ACCA Applied Skills · Financial Management
Specific Investment Decisions: Lease or Buy, Replacement, Capital Rationing
Specific investment decisions are special cases of NPV appraisal. Lease or buy compares the present value of two financing costs. Replacement uses equivalent annual cost to compare assets with unequal lives. Capital rationing ranks divisible projects with profitability index when funds are limited. Multi-period rationing uses linear programming ideas; check the current FM study guide for the expected depth.
What this chapter covers
This chapter applies the NPV method you already know to four common decision types. You are not learning new theory. You are learning how to set up the cash flows and which comparison to make.
Lease or buy compares two ways of getting an asset. You discount the cost of each at the right rate and choose the lower present value cost. Asset replacement asks how often to replace an asset when lives differ. You convert each cycle's cost into an equivalent annual cost so you can compare like with like. Capital rationing deals with a limit on funds. The method depends on whether projects are divisible. Single-period rationing is the main calculation. Multi-period rationing involves linear programming ideas. Check the current FM study guide for the expected depth of multi-period rationing.
The chapter builds on basic investment appraisal: relevant cash flows, tax and capital allowances, inflation and discounting. It also links to the cost of capital and financing topics, because the lease or buy discount rate is usually the after-tax cost of borrowing. In the exam it appears in objective test questions and as part of a 20-mark constructed response question.
Investment appraisal is a core area of FM, and these decisions are favourite exam scenarios because they test whether you can adapt NPV to a new setting. Objective test questions on equivalent annual cost and profitability index are short, mechanical and all-or-nothing, so accuracy gives reliable marks. Constructed response questions often combine a calculation with a short discussion, such as the limitations of capital rationing methods or non-financial factors in lease or buy. Practise both and you collect marks from two sections.
Specific investment decisions (lease or buy, asset replacement, capital rationing): topics in the order to study them
- 1Lease or Buy DecisionsIt is the closest to basic NPV and needs only tax, capital allowances and the right discount rate, so it refreshes the core skills first.
- 2Asset Replacement and Equivalent Annual CostIt reuses present value cost from lease or buy and adds the idea of comparing assets with different lives.
- 3Single-Period Capital RationingIt introduces ranking by profitability index for divisible projects, and testing combinations for indivisible ones. You need both before the wider case.
- 4Multi-Period Capital Rationing and Linear ProgrammingIt extends single-period rationing to several constrained periods, so study it last. Check the current FM study guide for the expected depth, and focus on understanding the ideas and limitations.
How to prepare Specific investment decisions (lease or buy, asset replacement, capital rationing)
Work through the chapter by method, not by memorising solutions. Each decision type has a short, fixed set of steps. Learn the steps, then practise until you can apply them under time pressure.
- Revise basic NPV first: relevant cash flows, tax, capital allowances, working capital and discount factors. Errors here carry into every topic.
- For lease or buy, list the cash flows of each option separately. Discount at the after-tax cost of borrowing and compare present value costs. Then note the non-financial points.
- For replacement, calculate the present value cost of one replacement cycle for each option. Divide by the annuity factor for that life to get the equivalent annual cost. Choose the lower cost.
- For single-period rationing, check first whether projects are divisible. If they are, calculate the profitability index for each project, rank them, allocate funds and take only part of the last project. If they are indivisible, do not rely on ranking. Test the feasible combinations directly and choose the one with the highest total NPV.
- For multi-period rationing, learn the concepts: why single-period ranking no longer works, what linear programming is used for, and what a shadow price means. Check the current FM study guide for the expected depth.
- Finish with timed mixed questions. Do objective test questions in about a few minutes each, then one full constructed response question with a clear layout and a short written conclusion.
Common mistakes in Specific investment decisions (lease or buy, asset replacement, capital rationing)
Using the cost of equity or WACC to discount lease or buy cash flows.
Fix: Treat lease or buy as a financing decision and use the after-tax cost of borrowing unless the question says otherwise.
Forgetting tax relief on lease payments or capital allowances, or getting the timing wrong.
Fix: Draw a timeline. Put tax on each cash flow in the year the question's tax rules say it is received or paid.
Comparing total present value costs of assets with different lives.
Fix: Whenever lives differ, divide each present value cost by the matching annuity factor and compare the equivalent annual costs.
