FNCE 370v10: Assignment 3

Assignment 3 is worth 5% of your final mark. Complete and submit Assignment 3 after you complete Lesson 9.

Question Marks available Marks awarded Reference

1 12 Lesson 7

2 5 Lesson 7

3 13 Lesson 7

4 8 Lesson 8

5 13 Lesson 8

6 9 Lesson 8

7 8 Lesson 9

8 18 Lesson 9

9 14 Lesson 9

Total 100

Note on Decimal Places

When working through numerical problems, use as many decimal places as shown on your financial calculator. Do not round your calculated answers until you have reached the final answer. When you reach your final answer, round as follows, unless the question specifies otherwise.

• Percentages: round to two decimal places

• Dollars: round to two decimal places

• Others: round to four decimal places

Questions

1. Choo Choo Inc. is a manufacturer of model trains. The company is considering the purchase of an industrial 3D printer, which will allow the firm to produce custom-made model trains for its high-end customers. The printer will cost $2,500,000, and it is expected to produce net cash flows of $600,000 per year for the next six years. Liquidation of the equipment will net the firm $350,000 in cash at the end of six years. The firm requires a 15% rate of return on all investments. Ignore the effects of taxes. (12 marks total)

a. What is the payback period for the proposed investment in the 3D printer? Provide your answer in number of years and months. (1 mark)

b. What is the printer’s discounted payback period? Provide your answer in number of years and months. (2 marks)

c. Choo Choo’s cutoff period is set at five years. Based on the payback period investment criterion, will the company purchase the printer? Will it purchase the printer based on the discounted payback period investment criterion? (1 mark)

d. What is the printer’s net present value (NPV)? Should the company purchase the printer based on the NPV investment criterion? (2.5 marks)

e. What is the printer’s profitability index (PI)? Should the company purchase the printer based on the PI investment criterion? (1.5 marks)

f. What is the printer’s internal rate of return (IRR)? (2 marks)

g. Check that at the internal rate of return (IRR) the net present value of the printer is $0. Should the company purchase the printer based on the IRR investment criterion? (1.5 marks)

h. Based on your answers in parts a to f above, what decision do you recommend for Choo Choo? (0.5 mark)

2. What is capital rationing? Define the two possible types of capital rationing, and discuss how capital rationing affects the attainment of management’s goal of maximizing shareholders’ value. (5 marks)

3. We have two mutually exclusive investments with the following cash flows: (13 marks total)

Year Investment A Investment B

0 –$100 –$100

1 10 50

2 30 40

3 50 30

4 70 20

a. Using a financial calculator, calculate the IRR for each of the investments. State your answers in percentages rounded to two decimal places. (2 marks)

b. Calculate the NPV profile for each investment, using the discount rates of 0%, 5%, 10%, 15%, 20%, and 25%. Perform this task in an Excel spreadsheet. Cautionary note: If you use the =NPV() function in Excel to calculate the NPVs, it will provide incorrect answers. The NPV() function actually calculates the present value of all cash inflows. The NPV should be calculated as =NPV(all cash inflows) – initial cash outflow. (2 marks)

c. Plot the NPV profile for both projects using the X-Y scatter function in Excel. (2 marks)

d. If the required return on this project is 17%, would both NPV and IRR give us the same conclusion? Explain your answer. (2.5 marks)

e. If the required return on this project is 10%, would both NPV and IRR give us the same conclusion? Explain your answer. (2.5 marks)

f. Calculate the crossover rate at which we are indifferent between the two investments. (2 marks)

4. Given the following project information, calculate the after-tax operating cash flow (ATOCF) using the four approaches of calculating operating cash flow. (8 marks)

Project cost = $950,000

Project life = five years

Projected number of units sold per year = 10,000

Projected price per unit = $200

Projected variable cost per unit = 150

Fixed costs per year = $150,000

Required rate of return = 15%

Marginal tax rate = 35%

Depreciation = Straight-line to zero over five years (ignore half-year rule)

5. We have two independent and mutually exclusive projects, A and B. Project A requires an initial investment of $1500, and will yield $800 of cash inflows for the next three years. Project B requires an initial investment of $5000, and will yield $1,500 of cash inflows for the next five years. The required return on each project is 10%. (13 marks total)

a. What are the net present values of Project A and Project B? (2 marks)

b. What is the problem with using the NPV investment criterion in this case? What alternative criterion should be used? (1 mark)

c. Which project should be chosen? (2 marks)

The cash flows and required return given are all in nominal terms. Given that the inflation rate is 3%, answer the following questions:

d. What is the real rate of return based on the exact Fisher equation? (1 mark)

e. What are the real cash flows from Project A and Project B? (2 marks)

f. What are the real net present values of Project A and Project B? (Hint: The real NPV should be the same as the nominal NPV.) (2 marks)

g. Which project should be chosen based on the real cash flows and real rate of return? (3 marks)

6. Holmes Inc. purchased computer equipment two years ago at a total cost of $1,000,000. These computers could be sold today for $300,000. If these computers are sold in five years, they will be worth $50,000. The CCA rate for these computers is 30%.

