Investment Decisions: Capital Budgeting — Practice

Question 1

A company spent ₹5 lakh last year on a feasibility study for a new project, and the project, if undertaken, will use a piece of idle land the company already owns, which could otherwise be sold today for ₹20 lakh. Explain how each of these two amounts should be treated in the capital budgeting analysis for this project.

Accepted Answer

The ₹5 lakh spent on the feasibility study last year is a sunk cost: it has already been incurred and will not change regardless of whether the project is accepted or rejected today, so it is irrelevant to the capital budgeting decision and must be excluded entirely from the analysis, despite the natural but mistaken instinct to want to 'recover' money already spent. The ₹20 lakh represents an opportunity cost: although using the land for this project involves no new cash outlay, using it for this project means forgoing the ₹20 lakh the company could otherwise have realised by selling the land today, and this forgone amount is a genuine, relevant cost of undertaking the project, which must be included as part of the initial outlay even though no fresh cash is actually paid out for the land itself.

Question 2

A project's annual accounting profit before depreciation and tax is ₹10 lakh, annual depreciation is ₹4 lakh, and the tax rate is 30%. Compute the annual operating cash flow, showing why depreciation is added back after computing its effect on tax.

Accepted Answer

Profit before depreciation and tax = ₹10 lakh. Less depreciation ₹4 lakh gives profit before tax = ₹6 lakh. Less tax at 30% = ₹1.8 lakh gives profit after tax = ₹4.2 lakh. Add back depreciation ₹4 lakh, since it is a non-cash charge, giving annual operating cash flow = ₹4.2 lakh + ₹4 lakh = ₹8.2 lakh. Depreciation must first be deducted before computing tax because it genuinely reduces the company's taxable profit and therefore its actual cash tax payment, a real cash effect that must be captured; it is only the depreciation charge itself, not its tax effect, that is a non-cash item, so simply ignoring depreciation altogether and computing tax on the full ₹10 lakh would overstate the actual cash tax paid and understate the true operating cash flow, which is why the correct approach is to deduct depreciation to compute tax accurately, and then add the same depreciation figure back afterward to remove only its non-cash component from the final cash flow figure.

Question 3

A project requires an initial investment of ₹40 lakh in machinery with no salvage value, has a life of 4 years, and is expected to generate annual cash flow after tax of ₹14 lakh in each of the 4 years. The cost of capital is 12%, and the present value annuity factor for 4 years at 12% is 3.037. Compute the NPV and state whether the project should be accepted.

Accepted Answer

Present value of annual cash inflows = Annual cash flow × PV annuity factor = ₹14 lakh × 3.037 = ₹42.518 lakh. NPV = Present value of inflows − Initial outlay = ₹42.518 lakh − ₹40 lakh = ₹2.518 lakh, a positive NPV. Since the NPV is positive, the project is expected to generate a return exceeding the 12% cost of capital and to add approximately ₹2.518 lakh of value to the firm in present-value terms, so the project should be accepted under the NPV rule, consistent with the wealth maximisation objective, since accepting it increases shareholder wealth by this positive present-value amount.

Question 4

A project has an NPV of ₹3.2 lakh at a discount rate of 10%, and an NPV of −₹1.8 lakh at a discount rate of 14%. Estimate the project's IRR using interpolation.

Accepted Answer

IRR = Lower rate + [NPV at lower rate ÷ (NPV at lower rate − NPV at higher rate)] × (Higher rate − Lower rate) = 10% + [3.2 ÷ (3.2 − (−1.8))] × (14% − 10%) = 10% + [3.2 ÷ 5.0] × 4% = 10% + 0.64 × 4% = 10% + 2.56% = 12.56%. The estimated IRR is approximately 12.56%, the discount rate at which this project's NPV is expected to equal zero, found by interpolating proportionally between the 10% rate, where NPV is positive, and the 14% rate, where NPV is negative, based on how far the NPV must fall from its value at 10% to reach zero relative to the total change in NPV across the two rates.

Question 5

A firm has a capital budget of ₹60 lakh and is considering three independent, divisible projects: Project X requires ₹30 lakh with PI of 1.4; Project Y requires ₹40 lakh with PI of 1.3; Project Z requires ₹20 lakh with PI of 1.25. Using profitability index ranking, determine which projects the firm should fund to maximise total NPV within its budget, assuming projects are divisible.

