Test 12: answer key

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

Scenario. Godavari Chemical evaluates a one-year project with initial outlay ₹10,00,000 and nominal year-end cash inflow ₹6,60,000. The nominal discount rate is 10 percent and inflation is 5 percent. Use the Fisher relationship to compare nominal and real cash flow approaches.

What is the real year-end cash inflow for Godavari Chemical?

1. ₹6,28,571.43 (correct answer)
2. ₹6,93,000.00
3. ₹6,60,000.00
4. ₹6,00,000.00

Answer: A — ₹6,28,571.43

Working. Real cash inflow = Nominal cash inflow / (1 + inflation rate) = ₹6,60,000 / 1.05 = ₹6,28,571.43.

Explanation. Real cash flow is nominal cash flow divided by one plus inflation. Option a is correct because ₹6,60,000 divided by 1.05 equals ₹6,28,571.43. Option b incorrectly multiplies by 1.05. Option c ignores inflation. Option d incorrectly applies the nominal discount rate instead of the inflation adjustment.

Where it goes wrong. Multiplying nominal cash flow by 1.05 instead of dividing by 1.05.

Authority. Chapter 7: Investment Decisions - Capital Budgeting, Section 5 Estimation of Project Cash Flows

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

Using a nominal discount rate of 10 percent and inflation of 5 percent, what is the real discount rate under the Fisher relationship?

1. 5.00 percent
2. 4.76 percent (correct answer)
3. 15.00 percent
4. 10.00 percent

Answer: B — 4.76 percent

Working. Real rate = ((1 + nominal rate) / (1 + inflation rate)) - 1 = (1.10 / 1.05) - 1 = 0.047619 = 4.76 percent.

Explanation. The Fisher relationship gives 1 plus nominal rate equal to 1 plus real rate multiplied by 1 plus inflation. Option b is correct because 1.10 divided by 1.05 minus 1 equals 4.76 percent. Option a is the simple subtraction trap. Option c adds the rates. Option d repeats the nominal rate.

Where it goes wrong. Subtracting inflation from nominal rate and reporting 5 percent.

Authority. Chapter 7: Investment Decisions - Capital Budgeting, Section 5 Estimation of Project Cash Flows

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

What is the nominal NPV of the Godavari Chemical project?

1. ₹4,00,000
2. ₹6,00,000
3. -₹4,00,000 (correct answer)
4. -₹6,00,000

Answer: C — -₹4,00,000

Working. NPV = -₹10,00,000 + ₹6,60,000 / 1.10 = -₹10,00,000 + ₹6,00,000 = -₹4,00,000.

Explanation. Nominal NPV discounts nominal cash flow at the nominal rate and deducts initial outlay. Option c is correct because ₹6,60,000 divided by 1.10 is ₹6,00,000, and ₹6,00,000 minus ₹10,00,000 is negative ₹4,00,000. Option a drops the negative sign. Option b ignores the outlay. Option d discounts twice or uses an incorrect factor.

Where it goes wrong. Discounting real cash flow at nominal rate without consistency or ignoring the initial outlay.

Authority. Chapter 7: Investment Decisions - Capital Budgeting, Section 9.1 Net Present Value Technique

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

Scenario. Shakti Forgings has sales ₹50,00,000, variable cost 60 percent of sales, fixed operating cost ₹8,00,000, interest ₹2,00,000, tax rate 30 percent and no preference dividend. The management examines combined leverage and margin of safety.

What is the degree of combined leverage for Shakti Forgings?

1. 1.20
2. 1.67
3. 0.40
4. 2.00 (correct answer)

Answer: D — 2.00

Working. Contribution = Sales - Variable cost = ₹50,00,000 - 60 percent of ₹50,00,000 = ₹20,00,000. EBIT = ₹20,00,000 - ₹8,00,000 = ₹12,00,000. EBT = ₹12,00,000 - ₹2,00,000 = ₹10,00,000. DOL = 20,00,000 / 12,00,000 = 1.6667. DFL = 12,00,000 / 10,00,000 = 1.20. DCL = 1.6667 × 1.20 = 2.00.

Explanation. Contribution is ₹20,00,000, EBIT is ₹12,00,000 and EBT is ₹10,00,000. DOL is 1.67 and DFL is 1.20, so DCL is 2.00. Option d is correct. Option a is only DFL. Option b is only DOL. Option c uses fixed cost as a fraction of sales and is not DCL.

