Strategic Cost Management · Asset Life Cycle Costing

Life Cycle Costing Numerical Problems with Solutions

Updated 11 October 2026 · Fact-checked

Life cycle costing numericals add every cost a product or asset causes from design to disposal, then divide by lifetime units or discount the cash flows. To solve them, list costs by phase, total them, find cost per unit and lifetime profit, and compare alternatives using present value at the given rate.

Understand Life Cycle Costing Numerical Problems

Life cycle costing (LCC) looks at the whole cost of a product or asset, not just the production cost in one year. It starts with research, design and development, runs through production, marketing, distribution and after-sales service, and ends with decommissioning or disposal.

Why does this matter? Traditional costing often treats pre-production costs such as R&D and design as period costs, so a product can look profitable while it never recovers its total spend. LCC collects all these costs against the product over its full life and shows true lifetime profitability.

For an asset, the purchase price is only part of the story. Running, maintenance, energy and disposal costs can exceed the price. LCC lets you compare a cheap machine with high running costs against a costly one with low running costs.

Numericals come in two kinds. In the first, you use undiscounted totals: total lifetime cost, cost per unit, lifetime profit and the price needed to earn a target margin. In the second, cash flows fall in different years, so you discount them at the given rate and compare present values.

Remember that most of a product's cost is committed (locked in) during design, even though it is spent later. That is why LCC links so closely to target costing and why questions often ask where management should focus cost reduction.

Key rules to remember

Total life cycle cost: Total LCC = Upstream costs (R&D, design) + Manufacturing costs + Marketing and distribution costs + After-sales and warranty costs + Disposal costs; Fixed costs are counted once for the whole life. Variable costs are rate × lifetime units.
Life cycle cost per unit: LCC per unit = Total LCC ÷ Total units produced and sold over the life; Use the lifetime volume given in the question, not one year's volume.
Lifetime profit: Lifetime profit = Total lifetime revenue − Total LCC; Revenue = lifetime units × selling price. If prices change by phase, add up each phase.
Price for a target margin: Price = LCC per unit ÷ (1 − margin on sales), or LCC per unit × (1 + mark-up on cost); Check whether the target is on sales or on cost.
Present value of a single amount: PV = Amount × 1 ÷ (1 + r)^n; r is the discount rate per year. n is the year in which the cash flow occurs.
Present value of an equal annual amount: PV = Annual amount × Annuity factor, where annuity factor = [1 − (1 + r)^−n] ÷ r; Use the factor given in the question if the table is supplied.
Discounted life cycle cost: PV of LCC = Initial cost + PV of running costs + PV of disposal cost − PV of salvage value; Salvage or resale proceeds are inflows, so they reduce the cost. Choose the lowest PV of cost.
Equivalent annual cost: EAC = PV of LCC ÷ Annuity factor for the asset's life; Use it when the alternatives have unequal lives.

How to solve Life Cycle Costing Numerical Problems questions

Use the same sequence for every LCC question. It keeps the working tidy and lets the examiner award method marks even if one figure goes wrong.

1Read the requirement first. Note whether you need total cost, cost per unit, profit, price, or a choice between alternatives, and whether discounting is required.
2Draw a table with phases as rows: R&D and design, production, marketing and distribution, after-sales, disposal. Put each cost in its row.
3Separate fixed (one-time or lifetime) costs from per-unit costs. Multiply per-unit costs by the lifetime units. Do not multiply fixed costs.
4Total each phase and then the whole life. Divide by lifetime units for cost per unit.
5Compute lifetime revenue and profit, or the required price, if asked.
6If cash flows fall in different years, set up a timeline. Apply discount factors to each flow, treat salvage as a deduction, and total the present values for each alternative.
7Compare alternatives. If lives differ, convert to equivalent annual cost. Pick the lowest cost (or highest net benefit).
8Write a one-line recommendation and mention any non-financial point, such as the share of cost committed at design stage or reliability.

Quickest way: Phase table plus discount factor shortcut

When to use it: Use this when time is short, in either a 14-mark question or a case-based MCQ set that asks for a figure.

Write the units and rate at the top of your page so you do not look back at the question.
Compute one-time costs in a single line, then per-unit costs as one combined rate per unit, then add them.
For cost per unit, divide the lifetime total by units once. Do not compute unit cost phase by phase unless asked.
For discounting, find the annuity factor first, and multiply every equal annual cost by it in one step.
Compare only the differences between alternatives if all other costs are identical. This cuts the working and reduces errors.
In MCQs, check your answer against the options by estimating roughly: if your total is far off, a fixed cost was probably multiplied by units.

Common mistakes in Life Cycle Costing Numerical Problems

Multiplying a lifetime fixed cost, such as R&D or tooling, by the number of units.
Students apply a per-unit habit to every figure in the question.
Fix: Read the wording. If the cost is stated as a total or lump sum, add it once. Multiply only costs given per unit.
Leaving out pre-production and end-of-life costs, such as design, setup, decommissioning and disposal.
Students focus on the production cost they know from basic costing.
Fix: Build the phase table every time and tick off each phase. A blank row should be a conscious decision, not an oversight.
Dividing total LCC by one year's output instead of lifetime output.
The annual volume is the number most prominent in the question.
Fix: Compute total lifetime units first (annual units × years, or the stated total) and use that as the divisor.
Adding salvage value to cost, or ignoring it.
Salvage is a cash inflow, and the sign gets lost when working quickly.
Fix: Discount salvage at its year's factor and subtract it from the present value of cost.
Discounting the initial outlay, or using the wrong year for a cash flow.
Students discount everything automatically, without checking timing.
Fix: Treat the cash spent today as year 0 with a factor of 1. Apply year-end factors only to later flows, as the question assumes.
Comparing alternatives with unequal lives by total present value alone.
The lowest PV looks like the answer, but a shorter life gives fewer years of service.
Fix: Convert to equivalent annual cost, or use a common time horizon, before recommending.

