Business Finance · Cost of capital and evaluating investment projects

Risk, Capital Rationing and Project Adjustments in Investment Appraisal

Updated 11 October 2026 · Fact-checked

Project risk is handled by raising the discount rate, or by testing how NPV changes when inputs change (sensitivity and scenarios). Capital rationing means funds are limited, so you rank projects. For divisible projects, rank by profitability index (NPV ÷ capital used). For indivisible projects, test combinations and pick the highest total NPV.

Understand Risk, Capital Rationing and Project Adjustments

NPV uses forecasts. Forecasts can be wrong. Risk here means the cash flows could differ from your estimates. A good appraisal does not just give one NPV. It also shows how fragile that NPV is.

There are three common ways to deal with risk. The first is a risk-adjusted discount rate (RADR). You add a premium to the discount rate for riskier projects. A project in a business with higher systematic risk is discounted at a higher rate, often taken from CAPM using a suitable beta. The weakness is that the premium is the same for every year, so it assumes risk grows steadily with time.

The second is sensitivity analysis. You change one input at a time, such as sales volume, price or cost, and see how NPV moves. A useful measure is the percentage change in that input that makes NPV zero. The smaller that margin, the more sensitive the project is to that input. Its weakness is that it changes one variable at a time and gives no probabilities. Scenario analysis fixes this partly by changing several inputs together, for example best case, base case and worst case.

The third idea is capital rationing. Normally you accept every project with a positive NPV. But if funds are limited, you cannot. Hard rationing comes from outside, such as lenders refusing to lend. Soft rationing is set inside the firm, such as a budget limit. If projects can be scaled down (divisible), rank by profitability index and fund in order until money runs out. If they cannot (indivisible), you must compare combinations of whole projects.

Inflation and tax also change NPV. Keep real and nominal consistent. Tax reduces cash flows, and tax relief on capital allowances increases them. Both must be in the cash flows you discount.

Key rules to remember

Net present value: NPV = Σ CFₜ ÷ (1 + r)ᵗ − initial outlay; CFₜ is the net cash flow at time t after tax. Use the risk-adjusted r if one is given.
Risk-adjusted discount rate: r = risk-free rate + β × (market return − risk-free rate); CAPM-based rate for a project of similar risk. Alternatively, add a stated premium to the base rate.
Sensitivity margin: Sensitivity (%) = NPV ÷ PV of the cash flows affected by the variable × 100; This is the percentage fall in that variable that takes NPV to zero. Use the PV of the cash flows that depend on the variable.
Profitability index: PI = NPV ÷ capital invested in the rationed period; Use for divisible projects under single-period rationing. Some texts use PV of inflows ÷ outlay, which is PI + 1. State which you use.
Real and nominal rates: (1 + nominal rate) = (1 + real rate) × (1 + inflation rate); Discount real cash flows at the real rate and nominal cash flows at the nominal rate. Never mix them.
Expected NPV from scenarios: E(NPV) = Σ pᵢ × NPVᵢ; pᵢ are the probabilities of the scenarios. They must sum to 1.

How to solve Risk, Capital Rationing and Project Adjustments questions

Use this order for most questions on risk, rationing and adjustments.

1Read what is asked: a risk-adjusted NPV, a sensitivity figure, a scenario comparison or a project ranking.
2List the cash flows after tax. Include capital allowances, working capital and inflation if stated. Make sure all are nominal or all are real.
3Choose the discount rate. If a risk premium or beta is given, use the adjusted rate. Match nominal cash flows to a nominal rate.
4Compute the base-case NPV. Show each year's discount factor and cash flow.
5For sensitivity, find the PV of the cash flows linked to the variable. Divide NPV by that PV to get the percentage change that gives zero NPV.
6For rationing, check whether projects are divisible and how many periods are limited. Calculate PI for divisible projects and rank. For indivisible ones, list feasible combinations within the budget.
7State the decision, then comment briefly: limits of the method, assumptions, and any qualitative factors.

Quickest way: PI ranking and one-line sensitivity

When to use it: Use when time is short and the question is single-period rationing or asks which input matters most.

Compute each project's NPV once.
Divide NPV by the capital outlay to get PI.
Rank by PI and fill the budget from the top. The last project is taken in part only if divisible.
For sensitivity, write NPV ÷ PV of the variable's cash flows. The variable with the smallest percentage is the most critical.
If projects are indivisible, check a few combinations that use most of the budget and compare total NPV.

