Test 8: answer key

Question 1 · 2 marks · Investment Decisions - Capital Budgeting · medium

Scenario. Narmada Petrochem has a capital budget ceiling of ₹55 crore and five independent projects. Project A requires ₹30 crore and has NPV ₹6.00 crore; Project B requires ₹20 crore and has NPV ₹3.40 crore; Project C requires ₹10 crore and has NPV ₹1.40 crore; Project D requires ₹15 crore and has NPV ₹1.50 crore; Project E requires ₹5 crore and has NPV ₹0.40 crore. The finance manager is examining capital rationing under divisible and indivisible project assumptions.

Based on Profitability Index, which sequence ranks the five projects in descending order?

1. A, C, B, D, E
2. A, B, C, D, E (correct answer)
3. B, A, C, E, D
4. A, B, D, C, E

Answer: B — A, B, C, D, E

Working. PI A = 1 + 6.00/30 = 1.200; PI B = 1 + 3.40/20 = 1.170; PI C = 1 + 1.40/10 = 1.140; PI D = 1 + 1.50/15 = 1.100; PI E = 1 + 0.40/5 = 1.080.

Explanation. Profitability Index is present value of inflows divided by initial outlay, or 1 plus NPV divided by outlay. PI values are A 1.200, B 1.170, C 1.140, D 1.100 and E 1.080. The descending order is A, B, C, D and E.

Where it goes wrong. Ranking by absolute NPV instead of PI may put D above C because D has NPV ₹1.50 crore against C ₹1.40 crore, but PI ranking is relevant for divisible capital rationing.

Authority. Chapter 7: Investment Decisions - Capital Budgeting, Section 11.1 Capital Budgeting under Capital Rationing

Question 2 · 2 marks · Investment Decisions - Capital Budgeting · hard

If the projects are divisible and the capital ceiling is ₹55 crore, what is the maximum achievable NPV?

1. ₹9.80 crore
2. ₹9.40 crore
3. ₹10.10 crore (correct answer)
4. ₹10.80 crore

Answer: C — ₹10.10 crore

Working. A outlay 30 and NPV 6.00; B outlay 20 and NPV 3.40; balance 5; half of C gives outlay 5 and NPV 0.50 × 1.40 = 0.70. Total NPV = 6.00 + 3.40 + 0.70 = ₹10.10 crore.

Explanation. With divisible projects, the firm ranks by PI and takes A and B fully, using ₹50 crore. The remaining ₹5 crore is invested in half of C. NPV is 6.00 plus 3.40 plus 0.50 times 1.40, which equals ₹10.10 crore.

Where it goes wrong. Selecting A plus B plus E because the outlay exactly equals ₹55 crore ignores that half of C gives NPV ₹0.70 crore while E gives only ₹0.40 crore.

Authority. Chapter 7: Investment Decisions - Capital Budgeting, Section 11.1 Capital Budgeting under Capital Rationing

Question 3 · 2 marks · Investment Decisions - Capital Budgeting · hard

If the projects are indivisible, which feasible portfolio is most appropriate under the ₹55 crore ceiling?

1. A and B only, NPV ₹9.40 crore
2. A, C and D, NPV ₹8.90 crore
3. B, C, D and E, NPV ₹6.70 crore
4. A, B and E, NPV ₹9.80 crore (correct answer)

Answer: D — A, B and E, NPV ₹9.80 crore

Working. A+B+E outlay = 30+20+5 = 55; NPV = 6.00+3.40+0.40 = 9.80. A+B outlay = 50; NPV = 9.40. A+C+D outlay = 55; NPV = 6.00+1.40+1.50 = 8.90.

Explanation. For indivisible projects, the firm compares feasible combinations within the ceiling. A plus B plus E uses ₹55 crore and gives NPV ₹9.80 crore, which exceeds A plus B at ₹9.40 crore and A plus C plus D at ₹8.90 crore.

Where it goes wrong. Applying fractional PI ranking when projects are indivisible can suggest investing in half of C, which is not feasible here.

Authority. Chapter 7: Investment Decisions - Capital Budgeting, Section 11.1 Capital Budgeting under Capital Rationing

Question 4 · 2 marks · Financing Decisions - Capital Structure · medium

Scenario. Saraswati Ltd is an unlevered firm with EBIT ₹500 lakh, corporate tax rate 30 percent and unlevered cost of equity 15 percent. It plans to introduce debt of ₹300 lakh at a pre-tax cost of debt of 10 percent. The company operates in a perfect capital market with corporate taxes as per the Modigliani and Miller approach with taxes.

What is the value of the levered firm under the Modigliani and Miller approach with corporate taxes?

1. ₹2,333.33 lakh
2. ₹2,423.33 lakh (correct answer)
3. ₹2,523.33 lakh
4. ₹2,300.00 lakh

Answer: B — ₹2,423.33 lakh

Working. V_U = 500 × (1 − 0.30) / 0.15 = 350 / 0.15 = ₹2,333.33 lakh. V_L = V_U + T × D = 2,333.33 + 0.30 × 300 = ₹2,423.33 lakh.

