Test 2: answer key

Question 1 · 2 marks · Investment Decisions - Capital Budgeting Techniques · hard

Scenario. Pragati Infra Ltd. is appraising two projects with unequal useful lives. Project Alpha requires an initial cash outlay of ₹3,00,000 and generates a single year-end cash inflow of ₹4,50,000 at the end of Year 1; its life is one year. Project Beta requires an initial cash outlay of ₹6,00,000 and generates year-end cash inflows of ₹3,00,000 in each of Years 1, 2 and 3; its life is three years. For the appraisal, equity represents 60 percent and debt 40 percent of total capital on market-value weights. The cost of equity is 12 percent, the pre-tax cost of debt is 10 percent and the corporate tax rate is 30 percent. Interest is tax-deductible. Use PVIFs at 10 percent of 0.909, 0.826 and 0.751 for Years 1, 2 and 3 respectively. For Beta's IRR interpolation, use three-year PVAFs of 2.106 at 20 percent and 1.952 at 25 percent. Management requires the NPV, IRR and PI of each proposal separately; no identical replacement-cycle assumption or final mutually exclusive selection is supplied.

Using market-value weights, the tax-adjusted cost of debt and the supplied discount factors, which pair of NPVs is correctly calculated for Alpha and Beta?

1. Alpha ₹1,09,050; Beta ₹1,45,800 (correct answer)
2. Alpha ₹1,09,050; Beta (₹79,500)
3. Alpha ₹1,50,000; Beta ₹1,45,800
4. Alpha ₹1,09,050; Beta ₹7,45,800

Answer: A — Alpha ₹1,09,050; Beta ₹1,45,800

Working. Step 1 - After-tax Kd = 10% × (1 - 30%) = 7%. Step 2 - WACC = (0.60 × 12%) + (0.40 × 7%) = 7.20% + 2.80% = 10%. Step 3 - Alpha PV of inflows = ₹4,50,000 × 0.909 = ₹4,09,050; Alpha NPV = ₹4,09,050 - ₹3,00,000 = ₹1,09,050. Step 4 - Beta PV of inflows = ₹3,00,000 × 0.909 + ₹3,00,000 × 0.826 + ₹3,00,000 × 0.751 = ₹2,72,700 + ₹2,47,800 + ₹2,25,300 = ₹7,45,800; Beta NPV = ₹7,45,800 - ₹6,00,000 = ₹1,45,800. Beta has the higher absolute NPV by ₹36,750.

Explanation. Option a is correct. The after-tax cost of debt is 10 percent × (1 - 0.30) = 7 percent. WACC is (60 percent × 12 percent) + (40 percent × 7 percent) = 10 percent. At this rate, Alpha's present value of inflows is ₹4,50,000 × 0.909 = ₹4,09,050, giving NPV of ₹1,09,050. Beta's present value of inflows is ₹3,00,000 × (0.909 + 0.826 + 0.751) = ₹7,45,800, giving NPV of ₹1,45,800. Option b omits Beta's Year 3 inflow, leaving only the first two discounted inflows and a negative NPV. Option c fails to discount Alpha's Year 1 inflow and therefore reports the undiscounted surplus of ₹1,50,000. Option d reports Beta's present value of inflows without deducting its ₹6,00,000 initial outlay, so it is not NPV.

Where it goes wrong. Do not use the pre-tax debt cost in WACC, and do not report the present value of inflows as NPV without deducting the initial cash outlay. Unequal project lives also require care before making a final mutually exclusive choice; this question asks for each project's separate appraisal measure only.

Authority. Chapter 4: Cost of Capital; Section 9: Weighted Average Cost of Capital (WACC); Chapter 7: Investment Decisions; Section 9.1: Net Present Value Method (NPV); Section 9: Discounting Techniques - Scenario 3: Disparity in Life of Proposals (Unequal Lives)

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

Using the supplied three-year PVAFs and linear interpolation between 20 percent and 25 percent for Beta, which IRR comparison is correct?