Ranking projects by NPV rather than profitability index under capital rationing.
Fix: Under a funds limit, check divisibility first. For divisible projects, rank by profitability index (NPV per unit of scarce capital). For indivisible projects, ranking by profitability index is not reliable, so test the feasible combinations and choose the highest total NPV.
Treating indivisible projects as if they could be funded partly.
Fix: Check divisibility first. If projects cannot be split, compare feasible combinations and pick the highest total NPV.
Applying single-period profitability index ranking when funds are limited in several periods.
Fix: Check how many periods have a funds limit. If more than one, simple ranking may not give the best answer. Say that linear programming is the technique used and explain why.
Last-day revision: Specific investment decisions (lease or buy, asset replacement, capital rationing)
- Lease or buy: compare the present value cost of each option and choose the lower one.
- The lease or buy discount rate is normally the after-tax cost of borrowing, because it is a financing decision.
- Include tax relief on lease payments and on capital allowances, with the correct timing.
- Equivalent annual cost = present value cost of one cycle ÷ annuity factor for the cycle length.
- Choose the asset or replacement cycle with the lowest equivalent annual cost.
- Equivalent annual cost assumes the asset is replaced in the same way indefinitely, so costs are repeated.
- Profitability index = NPV ÷ initial investment, used to rank divisible projects when capital is limited in one period.
- Divisible projects: rank by profitability index and fund the last project partly. Indivisible projects: ranking by profitability index is not reliable, so test the feasible combinations directly for the highest total NPV.
- Indivisible projects cannot be split. Non-repeatable projects cannot be undertaken more than once. Mutually exclusive projects mean only one of a group can be chosen.
- Multi-period rationing cannot be solved by simple ranking. Linear programming is the technique used; check the current FM study guide for the depth you need.
- A shadow price is the extra NPV from one more unit of a scarce resource, valid only within a limited range.
- Always add a brief written conclusion that states the decision and one limitation.
Specific investment decisions (lease or buy, asset replacement, capital rationing) practice questions
- Harlow Co has an existing machine that could be kept for one more year, with running costs of $14,000 payable at the end of the year. It cou…
- Sigma Co is comparing buying a machine with leasing it. Under both options it would pay insurance of $2,000 a year and charge depreciation i…
- Zeta Co has two divisible projects, A and B, and has a capital limit of $100,000 in each of Year 0 and Year 1. Project A needs $40,000 in Ye…
- Which statement about capital rationing across more than one period is correct?
- Belmont Ltd is considering a machine with a present value of costs of $50,000 over a 4-year life. The cost of capital is 10% and the 4-year …
- Zeta Co is evaluating whether to lease or buy an item of equipment. The company can borrow at a pre-tax rate of 8% and pays tax at 25%. Whic…
- Kappa Co can lease a machine for $50,000 a year, payable at the end of each of the next 3 years. Tax is 20% and tax relief on lease payments…
- Omega Co is offered a lease requiring four annual payments of $30,000, the first payable immediately at the start of the lease. Tax is ignor…
Specific investment decisions (lease or buy, asset replacement, capital rationing) in other exams
The same ground in other exams, if you are preparing for more than one or want another angle on it.
Specific investment decisions (lease or buy, asset replacement, capital rationing): frequently asked questions
Which discount rate should I use in a lease or buy decision?
Normally the after-tax cost of borrowing, because the choice is about how to finance the asset. Read the question for any rate it tells you to use. Use that rate for both options so the comparison is consistent.
When do I use equivalent annual cost?
Use it when you compare assets or replacement cycles with different lives and costs, and the asset will be replaced repeatedly. It turns each present value cost into an annual figure. You then choose the lowest.
What is the difference between hard and soft capital rationing?
Hard rationing is an external limit, such as lenders refusing to provide more funds. Soft rationing is an internal limit set by management, for example budget controls. The calculations are the same, but the discussion points differ.
How much linear programming do I need for multi-period capital rationing?
Check the current FM study guide for the expected depth of multi-period rationing. At a minimum, know why simple ranking fails when several periods are constrained, that linear programming is the technique used, and what a shadow price means. Recent past questions will also show how it is examined.
How are these topics examined?
They appear in objective test questions that need a quick calculation, and in constructed response questions that combine numbers with short written points. Practise both formats. In written answers, state your decision and one relevant limitation.