The company is now considering whether it should replace these computers with newer and more powerful ones. The estimated total purchase cost of the new computers is $1.5 million. These computers can be sold for $300,000 in five years, and their CCA rate remains at 30%. The company expects to obtain before-tax cost savings of $300,000 per year from these new computers.

The company’s marginal tax rate is 35%, and its required rate of return on new equipment is 15%. Should the company replace the computer equipment?

(9 marks)

7. XYZ Co. is evaluating whether to invest in a project with the following information: (8 points total)

Project cost = $950,000

Project life = five years

Projected number of units sold per year = 10,000

Projected price per unit = $200

Projected variable cost per unit = 150

Fixed costs per year = $150,000

Required rate of return = 15%

Marginal tax rate = 35%

Assume straight-line depreciation to zero over five years, and ignore the half-year rule for accounting for depreciation.

a. Calculate the cash break-even sales quantity for this project. (1 mark)

b. Calculate the accounting break-even sales quantity for this project. (1 mark)

c. Calculate the financial break-even sales quantity for this project. (3 marks)

d. Calculate the Degree of Operating Leverage (DOL) at the cash break-even, accounting break-even, and financial break-even sales quantities. (3 marks)

8. You are considering a new product launch. The project will cost $680,000, have a four-year life, and have no salvage value; depreciation is straight-line to zero. Sales are projected at 100 units per year, price per unit will be $19,000, variable cost per unit will be $14,000, and fixed costs will be $150,000 per year. The required return on the project is 15%, and the relevant tax rate is 35%. Ignore the half-year rule for accounting for depreciation. (18 marks total)

a. Calculate the following six numbers for this project. Round your answers to two decimal places.

(i) NPV (2 marks)

(ii) Profitability Index (PI) (1 mark)

(iii) Payback period (in years) (1 mark)

(iv) Discounted payback period (in years) (1 mark)

(v) Internal Rate of Return (IRR in %) (1 mark)

(vi) Average Accounting Return (AAR in %) (2 marks)

Hint: Net Income = {[(Price – variable cost)*Quantity Sold] – Fixed Costs – Depreciation} * (1 – Tax rate)

b. Evaluate the sensitivity of the NPV, PI, Payback period, Discounted payback period, AAR, and IRR to a ±10% variation in the number of units sold per year. Ensure that you interpret your answers in words.

Hint #1: For example, for the NPV, increase the quantity sold by 10% and re-calculate the NPV. Then calculate the percentage change of this new NPV over the base case NPV from part (a). Repeat the process for a 10% decrease in quantity sold.

Hint #2: You must perform the process in Hint #1 for each of the six items in part (a). Note that IRR and AAR are already rates of returns. You do not have to calculate the percentage changes over the base case numbers for IRR and AAR. Instead, simply calculate the difference between the new numbers and the base case numbers for IRR and AAR.

Hint #3: It may be easier to perform these calculations in a spreadsheet. If you opt to do these calculations in a spreadsheet, ensure that you copy and paste the spreadsheet into your Word document. (10 marks)

9. You are considering a project that will supply an automobile production facility with 35,000 tonnes of machine screws annually for five years. To get the project started, you will need an initial investment of $1,500,000 in threading equipment. The project will last for five years. The accounting department estimates that annual fixed costs will be $300,000 and that variable costs should be $200 per tonne. The CCA rate for threading equipment is 20%. Accounting estimates a salvage value of $500,000 after costs of dismantling. The marketing department estimates that the auto makers will accept the contract at a selling price of $250 per tonne. The engineering department estimates you will need an initial net working capital investment of $450,000. You require a 15% return and face a marginal tax rate of 38% on this project. (14 marks total)

a. What is the NPV for this project? Should you pursue this project? (5 marks)

b. Suppose you believe that the accounting department’s initial cost and salvage projections are accurate only to within ?15%; the marketing department’s price estimate is accurate only to within ?10%; and the engineering department’s net working capital estimate is accurate only to within ?5%. What is your worst-case scenario for this project? Your best-case scenario? (9 marks)

Assignment 3 is worth 5% of your final mark. Complete and submit Assignment 3 after you complete Lesson 9.