1. Alpha 23.44 percent; Beta 50.00 percent
2. Alpha 50.00 percent; Beta 23.44 percent (correct answer)
3. Alpha 10.00 percent; Beta 20.00 percent
4. Alpha 50.00 percent; Beta 25.00 percent

Answer: B — Alpha 50.00 percent; Beta 23.44 percent

Working. Alpha: ₹4,50,000 / ₹3,00,000 = 1.50 = 1 + r; therefore r = 50%. Beta at 20%: PV = ₹3,00,000 × 2.106 = ₹6,31,800; NPV = ₹31,800. Beta at 25%: PV = ₹3,00,000 × 1.952 = ₹5,85,600; NPV = -₹14,400. IRR = 20% + [₹31,800 / (₹31,800 + ₹14,400)] × (25% - 20%) = 20% + 3.4416% = approximately 23.44%. Thus Alpha's IRR is higher.

Explanation. Option b is correct. Alpha has one cash inflow, so its IRR is the rate that makes ₹4,50,000 / (1 + r) equal to ₹3,00,000, which is 50 percent. For Beta, the 20 percent PVAF gives a positive NPV and the 25 percent PVAF gives a negative NPV. Interpolation gives approximately 23.44 percent. Option a reverses the project results. Option c mistakes the hurdle rate and one trial rate for the projects' internal rates; IRR is the rate that makes NPV zero. Option d takes the upper trial rate as Beta's IRR without interpolation, although Beta's NPV is already negative at 25 percent and positive at 20 percent.

Where it goes wrong. IRR is not the WACC or the trial discount rate. For Beta, retain the positive NPV at the lower rate and the negative NPV at the higher rate in the interpolation fraction; reversing these signs distorts the result.

Authority. Chapter 7: Investment Decisions; Section 9.3: Internal Rate of Return Method (IRR); Section 9: Discounting Techniques - Scenario 3: Disparity in Life of Proposals (Unequal Lives)

Question 3 · 2 marks · Investment Decisions - Capital Budgeting Techniques · medium

Which profitability index comparison is correctly calculated from the present value of cash inflows and the initial cash outlay?

1. Alpha 1.243; Beta 1.364
2. Alpha 1.500; Beta 1.243
3. Alpha 1.364; Beta 1.243 (correct answer)
4. Alpha 0.364; Beta 0.243

Answer: C — Alpha 1.364; Beta 1.243

Working. Alpha PI = ₹4,09,050 / ₹3,00,000 = 1.3635 ≈ 1.364. Beta PI = ₹7,45,800 / ₹6,00,000 = 1.243. Both indices exceed 1, so both proposals have positive NPVs at the stated discount rate. Alpha has the higher relative profitability index, while Beta has the higher absolute NPV.

Explanation. Option c is correct. PI is the present value of cash inflows divided by the initial cash outlay. Alpha's PI is ₹4,09,050 / ₹3,00,000 = 1.3635, approximately 1.364. Beta's PI is ₹7,45,800 / ₹6,00,000 = 1.243. Option a reverses the two project indices. Option b uses Alpha's undiscounted inflow of ₹4,50,000 rather than its discounted value. Option d divides NPV by initial outlay; that produces the net surplus ratio, not PI, which includes recovery of the initial outlay in its numerator relationship.

Where it goes wrong. Do not divide NPV by initial outlay and call the result PI. The numerator is the present value of all future cash inflows, not the net present value.

Authority. Chapter 7: Investment Decisions; Section 9.2: Profitability Index / Desirability Factor / Present Value Index Method

Question 4 · 2 marks · Financing Decisions - Leverages · medium

Scenario. Vardhman Textiles reports current annual sales of ₹120 lakh. Variable operating costs are 60 percent of sales and annual fixed operating costs are ₹28 lakh. The company has annual interest expense of ₹4 lakh, no preference share capital and an unchanged number of equity shares. Selling price and variable cost per unit, fixed operating costs and interest are expected to remain constant for the proposed change in sales volume. The company is considering a 15 percent increase in sales volume.