Where it goes wrong. Reporting DOL or DFL in place of DCL.

Authority. Chapter 6: Financing Decisions - Leverages, Sections 4.1 and 5.1

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

If sales decline by 10 percent and all else remains unchanged, what is the percentage change in EPS using DCL?

1. -20.00 percent (correct answer)
2. -16.67 percent
3. -12.00 percent
4. +20.00 percent

Answer: A — -20.00 percent

Working. Percentage change in EPS = DCL × Percentage change in sales = 2.00 × -10 percent = -20 percent.

Explanation. DCL measures percentage change in EPS for a percentage change in sales. Option a is correct because -10 percent multiplied by 2.00 equals -20 percent. Option b uses only DOL. Option c uses DFL only. Option d reverses the direction of the change.

Where it goes wrong. Using DOL instead of DCL or ignoring the negative direction.

Authority. Chapter 6: Financing Decisions - Leverages, Section 5.1 Degree of Combined Leverage

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

What is the margin of safety percentage for Shakti Forgings?

1. 40.00 percent
2. 60.00 percent (correct answer)
3. 20.00 percent
4. 80.00 percent

Answer: B — 60.00 percent

Working. PV ratio = Contribution / Sales = ₹20,00,000 / ₹50,00,000 = 0.40. BEP sales = Fixed operating cost / PV ratio = ₹8,00,000 / 0.40 = ₹20,00,000. MOS = (₹50,00,000 - ₹20,00,000) / ₹50,00,000 = 60 percent.

Explanation. PV ratio is 40 percent, so break-even sales are ₹8,00,000 divided by 0.40, equal to ₹20,00,000. Margin of safety is ₹50,00,000 minus ₹20,00,000 divided by ₹50,00,000, equal to 60 percent. Option b is correct. Option a is break-even sales as a percentage of sales. Option c is fixed cost divided by sales. Option d is an inflated figure.

Where it goes wrong. Dividing break-even sales by sales and reporting 40 percent.

Authority. Chapter 6: Financing Decisions - Leverages, Section 3.3 Margin of Safety and Operating Leverage

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

Scenario. SolarTech Projects has an initial outlay of ₹10,00,000 and equal annual cash inflow of ₹3,00,000 for five years. The discount rate is 10 percent. The project team compares traditional payback and discounted payback.

What is the discounted payback period for SolarTech Projects?

1. 3.33 years
2. 3.71 years
3. 4.26 years (correct answer)
4. 5.00 years

Answer: C — 4.26 years

Working. PV year 1 = 3,00,000 / 1.10 = 2,72,727. PV year 2 = 3,00,000 / 1.21 = 2,47,934. PV year 3 = 3,00,000 / 1.331 = 2,25,394. PV year 4 = 3,00,000 / 1.4641 = 2,04,904. Cumulative PV at year 4 = 9,50,959. PV year 5 = 3,00,000 / 1.61051 = 1,86,276. Discounted payback = 4 + (10,00,000 - 9,50,959) / 1,86,276 = 4 + 0.263 = 4.26 years.

Explanation. Discounted payback uses present values of cash inflows. Cumulative discounted inflow reaches ₹9,50,959 by year 4 and ₹11,37,235 by year 5, so payback lies between year 4 and year 5. Option c is correct at about 4.26 years. Option a is traditional payback. Option b is an incorrect interpolation. Option d ignores recovery before year 5.

Where it goes wrong. Using undiscounted cash flows or interpolating between wrong cumulative values.

Authority. Chapter 7: Investment Decisions - Capital Budgeting, Section 9.4 Discounted Payback Period Method

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

What is the traditional payback period for SolarTech Projects?

1. 4.26 years
2. 2.50 years
3. 3.71 years
4. 3.33 years (correct answer)

Answer: D — 3.33 years

Working. Traditional payback = Initial outlay / Annual cash inflow = ₹10,00,000 / ₹3,00,000 = 3.33 years.

Explanation. Traditional payback divides initial outlay by equal annual cash inflow. Option d is correct because ₹10,00,000 divided by ₹3,00,000 equals 3.33 years. Option a is discounted payback. Option b is an incorrect ratio. Option c is an interpolation error.

Where it goes wrong. Reporting discounted payback when the question asks for traditional payback.

Authority. Chapter 7: Investment Decisions - Capital Budgeting, Section 8.1 Payback Period