Question Marks available Marks awarded Reference

1 12 Lesson 7

2 5 Lesson 7

3 13 Lesson 7

4 8 Lesson 8

5 13 Lesson 8

6 9 Lesson 8

7 8 Lesson 9

8 18 Lesson 9

9 14 Lesson 9

Total 100

Note on Decimal Places

When working through numerical problems, use as many decimal places as shown on your financial calculator. Do not round your calculated answers until you have reached the final answer. When you reach your final answer, round as follows, unless the question specifies otherwise.

• Percentages: round to two decimal places

• Dollars: round to two decimal places

• Others: round to four decimal places

Questions

1. Choo Choo Inc. is a manufacturer of model trains. The company is considering the purchase of an industrial 3D printer, which will allow the firm to produce custom-made model trains for its high-end customers. The printer will cost $2,500,000, and it is expected to produce net cash flows of $600,000 per year for the next six years. Liquidation of the equipment will net the firm $350,000 in cash at the end of six years. The firm requires a 15% rate of return on all investments. Ignore the effects of taxes. (12 marks total)

a. What is the payback period for the proposed investment in the 3D printer? Provide your answer in number of years and months. (1 mark)

b. What is the printer’s discounted payback period? Provide your answer in number of years and months. (2 marks)

c. Choo Choo’s cutoff period is set at five years. Based on the payback period investment criterion, will the company purchase the printer? Will it purchase the printer based on the discounted payback period investment criterion? (1 mark)

d. What is the printer’s net present value (NPV)? Should the company purchase the printer based on the NPV investment criterion? (2.5 marks)

e. What is the printer’s profitability index (PI)? Should the company purchase the printer based on the PI investment criterion? (1.5 marks)

f. What is the printer’s internal rate of return (IRR)? (2 marks)

g. Check that at the internal rate of return (IRR) the net present value of the printer is $0. Should the company purchase the printer based on the IRR investment criterion? (1.5 marks)

h. Based on your answers in parts a to f above, what decision do you recommend for Choo Choo? (0.5 mark)

2. What is capital rationing? Define the two possible types of capital rationing, and discuss how capital rationing affects the attainment of management’s goal of maximizing shareholders’ value. (5 marks)

3. We have two mutually exclusive investments with the following cash flows: (13 marks total)

Year Investment A Investment B

0 –$100 –$100

1 10 50

2 30 40

3 50 30

4 70 20

a. Using a financial calculator, calculate the IRR for each of the investments. State your answers in percentages rounded to two decimal places. (2 marks)

b. Calculate the NPV profile for each investment, using the discount rates of 0%, 5%, 10%, 15%, 20%, and 25%. Perform this task in an Excel spreadsheet. Cautionary note: If you use the =NPV() function in Excel to calculate the NPVs, it will provide incorrect answers. The NPV() function actually calculates the present value of all cash inflows. The NPV should be calculated as =NPV(all cash inflows) – initial cash outflow. (2 marks)

c. Plot the NPV profile for both projects using the X-Y scatter function in Excel. (2 marks)

d. If the required return on this project is 17%, would both NPV and IRR give us the same conclusion? Explain your answer. (2.5 marks)

e. If the required return on this project is 10%, would both NPV and IRR give us the same conclusion? Explain your answer. (2.5 marks)

f. Calculate the crossover rate at which we are indifferent between the two investments. (2 marks)

4. Given the following project information, calculate the after-tax operating cash flow (ATOCF) using the four approaches of calculating operating cash flow. (8 marks)

Project cost = $950,000

Project life = five years

Projected number of units sold per year = 10,000

Projected price per unit = $200

Projected variable cost per unit = 150

Fixed costs per year = $150,000

Required rate of return = 15%

Marginal tax rate = 35%

Depreciation = Straight-line to zero over five years (ignore half-year rule)

5. We have two independent and mutually exclusive projects, A and B. Project A requires an initial investment of $1500, and will yield $800 of cash inflows for the next three years. Project B requires an initial investment of $5000, and will yield $1,500 of cash inflows for the next five years. The required return on each project is 10%. (13 marks total)

a. What are the net present values of Project A and Project B? (2 marks)

b. What is the problem with using the NPV investment criterion in this case? What alternative criterion should be used? (1 mark)

c. Which project should be chosen? (2 marks)