What is Vardhman Textiles' degree of operating leverage at the current level of sales?

1. 0.42
2. 1.00
3. 6.00
4. 2.40 (correct answer)

Answer: D — 2.40

Working. Variable cost = ₹120 lakh × 60% = ₹72 lakh. Contribution = ₹120 lakh - ₹72 lakh = ₹48 lakh. EBIT = ₹48 lakh - ₹28 lakh = ₹20 lakh. DOL = Contribution / EBIT = ₹48 lakh / ₹20 lakh = 2.40.

Explanation. Option d is correct. DOL is contribution divided by EBIT. Contribution is ₹120 lakh less variable costs of ₹72 lakh, or ₹48 lakh. EBIT is ₹48 lakh less fixed operating costs of ₹28 lakh, or ₹20 lakh. DOL is therefore 2.40. Option a uses the inverse relationship, EBIT divided by contribution. Option b uses contribution divided by contribution after incorrectly adding fixed cost back to EBIT. Option c divides sales by EBIT, using revenue instead of contribution as the numerator.

Where it goes wrong. The numerator is contribution, not sales revenue. First deduct variable costs from sales, then deduct fixed operating costs to derive EBIT.

Authority. Chapter 6: Financing Decisions - Leverages; Section 3.1: Degree of Operating Leverage (DOL)

Question 5 · 2 marks · Financing Decisions - Leverages · medium

What is the degree of financial leverage at Vardhman Textiles' existing interest burden?

1. 1.25 (correct answer)
2. 0.80
3. 1.50
4. 5.00

Answer: A — 1.25

Working. EBIT = ₹20 lakh. Interest = ₹4 lakh. EBT = ₹20 lakh - ₹4 lakh = ₹16 lakh. Since there are no preference shares, DFL = EBIT / EBT = ₹20 lakh / ₹16 lakh = 1.25.

Explanation. Option a is correct. With no preference share capital, DFL is EBIT divided by earnings before tax, which is EBIT less interest. EBIT is ₹20 lakh and interest is ₹4 lakh, so DFL is ₹20 lakh / ₹16 lakh = 1.25. Option b reverses the ratio by dividing EBT by EBIT. Option c incorrectly uses contribution divided by EBT, mixing the operating and financial leverage bases. Option d divides EBIT by interest alone rather than by earnings after interest.

Where it goes wrong. Interest is deducted from EBIT before calculating the financial leverage denominator. Do not use contribution or interest alone as the denominator.

Authority. Chapter 6: Financing Decisions - Leverages; Section 4.1: Degree of Financial Leverage (DFL)

Question 6 · 2 marks · Financing Decisions - Leverages · hard

If sales volume rises by 15 percent under the stated cost assumptions, which combined-leverage result and percentage change in EPS are expected?

1. DCL 2.40; EPS increases by 36 percent
2. DCL 3.00; EPS increases by 45 percent (correct answer)
3. DCL 1.25; EPS increases by 18.75 percent
4. DCL 3.65; EPS increases by 54.75 percent

Answer: B — DCL 3.00; EPS increases by 45 percent

Working. DOL = 2.40. DFL = 1.25. DCL = DOL × DFL = 2.40 × 1.25 = 3.00. Percentage change in EPS = DCL × percentage change in sales = 3.00 × 15% = 45%.

Explanation. Option b is correct. DCL is the product of DOL and DFL, so it is 2.40 × 1.25 = 3.00. DCL measures the percentage change in EPS for a percentage change in sales. A 15 percent increase in sales therefore produces a 45 percent increase in EPS, assuming the stated fixed costs and interest remain unchanged. Option a applies DOL alone and calculates the change in EBIT, not EPS. Option c applies DFL alone and ignores the operating leverage effect. Option d adds DOL and DFL rather than multiplying them.

Where it goes wrong. Combined leverage is DOL multiplied by DFL, not their sum. DOL converts sales movement into EBIT movement; DFL then converts EBIT movement into EPS movement.