Accepted Answer

Ranking the projects by profitability index from highest to lowest: Project X at PI 1.4, Project Y at PI 1.3, Project Z at PI 1.25. Since projects are divisible and the goal is to maximise total NPV from a limited ₹60 lakh budget, the firm should fund projects in order of PI ranking until the budget is exhausted: fully fund Project X, requiring ₹30 lakh (PI 1.4, the highest), leaving ₹30 lakh of budget; fully fund Project Y, requiring ₹40 lakh — but only ₹30 lakh of budget remains, so the firm funds three-quarters of Project Y, using the remaining ₹30 lakh of the budget, rather than funding any of Project Z, since Project Y's PI of 1.3 exceeds Project Z's PI of 1.25, meaning every additional rupee allocated to Y (up to its full requirement) creates more value per rupee than allocating that same rupee to Z. This ranking approach, funding the highest-PI projects first and only moving to the next-ranked project once a higher-ranked one is either fully funded or the budget is exhausted, maximises total NPV generated from the fixed ₹60 lakh budget, which is precisely why PI, rather than NPV alone, is the correct ranking tool under capital rationing with divisible projects.

Question 6

Project A has a payback period of 2 years and generates no further cash flow after year 2. Project B has a payback period of 3 years but continues generating substantial cash flow through year 8. Explain why relying on payback period alone could lead a firm to make a value-destroying choice between these two projects.

Accepted Answer

Payback period measures only the time taken to recover the initial outlay and entirely ignores any cash flow occurring after that point, so on a pure payback period comparison, Project A, recovering its outlay in 2 years, would appear preferable to Project B, which takes 3 years. This comparison, however, completely ignores that Project B continues generating substantial cash flow for a further five years after its payback point, while Project A generates nothing at all beyond its own payback point, meaning Project B is very likely to have generated dramatically more total value, and a much higher NPV, over its full life than Project A, despite having the longer payback period. A firm relying on payback period alone, without also computing NPV or another discounted technique that accounts for the full stream of cash flows, risks rejecting Project B in favour of Project A purely because payback period is blind to exactly the cash flows that would reveal Project B's superiority, illustrating precisely why payback period is treated as a supplementary screening tool rather than a sound primary basis for an accept-or-reject decision.

Question 7

A project has an IRR of 35%, an unusually high figure. Explain why the IRR technique's implicit reinvestment assumption for this project is considered unrealistic, and how NPV's implicit assumption differs.

Accepted Answer

The IRR technique implicitly assumes that all intermediate cash flows generated by the project are reinvested at the project's own IRR, which in this case would mean assuming the firm can find further investment opportunities capable of earning a 35% return, repeatedly, to reinvest every rupee of intermediate cash flow this project throws off. This is considered unrealistic precisely because a 35% return is unusually high, and opportunities capable of consistently generating such an exceptional return are not typically available in unlimited supply to any firm; assuming the firm can costlessly and repeatedly find such opportunities for every rupee of intermediate cash flow overstates the true value the project is likely to actually deliver. NPV, by contrast, implicitly assumes intermediate cash flows are reinvested at the firm's cost of capital, a rate the firm has already established it can genuinely achieve, since the cost of capital reflects the actual return available to the firm from its normal financing and investment activities, making NPV's reinvestment assumption realistic and achievable in a way IRR's assumption, for an unusually high-IRR project, generally is not.

Question 8

A project has an initial outlay of ₹50 lakh, generates a cash inflow of ₹120 lakh in year 1, and then requires a cash outflow of ₹75 lakh in year 2 for mandatory environmental remediation. Explain why this project's cash flow pattern could produce more than one IRR, and why NPV remains reliable even in this situation.

Accepted Answer

This project's cash flow pattern changes sign twice: an outflow at time zero, followed by an inflow in year 1, followed by another outflow in year 2, and a project's cash flow stream can, in principle, produce as many different discount rates at which NPV equals zero as there are sign changes in its cash flow sequence, meaning this particular pattern, with two sign changes, could genuinely produce two distinct discount rates at which NPV equals exactly zero, an ambiguity known as the multiple IRR problem. Where multiple IRRs exist, the IRR decision rule breaks down, since there is no single, unambiguous rate to compare against the firm's cost of capital, and different discount rate ranges could give conflicting accept-or-reject signals depending on which of the multiple IRRs is compared. NPV remains reliable in this situation because it does not require finding any break-even rate at all; it simply computes a single, well-defined present value of the entire cash flow stream, outflows and inflows in whatever sequence they occur, at the firm's actual cost of capital, and that single NPV figure gives an unambiguous accept-or-reject signal regardless of how many times the cash flow stream changes sign, which is precisely why NPV, not IRR, should be relied upon whenever a project's cash flows are unconventional in this way.

