Test 10: answer key

Question 1 · 2 marks · Ratio Analysis · medium

Scenario. Vardhman Textiles reports sales of ₹2,400 crore, net profit after tax of ₹144 crore, EBIT of ₹240 crore, interest of ₹40 crore, profit before tax of ₹200 crore, average total assets of ₹1,200 crore and average shareholders equity of ₹600 crore. The applicable tax rate is 25 percent.

Using the three-step DuPont model, the return on equity of Vardhman Textiles is:

1. 12.0 percent
2. 24.0 percent (correct answer)
3. 18.0 percent
4. 30.0 percent

Answer: B — 24.0 percent

Working. Net profit margin = 144 / 2400 = 0.06 or 6 percent. Asset turnover = 2400 / 1200 = 2.0 times. Equity multiplier = 1200 / 600 = 2.0 times. ROE = 0.06 × 2.0 × 2.0 = 0.24 or 24.0 percent.

Explanation. The correct option is b. Three-step DuPont ROE equals net profit margin multiplied by asset turnover multiplied by equity multiplier. It gives 6 percent × 2.0 × 2.0 = 24.0 percent. Option a ignores the equity multiplier. Option c does not reconcile with the given figures. Option d overstates the product of the three components.

Where it goes wrong. Students may divide PAT by average total assets and stop at return on assets, or may use total assets instead of shareholders equity in the multiplier.

Authority. Chapter 3: Financial Analysis and Planning - Ratio Analysis, Du Pont analysis

Question 2 · 2 marks · Ratio Analysis · hard

Under the five-step DuPont decomposition, if the EBIT margin falls to 8 percent while tax burden, interest burden, asset turnover and equity multiplier remain unchanged, the revised return on equity is:

1. 16.0 percent
2. 20.0 percent
3. 19.2 percent (correct answer)
4. 24.0 percent

Answer: C — 19.2 percent

Working. Tax burden = PAT / PBT = 144 / 200 = 0.72. Interest burden = PBT / EBIT = 200 / 240 = 0.8333. Revised ROE = 0.72 × 0.8333 × 0.08 × 2.0 × 2.0 = 0.192 or 19.2 percent.

Explanation. The correct option is c. Five-step DuPont ROE equals tax burden × interest burden × EBIT margin × asset turnover × equity multiplier. Revised ROE is 0.72 × 0.8333 × 0.08 × 2.0 × 2.0 = 19.2 percent. Option a omits the interest burden effect. Option b uses an incorrect margin or omits a component. Option d is the original ROE before the EBIT margin decline.

Where it goes wrong. Students may use PAT margin directly and treat the five-step model as the three-step model, thereby missing the tax burden and interest burden components.

Authority. Chapter 3: Financial Analysis and Planning - Ratio Analysis, Du Pont analysis

Question 3 · 2 marks · Ratio Analysis · medium

ROE remains 24 percent while net profit margin is unchanged at 6 percent. Asset turnover falls from 2.0 to 1.6 and equity multiplier rises from 2.0 to 2.5. Which interpretation is most appropriate?

1. Operational efficiency improved and financial leverage fell
2. Financial leverage fell and compensated the fall in asset turnover
3. Both operational efficiency and financial leverage improved
4. Operational efficiency weakened while higher financial leverage compensated for it (correct answer)

Answer: D — Operational efficiency weakened while higher financial leverage compensated for it

Working. Revised ROE = 0.06 × 1.6 × 2.5 = 0.24 or 24 percent. Asset turnover declined from 2.0 to 1.6. Equity multiplier increased from 2.0 to 2.5.

Explanation. The correct option is d. A fall in asset turnover from 2.0 to 1.6 indicates weaker asset utilisation or operational efficiency. A rise in equity multiplier from 2.0 to 2.5 indicates higher financial leverage. The product 6 percent × 1.6 × 2.5 remains 24 percent. Options a, b and c contradict the direction of the two components.

Where it goes wrong. Students may see unchanged ROE and conclude that performance is unchanged, ignoring that ROE has been maintained by higher leverage rather than better operations.

Authority. Chapter 3: Financial Analysis and Planning - Ratio Analysis, Du Pont analysis

Question 4 · 2 marks · Cost of Capital · medium

Scenario. Deccan Cement has a risk-free rate of 7.2 percent, expected market return of 12.8 percent, levered equity beta of 1.25, debt-equity ratio of 0.6 and tax rate of 25 percent. The company is evaluating a proposed debt-equity ratio of 1.0 for a new project.

Using the Capital Asset Pricing Model, the current cost of equity of Deccan Cement is:

1. 14.20 percent (correct answer)
2. 13.60 percent
3. 15.00 percent
4. 12.80 percent

Answer: A — 14.20 percent

Working. Market risk premium = 12.8 percent − 7.2 percent = 5.6 percent. Cost of equity = 7.2 percent + 1.25 × 5.6 percent = 14.20 percent.