Authority. Chapter 6: Financing Decisions - Leverages; Section 5.1: Degree of Combined Leverage (DCL)

Question 7 · 2 marks · Management of Working Capital - Operating Cycle · hard

Scenario. Aryan Auto Components provides the following annual data: raw material consumed ₹36,00,000; average raw material stock ₹6,00,000; cost of production ₹72,00,000; average work-in-progress ₹4,00,000; cost of goods sold ₹90,00,000; average finished goods stock ₹7,50,000; annual credit sales ₹1,20,00,000; average receivables ₹12,00,000; annual credit purchases ₹72,00,000; and average trade payables ₹6,00,000. Assume a 360-day year and that the stated sales and purchases are on credit.

Which set of component periods and net operating cycle is correctly calculated for Aryan Auto Components?

1. Raw material 60 days; WIP 20 days; finished goods 30 days; debtors 36 days; creditors 30 days; net cycle 176 days
2. Raw material 60 days; WIP 20 days; finished goods 30 days; debtors 36 days; creditors 30 days; net cycle 86 days
3. Raw material 60 days; WIP 20 days; finished goods 30 days; debtors 36 days; creditors 30 days; net cycle 116 days (correct answer)
4. Raw material 60 days; WIP 20 days; finished goods 30 days; debtors 36 days; creditors 30 days; net cycle 96 days

Answer: C — Raw material 60 days; WIP 20 days; finished goods 30 days; debtors 36 days; creditors 30 days; net cycle 116 days

Working. Assume 360 days. Raw material storage = ₹6,00,000 / (₹36,00,000 / 360) = ₹6,00,000 / ₹10,000 = 60 days. WIP period = ₹4,00,000 / (₹72,00,000 / 360) = ₹4,00,000 / ₹20,000 = 20 days. Finished goods period = ₹7,50,000 / (₹90,00,000 / 360) = ₹7,50,000 / ₹25,000 = 30 days. Debtors period = ₹12,00,000 / (₹1,20,00,000 / 360) = ₹12,00,000 / ₹33,333.33 = 36 days. Credit period = ₹6,00,000 / (₹72,00,000 / 360) = ₹6,00,000 / ₹20,000 = 30 days. Net operating cycle = 60 + 20 + 30 + 36 - 30 = 116 days.

Explanation. Option c is correct. The component periods are 60 days for raw materials, 20 days for WIP, 30 days for finished goods, 36 days for debtors and 30 days of supplier credit. The net operating cycle is the sum of the inventory and receivables periods less the credit period enjoyed from suppliers: 60 + 20 + 30 + 36 - 30 = 116 days. Option a adds supplier credit instead of deducting it. Option b omits the finished goods holding period. Option d omits the WIP period.

Where it goes wrong. Supplier credit reduces the period for which the business must finance its operating cycle. Do not add the creditors period, and do not omit any inventory stage.

Authority. Chapter 9: Management of Working Capital; Unit I: Introduction to Working Capital Management; Section 6: Operating or Working Capital Cycle; Section 6.1: Working Capital Based on Operating Cycle

Question 8 · 1 marks · Management of Working Capital - Operating Cycle · medium

Approximately how many operating cycles does Aryan Auto Components complete in a 360-day year?

1. 2.05 cycles
2. 4.19 cycles
3. 3.75 cycles
4. 3.10 cycles (correct answer)

Answer: D — 3.10 cycles

Working. Number of operating cycles = 360 / 116 = 3.1034, approximately 3.10 cycles per year.

Explanation. Option d is correct. The number of operating cycles in a year is the number of days in the year divided by the net operating cycle. Using 360 days and 116 days gives approximately 3.10 cycles. Option a uses 176 days, which results from adding supplier credit. Option b uses 86 days, which results from omitting finished goods holding time. Option c uses 96 days, which results from omitting the WIP period.

Where it goes wrong. Do not divide the operating cycle by the days in the year. The required ratio is annual days divided by net operating-cycle days.

Authority. Chapter 9: Management of Working Capital; Unit I: Introduction to Working Capital Management; Section 6: Operating or Working Capital Cycle