,000 chairs using 4,000 hours
Make 1,000 benches using 1,000 hours
Total contribution margin $681,000

Per router hour, a chair earns $144 and a bench $105, so chairs get priority despite their lower margin per unit. Making 8,000 chairs uses 4,000 hours; the remaining 1,000 hours make 1,000 benches. Total contribution margin is $681,000. Giving benches priority instead (2,000 benches, then 6,000 chairs) would earn $642,000. With several constraints at once, the problem becomes a linear program, which spreadsheet solvers handle; ACCT-341 introduces optimization. In the longer run, managers can also relax the constraint (elevate it, in theory-of-constraints language) by adding a shift, buying a second router or outsourcing some machining, if the extra contribution exceeds the cost.

Decision 5: sell now or process further

Some products can be sold at an intermediate stage or processed further. Cedar Ridge could sell assembled but unfinished ready-to-paint chairs to a do-it-yourself retailer for $150, or finish them and sell them for $180. Finishing costs $22 per chair in incremental materials, labor and variable overhead; the finishing department has spare capacity. The costs incurred up to the split (Assembly costs) are the same either way and are irrelevant.

The same rule, compare incremental revenue with incremental cost beyond the split-off point, applies to joint products, such as the lumber and wood chips that come from a single log. How joint costs are allocated for inventory valuation is covered in ACCT-222, but joint costs are irrelevant to the decision to process further.

Decision 6: replacing equipment and the sunk cost trap

Cedar Ridge's old spray booth cost $80,000 four years ago and has a book value of $30,000. A new, more efficient booth costs $60,000 and would cut operating costs (energy, filters, rework) by $18,000 a year for four years. The old booth could be sold today for $5,000; in four years both booths would be worthless. The book value of the old booth is sunk: it reflects money spent four years ago and will be written off one way or another, through depreciation if kept or as a loss on disposal if sold.

# Replace the spray booth? Four-year totals, ignoring the time value of money (illustrative)
new_cost, salvage_old = 60_000, 5_000
annual_saving, years = 18_000, 4
book_value_old = 30_000   # sunk: shown only to prove it cancels out

keep = 0                                             # baseline
replace = -new_cost + salvage_old + annual_saving * years
print(f"Net advantage of replacing over {years} years: ${replace - keep:,}")

# Including book value in both alternatives changes nothing
keep_bv = -book_value_old                            # depreciated over 4 years
replace_bv = -book_value_old + replace               # written off as a loss now
print(f"With book value in both: ${replace_bv - keep_bv:,}")

Net advantage of replacing over 4 years: $17,000
With book value in both: $17,000

Replacing yields a net advantage of $17,000 over four years before considering the time value of money: $72,000 of savings plus $5,000 of salvage, less $60,000. The old booth's $30,000 book value affects both alternatives equally and cancels. Managers sometimes resist replacing an asset because they do not want to record a loss on disposal, which is exactly the sunk cost trap; the loss is an accounting entry, not a future cash flow. A complete analysis would discount the cash flows, include tax effects of depreciation and the disposal (CCA or MACRS), and test the estimate of savings, as FIN-201 shows.

Pricing decisions and target costing

Relevant costing also informs pricing. For short-term or one-off pricing with idle capacity, the floor is the incremental cost. For long-term pricing, prices must cover full costs and a return on investment, which is why many companies use cost-plus pricing based on absorption or full cost (lesson 5 priced custom jobs at cost plus 40 percent). Target costing reverses the logic: start with the price the market will bear, subtract the desired profit, and design the product and process so that its cost does not exceed the target. If Cedar Ridge believes a new armchair will sell for $240 and wants a 25 percent margin on price, the target cost is $180, and designers must find a way to build it for that.