Explanation. The correct option is a. CAPM cost of equity equals risk-free rate plus beta multiplied by the market risk premium. It is 7.2 percent + 1.25 × 5.6 percent = 14.20 percent. Option b uses an incorrect beta or risk premium. Option c uses an incorrect risk premium. Option d is the market return, not the cost of equity.

Where it goes wrong. Students may use the market return directly or may multiply beta by the market return instead of the market risk premium.

Authority. Chapter 4: Cost of Capital, Capital Asset Pricing Model approach

Question 5 · 2 marks · Cost of Capital · hard

If the proposed debt-equity ratio of 1.0 is adopted, the relevered equity beta is closest to:

1. 1.25
2. 1.51 (correct answer)
3. 1.09
4. 1.72

Answer: B — 1.51

Working. Unlevered beta = 1.25 / [1 + (1 − 0.25) × 0.6] = 1.25 / 1.45 = 0.8621. Relevered beta = 0.8621 × [1 + (1 − 0.25) × 1.0] = 0.8621 × 1.75 = 1.5086, approximately 1.51.

Explanation. The correct option is b. First unlever the current beta using the current debt-equity ratio and tax rate. Then relever it at the proposed debt-equity ratio. The relevered beta is about 1.51. Option a is the current levered beta. Option c results from an incorrect tax adjustment. Option d overstates the relevered beta.

Where it goes wrong. Students may relever the already levered beta without first unlevering it, or may ignore the tax shield in the debt-equity adjustment.

Authority. Chapter 4: Cost of Capital, Capital Asset Pricing Model approach and beta adjustment

Question 6 · 2 marks · Cost of Capital · hard

Using the relevered beta of approximately 1.5086, the cost of equity under the proposed capital structure is closest to:

1. 14.20 percent
2. 14.83 percent
3. 15.65 percent (correct answer)
4. 16.40 percent

Answer: C — 15.65 percent

Working. Cost of equity = 7.2 percent + 1.5086 × 5.6 percent = 7.2 percent + 8.448 percent = 15.648 percent, approximately 15.65 percent.

Explanation. The correct option is c. Cost of equity equals 7.2 percent + 1.5086 × 5.6 percent = 15.65 percent approximately. Option a is the current cost of equity. Option b uses an incorrect relevered beta. Option d overstates the risk premium effect.

Where it goes wrong. Students may use the original beta after computing the relevered beta, or may round the beta too early and select a materially different value.

Authority. Chapter 4: Cost of Capital, Capital Asset Pricing Model approach

Question 7 · 2 marks · Ratio Analysis · medium

Scenario. Sunrise Engineering reports sales of ₹3,600 lakh, net fixed assets of ₹900 lakh, total assets of ₹1,800 lakh, current assets of ₹600 lakh and current liabilities of ₹300 lakh. Operating current assets excluding cash are ₹600 lakh and operating current liabilities excluding short-term bank borrowing are ₹300 lakh. Capital employed is total assets less current liabilities.

The fixed asset turnover ratio and the operating working capital turnover ratio are:

1. 4.0 times and 8.0 times
2. 9.0 times and 4.0 times
3. 4.0 times and 10.0 times
4. 4.0 times and 12.0 times (correct answer)

Answer: D — 4.0 times and 12.0 times

Working. Fixed asset turnover = 3,600 / 900 = 4.0 times. Operating working capital = 600 − 300 = 300 lakh. Operating working capital turnover = 3,600 / 300 = 12.0 times.

Explanation. The correct option is d. Fixed asset turnover is sales divided by net fixed assets, giving 4.0 times. Operating working capital is operating current assets minus operating current liabilities, giving ₹300 lakh. Operating working capital turnover is 3,600 / 300 = 12.0 times. Options a, b and c use incorrect operating working capital or fixed asset figures.

Where it goes wrong. Students may use total current assets minus total current liabilities instead of operating current assets and operating current liabilities, or may divide by total assets for fixed asset turnover.

Authority. Chapter 3: Financial Analysis and Planning - Ratio Analysis, Activity ratios

Question 8 · 1 marks · Ratio Analysis · medium

The capital turnover ratio, using capital employed as total assets less current liabilities, is:

1. 2.4 times (correct answer)
2. 2.0 times
3. 3.0 times
4. 1.2 times

Answer: A — 2.4 times

Working. Capital employed = 1,800 − 300 = 1,500 lakh. Capital turnover = 3,600 / 1,500 = 2.4 times.

Explanation. The correct option is a. Capital employed is ₹1,800 lakh − ₹300 lakh = ₹1,500 lakh. Capital turnover is ₹3,600 lakh / ₹1,500 lakh = 2.4 times. Option b uses total assets as the denominator. Option c uses an incorrect capital employed figure. Option d halves the correct turnover.

Where it goes wrong. Students may use total assets instead of capital employed, or may deduct all current assets rather than current liabilities.

Authority. Chapter 3: Financial Analysis and Planning - Ratio Analysis, Activity ratios