Explanation. Under MM with taxes, value of levered firm equals value of unlevered firm plus tax shield. Unlevered value is EBIT after tax divided by unlevered cost of equity. Tax shield is tax rate multiplied by debt.

Where it goes wrong. Using EBIT without tax adjustment gives an inflated unlevered value and an incorrect levered value.

Authority. Chapter 5: Financing Decisions - Capital Structure, Section 2.4 Modigliani-Miller Approach with tax

Question 5 · 2 marks · Financing Decisions - Capital Structure · hard

What is the cost of equity of the levered firm under the MM approach with taxes?

1. 15.00 percent
2. 15.25 percent
3. 15.49 percent (correct answer)
4. 16.00 percent

Answer: C — 15.49 percent

Working. E = V_L − D = 2,423.33 − 300 = ₹2,123.33 lakh. K_e = 15% + (15% − 10%) × (1 − 0.30) × (300 / 2,123.33) = 15% + 5% × 0.70 × 0.14129 = 15.49 percent approx.

Explanation. The levered cost of equity equals unlevered cost of equity plus a financial risk premium based on after-tax debt-to-equity ratio. Market value of equity is levered firm value minus debt.

Where it goes wrong. Using debt divided by firm value instead of debt divided by equity understates the financial risk premium.

Authority. Chapter 5: Financing Decisions - Capital Structure, Section 2.4 Modigliani-Miller Approach with tax

Question 6 · 2 marks · Financing Decisions - Capital Structure · medium

What is the weighted average cost of capital of the levered firm under the MM approach with taxes?

1. 15.00 percent
2. 14.00 percent
3. 14.75 percent
4. 14.44 percent (correct answer)

Answer: D — 14.44 percent

Working. WACC = EBIT × (1 − T) / V_L = 500 × 0.70 / 2,423.33 = 350 / 2,423.33 = 14.44 percent approx.

Explanation. Under MM with taxes, WACC declines with leverage. It can be computed as EBIT after tax divided by levered firm value.

Where it goes wrong. Using the unlevered cost of equity as WACC ignores the tax shield benefit of debt.

Authority. Chapter 5: Financing Decisions - Capital Structure, Section 2.4 Modigliani-Miller Approach with tax

Question 7 · 2 marks · Investment Decisions - Capital Budgeting · medium

Scenario. Apex Solar Ltd is evaluating a project with an initial outlay of ₹100 lakh and expected cash inflows of ₹40 lakh in Year 1, ₹50 lakh in Year 2 and ₹30 lakh in Year 3. The cost of capital and reinvestment rate is 12 percent. The management is comparing the conventional Internal Rate of Return with Modified Internal Rate of Return.

What is the Modified Internal Rate of Return of the Apex Solar project?

1. 10.85 percent approx (correct answer)
2. 12.00 percent
3. 11.50 percent
4. 9.80 percent

Answer: A — 10.85 percent approx

Working. Terminal value = 40 × (1.12)^2 + 50 × (1.12) + 30 = 50.176 + 56.00 + 30 = ₹136.176 lakh. MIRR = (136.176 / 100)^(1/3) − 1 = 10.85 percent approx.

Explanation. MIRR brings all inflows to terminal value at the reinvestment rate and equates that terminal value to the initial outlay. The terminal value is compared with the initial outlay over three years.

Where it goes wrong. Using the simple average of cash inflows or treating MIRR as the same as IRR overstates or misstates the reinvestment assumption.

Authority. Chapter 7: Investment Decisions - Capital Budgeting, Section 9.5 Modified Internal Rate of Return

Question 8 · 1 marks · Investment Decisions - Capital Budgeting · medium

Which statement most appropriately distinguishes MIRR from conventional IRR?

1. IRR assumes reinvestment at the cost of capital while MIRR assumes reinvestment at IRR.
2. MIRR assumes reinvestment at the cost of capital and uses terminal value while IRR assumes reinvestment at IRR. (correct answer)
3. Both IRR and MIRR assume reinvestment at IRR.
4. MIRR ignores the initial outlay in project evaluation.

Answer: B — MIRR assumes reinvestment at the cost of capital and uses terminal value while IRR assumes reinvestment at IRR.

Working. MIRR = (Terminal value of inflows at cost of capital / Present value of outflows)^(1/n) − 1. IRR solves NPV equals zero using IRR as discount rate.

Explanation. MIRR explicitly assumes interim cash flows are reinvested at the cost of capital and converts them into a terminal value. Conventional IRR assumes reinvestment at the IRR itself.

Where it goes wrong. Reversing the reinvestment assumptions of IRR and MIRR is a common conceptual error.

Authority. Chapter 7: Investment Decisions - Capital Budgeting, Section 9.5 Modified Internal Rate of Return