Worked examples

Example 1

Sahyadri Appliances plans a new mixer-grinder. Over its life it expects to produce and sell 40,000 units at ₹300 each. Costs: R&D ₹12,00,000; design ₹3,00,000; variable manufacturing cost ₹150 per unit; fixed production cost over the life ₹4,00,000; marketing and distribution ₹2,00,000 fixed plus ₹20 per unit; warranty and after-sales service ₹10 per unit; decommissioning and disposal ₹1,00,000. Compute (a) total life cycle cost, (b) life cycle cost per unit, (c) lifetime profit.

Show the solution

Upstream costs: R&D ₹12,00,000 + design ₹3,00,000 = ₹15,00,000.
Manufacturing: variable 40,000 × ₹150 = ₹60,00,000, plus fixed ₹4,00,000 = ₹64,00,000.
Marketing and distribution: fixed ₹2,00,000 + variable 40,000 × ₹20 = ₹8,00,000, giving ₹10,00,000.
After-sales: 40,000 × ₹10 = ₹4,00,000.
Disposal: ₹1,00,000.
Total LCC = ₹15,00,000 + ₹64,00,000 + ₹10,00,000 + ₹4,00,000 + ₹1,00,000 = ₹94,00,000.
Cost per unit = ₹94,00,000 ÷ 40,000 = ₹235.
Revenue = 40,000 × ₹300 = ₹1,20,00,000. Lifetime profit = ₹1,20,00,000 − ₹94,00,000 = ₹26,00,000, or ₹65 per unit.

Answer: (a) Total LCC = ₹94,00,000. (b) LCC per unit = ₹235. (c) Lifetime profit = ₹26,00,000 (₹65 per unit). Note that ₹15,00,000 of upstream spend is incurred before any sale, so a cost view that ignores it would overstate profit.

Example 2

Konkan Textiles must choose between Machine A and Machine B for a 5-year period. Cost of capital is 10%. Machine A: purchase ₹10,00,000; operating cost ₹2,00,000 a year; salvage ₹1,00,000 at the end of year 5. Machine B: purchase ₹14,00,000; operating cost ₹1,20,000 a year; salvage ₹2,00,000 at the end of year 5. Operating costs arise at each year end. At 10%, the 5-year annuity factor is 3.7908 and the year-5 discount factor is 0.6209. Which machine should be chosen on discounted life cycle cost?

Show the solution

Both machines have the same 5-year life, so present values can be compared directly.
Machine A: PV of operating cost = ₹2,00,000 × 3.7908 = ₹7,58,160.
Machine A: PV of salvage = ₹1,00,000 × 0.6209 = ₹62,090.
Machine A: PV of life cycle cost = ₹10,00,000 + ₹7,58,160 − ₹62,090 = ₹16,96,070.
Machine B: PV of operating cost = ₹1,20,000 × 3.7908 = ₹4,54,896.
Machine B: PV of salvage = ₹2,00,000 × 0.6209 = ₹1,24,180.
Machine B: PV of life cycle cost = ₹14,00,000 + ₹4,54,896 − ₹1,24,180 = ₹17,30,716.
Difference = ₹17,30,716 − ₹16,96,070 = ₹34,646 in favour of Machine A.

Answer: Choose Machine A. Its discounted life cycle cost is ₹16,96,070 against ₹17,30,716 for Machine B, a saving of ₹34,646. B's lower running cost does not recover its higher purchase price at 10% over five years. Check non-financial factors such as reliability and fabric quality before finalising.

Exam tips

Always show a phase-wise cost table. Even if one figure is wrong, the structure earns method marks.
Read whether each cost is a lump sum or per unit. This single check decides most numerical errors in LCC problems.
For asset comparisons, state the discount rate, the timing assumption and the equal-life assumption in a line. Then give a clear recommendation, as the paper expects a decision, not just figures.
In case-based MCQs, the answer often needs only one or two calculations. Do not build the full table unless two or more phases are involved.
Add a short comment on committed costs or non-financial factors in 14-mark answers. It shows application and often earns the last marks.

Practice questions from Asset Life Cycle Costing

Life Cycle Costing Numerical Problems in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Life Cycle Costing Numerical Problems: frequently asked questions

How do I calculate the life cycle cost of a product?

List all costs by phase: R&D and design, production, marketing and distribution, after-sales and disposal. Add fixed costs once and multiply per-unit costs by lifetime units. The total is the life cycle cost, and dividing by lifetime units gives cost per unit.

When do I use discounting in life cycle costing?

Use it when costs and benefits arise in different years and the question gives a discount rate or cost of capital. Without a rate, the question expects simple undiscounted totals. Today's outlay is not discounted, while future flows are.

How is life cycle costing different from traditional costing?

Traditional costing often expenses R&D and design in the period they occur and reports annual profit. Life cycle costing tracks all costs of a product across its whole life and shows lifetime profitability. This helps management see the full cost before launch.

What should I do if the alternatives have unequal lives?

Do not compare total present values directly. Convert each present value of cost into an equivalent annual cost by dividing by the annuity factor for its own life, then choose the lower figure.