Common mistakes in Risk, Capital Rationing and Project Adjustments

Ranking by NPV alone under capital rationing.
NPV is the usual rule, so students keep using it when funds are limited.
Fix: With limited funds and divisible projects, rank by NPV per unit of capital (PI). With indivisible ones, compare total NPV of combinations.
Taking the sensitivity percentage as NPV ÷ total PV of all inflows.
Students forget the variable affects only some cash flows.
Fix: Divide NPV by the PV of the cash flows that depend on that variable, such as sales revenue or variable costs.
Mixing real cash flows with a nominal discount rate.
Inflation is mentioned late in the question and gets ignored.
Fix: Decide first whether cash flows are real or nominal. Use the matching rate, and convert with (1 + nominal) = (1 + real)(1 + inflation).
Claiming that a risk-adjusted rate removes risk.
The higher rate looks like a safety margin.
Fix: Say it only compensates for risk through a higher required return. It assumes the premium applies equally to every year and does not show the spread of outcomes.
Ignoring tax on cash flows or capital allowances.
Students treat accounting profit as cash flow.
Fix: Tax the operating cash flows. Add the tax saved by capital allowances separately, and keep the timing stated in the question.
Treating the sensitivity of one variable as the total project risk.
Sensitivity gives a single clear figure.
Fix: Note that other variables are held constant and no probabilities are used. Mention scenarios or simulation as a fuller view.

Worked examples

Example 1

A project costs ₹10,00,000 now. It produces net after-tax cash flows of ₹4,00,000 at the end of each of years 1 to 4. Of this, sales revenue after tax is ₹6,00,000 a year and costs after tax are ₹2,00,000 a year. The discount rate is 10%. The annuity factor for 4 years at 10% is 3.170. Find the NPV and the percentage fall in sales revenue that makes NPV zero.

Show the solution

PV of net cash flows = 4,00,000 × 3.170 = ₹12,68,000.
NPV = 12,68,000 − 10,00,000 = ₹2,68,000.
PV of after-tax sales revenue = 6,00,000 × 3.170 = ₹19,02,000.
Sensitivity = 2,68,000 ÷ 19,02,000 = 0.1409, about 14.1%.
So after-tax sales revenue can fall by about 14.1% before NPV reaches zero.

Answer: NPV = ₹2,68,000. Sales revenue can fall by about 14.1% before NPV is zero.

Example 2

A firm has ₹10,00,000 to invest this year only. Projects are divisible and cannot be repeated. A needs ₹6,00,000 and has NPV ₹1,20,000. B needs ₹5,00,000 and has NPV ₹1,25,000. C needs ₹4,00,000 and has NPV ₹60,000. Find the best plan and total NPV.

Show the solution

PI of A = 1,20,000 ÷ 6,00,000 = 0.20.
PI of B = 1,25,000 ÷ 5,00,000 = 0.25.
PI of C = 60,000 ÷ 4,00,000 = 0.15.
Rank: B (0.25), A (0.20), C (0.15).
Fund B fully: ₹5,00,000 used, NPV ₹1,25,000. Remaining ₹5,00,000.
Fund A with the remaining ₹5,00,000. That is 5 ÷ 6 of A, giving NPV = 1,20,000 × 5 ÷ 6 = ₹1,00,000.
Nothing is left for C.
Total NPV = 1,25,000 + 1,00,000 = ₹2,25,000.

Answer: Invest in all of B and 5/6 of A. Total NPV = ₹2,25,000.

Exam tips

Read whether projects are divisible and whether rationing lasts one period or several. This decides the method.
Show the sensitivity formula and the PV you divide by. Marks go for method even if the arithmetic slips.
For written parts, give one limit of each method: RADR uses a constant premium, sensitivity changes one variable at a time, scenarios need subjective probabilities.
In MCQs on inflation, check whether the cash flows are real or nominal before choosing the rate.
Round only at the end and state your assumptions, such as cash flows at year end.

Practice questions from Cost of capital and evaluating investment projects

Risk, Capital Rationing and Project Adjustments in other exams

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

Risk, Capital Rationing and Project Adjustments: frequently asked questions

What is a risk-adjusted discount rate?

It is a discount rate that includes a premium for the project's risk. Riskier projects get a higher rate, so their NPV is lower. It can come from CAPM using a beta for the project's business or from a stated premium.

How do I do sensitivity analysis on NPV?

Work out the base NPV. Then find the PV of the cash flows linked to the variable you are testing. Divide NPV by that PV to get the percentage change that makes NPV zero.

What is the profitability index in capital rationing?

It is NPV divided by the capital invested. It shows the NPV earned per rupee of scarce funds. Rank divisible projects by it and fund from the highest down until the money runs out.

How do inflation and tax affect NPV?

Inflation changes the size of nominal cash flows and the nominal discount rate, so you must keep them consistent. Tax reduces operating cash flows, while capital allowances reduce tax and raise cash flow in the years they are claimed.