Capital Investment Appraisal under Rationing and Risk
A manufacturer has BDT 100 million available for capital projects this year and cannot raise further finance without breaching its debt covenant. Four independent projects are proposed, all with a five-year life and no residual value. Project A requires BDT 40 million and yields annual cash inflows of BDT 13 million. Project B requires BDT 30 million and yields BDT 10 million annually. Project C requires BDT 50 million and yields BDT 15 million annually. Project D requires BDT 20 million and yields BDT 6.5 million annually. The company's weighted average cost of capital is 12 per cent; the five-year annuity factor at 12 per cent is 3.605. The finance director wants to rank by payback because 'it is simpler and the cash comes back faster'. One director argues for accepting every project with a positive net present value regardless of the capital limit.
1. Compute NPV and profitability index for each project and recommend the optimal combination within the BDT 100 million limit.
Read the worked answer
PV of inflows = annual inflow x 3.605.
- A: 13 x 3.605 = 46.87; NPV = 46.87 - 40 = 6.87; PI = 46.87/40 = 1.172
- B: 10 x 3.605 = 36.05; NPV = 36.05 - 30 = 6.05; PI = 36.05/30 = 1.202
- C: 15 x 3.605 = 54.08; NPV = 54.08 - 50 = 4.08; PI = 54.08/50 = 1.082
- D: 6.5 x 3.605 = 23.43; NPV = 23.43 - 20 = 3.43; PI = 23.43/20 = 1.172
Ranking by PI: B (1.202), then A and D (1.172), then C (1.082).
With BDT 100 million: B + A + D = 30 + 40 + 20 = 90 million, NPV = 6.05 + 6.87 + 3.43 = 16.35 million, leaving 10 million idle. B + C + D = 30 + 50 + 20 = 100 million, NPV = 6.05 + 4.08 + 3.43 = 13.56 million. A + C = 90 million, NPV = 10.95 million. B + A + C exceeds the limit (120 million).
The optimal feasible combination is B + A + D with NPV BDT 16.35 million, even though 10 million is unspent. The examiner rewards checking combinations where indivisible projects create slack, not blind PI ranking.
2. Critique the finance director's payback preference and the director's 'accept all positive NPV' argument.
Read the worked answer
Payback ignores cash flows after the payback period, ignores the time value of money, and uses an arbitrary cut-off. Ranking by payback would favour short-payback projects regardless of value created. For example, D pays back in about 3.1 years and A in about 3.1 years, while C takes 3.3 years, but payback says nothing about the BDT 4.08 million NPV that C creates. Payback is useful as a liquidity screen, not as the primary ranking tool under rationing.
The 'accept all positive NPV' argument ignores capital rationing. When capital is limited, accepting all positive-NPV projects is infeasible; the firm must select the combination that maximises total NPV subject to the constraint. Accepting all four would require BDT 140 million, breaching the covenant.
The correct approach is NPV maximisation under the capital constraint, using PI as a guide where projects are divisible, and checking combinations where they are not. Qualitative factors include strategic fit, risk differences not captured in a single discount rate, and the option value of keeping capacity for future projects.
3. Explain how risk could be incorporated and what sensitivity analysis would reveal.
Read the worked answer
A single 12 per cent discount rate assumes all projects carry the same risk. Risk can be incorporated by using a risk-adjusted discount rate per project, certainty-equivalent cash flows, scenario analysis, or simulation. Projects with more uncertain inflows should be discounted at a higher rate.
Sensitivity analysis asks how far a variable can move before NPV falls to zero. For Project A, NPV is 6.87 on a base inflow of 13 million. The fall in annual inflow that makes NPV zero is 6.87 / 3.605 = BDT 1.91 million, i.e. about 14.7 per cent. For Project C, the margin is 4.08 / 3.605 = BDT 1.13 million, about 7.5 per cent of 15 million. C is therefore more sensitive to volume or price declines.
Break-even analysis on cost of capital: find the rate at which NPV is zero for each project. The examiner rewards linking the sensitivity margin to the project's risk profile and recommending that the more sensitive project (C) be scrutinised more closely before selection.