Question 9

Two mutually exclusive projects are being compared at a cost of capital of 10%. Project Large has an initial outlay of ₹80 lakh and an IRR of 16%. Project Small has an initial outlay of ₹30 lakh and an IRR of 22%. Project Large has the higher NPV. Explain, using the concept of incremental analysis, why choosing Project Large despite its lower IRR is consistent with, and can be verified by, comparing the two projects' cash flows incrementally.

Accepted Answer

Project Small shows the higher IRR at 22% against Project Large's 16%, which on a pure percentage-return basis makes Small appear more attractive, yet Project Large is stated to have the higher NPV, illustrating the classic scale-driven conflict between the two techniques when comparing mutually exclusive projects of different size. To resolve this using incremental analysis, the firm should compute the incremental cash flows obtained by subtracting Project Small's cash flows, year by year, from Project Large's cash flows, which effectively represents the additional ₹50 lakh of investment (₹80 lakh minus ₹30 lakh) that choosing Large over Small requires, together with the additional cash flows that this extra investment is expected to generate. If the IRR of this incremental cash flow stream exceeds the 10% cost of capital, it means the additional ₹50 lakh invested in choosing Large over Small is itself earning a return above the cost of capital, and is therefore itself a worthwhile additional investment, which means Large should be preferred overall, consistent with what its higher NPV already indicates; the fact that Large's own standalone IRR of 16% is lower than Small's 22% is not a contradiction, since Large's IRR is a blended figure across its entire ₹80 lakh outlay, while the incremental IRR isolates specifically whether the extra ₹50 lakh invested beyond Small's scale is itself justified, which is the genuinely relevant question when choosing between the two, and this incremental check, in every case, agrees with NPV, confirming why NPV is treated as the decisive technique.

Question 10

A machine originally costing ₹30 lakh has a book value of ₹8 lakh at the end of its project life, and is expected to be sold for ₹12 lakh at that time. The tax rate is 30%. Compute the terminal cash flow relating to the machine's disposal, showing the tax effect.

Accepted Answer

Since the expected sale value of ₹12 lakh exceeds the book value of ₹8 lakh, the disposal generates a profit on sale of ₹12 lakh − ₹8 lakh = ₹4 lakh, which, being a gain relative to book value, is taxable at the applicable rate: tax on this profit = 30% × ₹4 lakh = ₹1.2 lakh. Terminal cash flow from disposal = Sale proceeds − Tax on profit on sale = ₹12 lakh − ₹1.2 lakh = ₹10.8 lakh. This net figure of ₹10.8 lakh, not the gross ₹12 lakh sale proceeds, is the amount that should be included as the terminal cash inflow relating to the asset's disposal, since the ₹1.2 lakh tax liability arising specifically because of this sale is a genuine cash outflow the firm must pay as a direct consequence of disposing of the asset at a price above its book value, and omitting this tax effect would overstate the true terminal cash flow the project actually delivers.

Question 11

A project requires an initial investment of ₹25 lakh with no salvage value, and generates accounting profit after tax of ₹4 lakh, ₹5 lakh, ₹6 lakh and ₹5 lakh over its 4-year life. Compute the accounting rate of return using average investment as the base, and state one limitation of this measure that a discounted technique avoids.

Accepted Answer

Average accounting profit after tax = (4 + 5 + 6 + 5) ÷ 4 = 20 ÷ 4 = ₹5 lakh. Average investment, with no salvage value, = Initial investment ÷ 2 = ₹25 lakh ÷ 2 = ₹12.5 lakh. ARR = Average profit ÷ Average investment = 5 ÷ 12.5 = 40%. One limitation this measure carries, which a discounted technique such as NPV avoids, is that ARR uses accounting profit rather than cash flow and applies no time value of money adjustment at all, treating ₹5 lakh of profit in year 1 as equally valuable as ₹5 lakh of profit in year 4, even though the year 1 amount, being received sooner, is genuinely worth more; NPV, by discounting each year's cash flow individually at the cost of capital, correctly distinguishes between cash flows arriving at different points in the project's life rather than working only with simple averages that erase this timing information entirely.

Question 12

A company is deciding whether to replace an old machine with a new one. The old machine has a current book value of ₹6 lakh and could be sold today for ₹9 lakh, with the tax rate at 30%. The new machine costs ₹40 lakh. Compute the net initial outlay for this replacement decision, and explain why using the old machine's book value rather than its sale value would be an error.

