Capital Rationing with a Contingent Expansion
Northstar Specialty Chemicals has a hard capital budget of ₹12 crore for the coming year and cannot raise additional equity or debt without breaching its covenant. Four independent projects are under review; all have positive NPV at the firm's 12% cost of capital and are indivisible in practice. Project A requires ₹5 crore and has an NPV of ₹2.10 crore over five years. Project B requires ₹4 crore and has an NPV of ₹1.40 crore over four years. Project C requires ₹6 crore and has an NPV of ₹2.70 crore over six years. Project D requires ₹3 crore and has an NPV of ₹1.05 crore over three years. Project C also creates a right, not an obligation, to invest ₹4 crore at the end of year 2 in a follow-on line. Management estimates the follow-on's NPV at that future date will be ₹1.60 crore with probability 0.6 and zero otherwise; the risk-adjusted discount rate is 12%. The CFO wants a ranking that reflects both the current budget and the option, not just a simple PI league table.
1. Rank the projects by profitability index and choose the optimal portfolio under the ₹12 crore budget, ignoring the option. Show the feasible combinations.
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PI = 1 + NPV/outlay: A 1.42, B 1.35, C 1.45, D 1.35. PI ranking is C, A, B/D, but indivisibility matters. Feasible portfolios within ₹12 crore:
- C + A: outlay 11, NPV 4.80
- A + B + D: outlay 12, NPV 4.55
- C + B: outlay 10, NPV 4.10
- C + D: outlay 9, NPV 3.75
- A + B: outlay 9, NPV 3.50
- A + D: outlay 8, NPV 3.15
- B + D: outlay 7, NPV 2.45 Choose C + A: highest NPV and preserves ₹1 crore of budget.
2. Value the expansion option and recalculate C's adjusted NPV and PI. Does the choice change?
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Decision-tree value of the option today = 0.6 × 1.60 / 1.12² = ₹0.765 crore. Adjusted C NPV = 2.70 + 0.765 = ₹3.465 crore. With C + A, adjusted NPV = 3.465 + 2.10 = ₹5.565 crore, still above A + B + D at ₹4.55 crore. The current choice does not change if the ₹4 crore follow-on outlay falls outside the current budget. But on a total-investment basis, C's present outlay is 6 + 4/1.12² = ₹9.189 crore, and its PI is (3.465 + 9.189)/9.189 = 1.377, below A's 1.42. The option is contingent, so the current budget should not treat the future outlay as certain. The CFO should, however, check that the year-2 ₹4 crore is available and not crowded out by other commitments.
3. What if the board cuts the current budget to ₹10 crore? Recompute the best combination and comment on whether the option makes C still preferable to B.
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At ₹10 crore, C + A is infeasible. Best combinations: C + B = 4.10 + 0.765 = ₹4.865 crore adjusted NPV; C + D = 3.75 + 0.765 = ₹4.515 crore; A + B = ₹3.50 crore; A + D = ₹3.15 crore. Choose C + B. Without the option, C + B (4.10) still beats C + D (3.75) and A + B (3.50), so the option strengthens but does not reverse the ranking here. If the future outlay is treated as a firm commitment, C's adjusted PI falls and B + D or A + B may become competitive; the decision then depends on whether the option can be deferred or funded from year-2 cash flow.