Accepted Answer

Since the old machine's sale value of ₹9 lakh exceeds its book value of ₹6 lakh, selling it today generates a taxable profit on sale of ₹9 lakh − ₹6 lakh = ₹3 lakh, giving rise to tax payable of 30% × ₹3 lakh = ₹0.9 lakh, so the net cash inflow from disposing of the old machine = ₹9 lakh − ₹0.9 lakh = ₹8.1 lakh. Net initial outlay for the replacement = Cost of new machine − Net proceeds from sale of old machine = ₹40 lakh − ₹8.1 lakh = ₹31.9 lakh. Using the old machine's book value of ₹6 lakh instead of its actual sale value of ₹9 lakh, net of tax, would be an error because the relevant cash flow to the firm from the replacement decision is what the firm actually receives, in cash, by disposing of the old machine today, which is its market sale value adjusted for the real tax consequence of that specific sale, not the book value, which is merely an accounting record of unamortised historical cost and does not represent any cash the firm actually forgoes or receives by choosing to replace the machine now.

Question 13

Explain what the discounted payback period measures differently from the ordinary payback period, and why it is considered an improvement, even though it still shares one of the ordinary payback period's core limitations.

Accepted Answer

The discounted payback period measures the time required for the present value of a project's cumulative cash inflows, discounted at the firm's cost of capital, to equal the initial outlay, rather than simply summing the undiscounted cash inflows as the ordinary payback period does. It is considered an improvement because it explicitly incorporates the time value of money into the recovery calculation, recognising that a rupee of cash inflow received in year 3 is worth less, in present-value terms, than a rupee received in year 1, a distinction the ordinary payback period ignores entirely by treating every year's cash inflow as equally valuable regardless of timing. However, the discounted payback period still shares one of the ordinary payback period's core limitations: it still ignores every cash flow occurring after the recovery point is reached, whether that recovery is measured in discounted or undiscounted terms, meaning it can still favour a project that recovers its investment quickly but generates comparatively little value afterward, over a project with a longer recovery period but substantially greater total value over its remaining life, exactly the same blind spot that limits the ordinary payback period's usefulness as a sole decision criterion.

Question 14

A firm's normal cost of capital is 12%, used for its regular projects, but it is evaluating a diversification project entering an entirely new business line considered materially riskier than its existing operations. Explain why using the firm's normal 12% cost of capital to discount this new project's cash flows could lead to an incorrect accept-or-reject decision, and what adjustment is appropriate.

Accepted Answer

The firm's normal cost of capital of 12% reflects the risk of its existing business operations, since it is derived from the returns investors require given the risk profile of the firm's current activities; using this same rate to discount a materially riskier diversification project, entering an entirely different business line, would understate the true return investors would actually require to bear the higher risk specific to this new venture, and discounting the new project's cash flows at too low a rate would tend to overstate its NPV, potentially making a genuinely value-destroying or merely marginal project appear attractive simply because it was evaluated against the wrong, too-lenient benchmark. The appropriate adjustment is to apply a risk-adjusted discount rate specific to the new project's own risk level, typically higher than the firm's normal cost of capital to reflect the greater risk of the new business line, rather than mechanically applying the firm's blended, existing-business cost of capital to every new investment proposal regardless of how different that proposal's risk profile is from the firm's current operations.

Question 15

For a single, independent project with conventional cash flows, being evaluated on its own rather than compared against a mutually exclusive alternative, explain why the NPV and IRR decision rules will always reach the same accept-or-reject conclusion.

Accepted Answer

For a single, independent project with conventional cash flows, an initial outflow followed only by inflows, NPV is a decreasing function of the discount rate used, since discounting future inflows at a higher rate reduces their present value; the IRR is, by definition, the specific discount rate at which this NPV function crosses zero. If the project's IRR exceeds the firm's cost of capital, it means the cost of capital lies to the left of the point where NPV crosses zero on this decreasing curve, which means NPV, evaluated at the cost of capital, must still be positive; conversely, if the IRR is below the cost of capital, NPV evaluated at the cost of capital must be negative. Because of this direct, one-to-one relationship between where the cost of capital sits relative to the IRR and the sign of NPV at that cost of capital, for a single conventional project evaluated independently, on its own accept-or-reject merits rather than in comparison to another project, the NPV rule, accept if NPV is positive, and the IRR rule, accept if IRR exceeds the cost of capital, will always agree, and the well-known conflicts between the two techniques arise specifically when comparing or ranking mutually exclusive projects against each other, not when evaluating a single project's own acceptability in isolation.

Practice — Investment Decisions: Capital Budgeting

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