The cash flows and required return given are all in nominal terms. Given that the inflation rate is 3%, answer the following questions:

d. What is the real rate of return based on the exact Fisher equation? (1 mark)

e. What are the real cash flows from Project A and Project B? (2 marks)

f. What are the real net present values of Project A and Project B? (Hint: The real NPV should be the same as the nominal NPV.) (2 marks)

g. Which project should be chosen based on the real cash flows and real rate of return? (3 marks)

6. Holmes Inc. purchased computer equipment two years ago at a total cost of $1,000,000. These computers could be sold today for $300,000. If these computers are sold in five years, they will be worth $50,000. The CCA rate for these computers is 30%.

The company is now considering whether it should replace these computers with newer and more powerful ones. The estimated total purchase cost of the new computers is $1.5 million. These computers can be sold for $300,000 in five years, and their CCA rate remains at 30%. The company expects to obtain before-tax cost savings of $300,000 per year from these new computers.

The company’s marginal tax rate is 35%, and its required rate of return on new equipment is 15%. Should the company replace the computer equipment?

(9 marks)

7. XYZ Co. is evaluating whether to invest in a project with the following information: (8 points total)

Project cost = $950,000

Project life = five years

Projected number of units sold per year = 10,000

Projected price per unit = $200

Projected variable cost per unit = 150

Fixed costs per year = $150,000

Required rate of return = 15%

Marginal tax rate = 35%

Assume straight-line depreciation to zero over five years, and ignore the half-year rule for accounting for depreciation.

a. Calculate the cash break-even sales quantity for this project. (1 mark)

b. Calculate the accounting break-even sales quantity for this project. (1 mark)

c. Calculate the financial break-even sales quantity for this project. (3 marks)

d. Calculate the Degree of Operating Leverage (DOL) at the cash break-even, accounting break-even, and financial break-even sales quantities. (3 marks)

8. You are considering a new product launch. The project will cost $680,000, have a four-year life, and have no salvage value; depreciation is straight-line to zero. Sales are projected at 100 units per year, price per unit will be $19,000, variable cost per unit will be $14,000, and fixed costs will be $150,000 per year. The required return on the project is 15%, and the relevant tax rate is 35%. Ignore the half-year rule for accounting for depreciation. (18 marks total)

a. Calculate the following six numbers for this project. Round your answers to two decimal places.

(i) NPV (2 marks)

(ii) Profitability Index (PI) (1 mark)

(iii) Payback period (in years) (1 mark)

(iv) Discounted payback period (in years) (1 mark)

(v) Internal Rate of Return (IRR in %) (1 mark)

(vi) Average Accounting Return (AAR in %) (2 marks)

Hint: Net Income = {[(Price – variable cost)*Quantity Sold] – Fixed Costs – Depreciation} * (1 – Tax rate)

b. Evaluate the sensitivity of the NPV, PI, Payback period, Discounted payback period, AAR, and IRR to a ±10% variation in the number of units sold per year. Ensure that you interpret your answers in words.

Hint #1: For example, for the NPV, increase the quantity sold by 10% and re-calculate the NPV. Then calculate the percentage change of this new NPV over the base case NPV from part (a). Repeat the process for a 10% decrease in quantity sold.

Hint #2: You must perform the process in Hint #1 for each of the six items in part (a). Note that IRR and AAR are already rates of returns. You do not have to calculate the percentage changes over the base case numbers for IRR and AAR. Instead, simply calculate the difference between the new numbers and the base case numbers for IRR and AAR.

Hint #3: It may be easier to perform these calculations in a spreadsheet. If you opt to do these calculations in a spreadsheet, ensure that you copy and paste the spreadsheet into your Word document. (10 marks)

9. You are considering a project that will supply an automobile production facility with 35,000 tonnes of machine screws annually for five years. To get the project started, you will need an initial investment of $1,500,000 in threading equipment. The project will last for five years. The accounting department estimates that annual fixed costs will be $300,000 and that variable costs should be $200 per tonne. The CCA rate for threading equipment is 20%. Accounting estimates a salvage value of $500,000 after costs of dismantling. The marketing department estimates that the auto makers will accept the contract at a selling price of $250 per tonne. The engineering department estimates you will need an initial net working capital investment of $450,000. You require a 15% return and face a marginal tax rate of 38% on this project. (14 marks total)

a. What is the NPV for this project? Should you pursue this project? (5 marks)

b. Suppose you believe that the accounting department’s initial cost and salvage projections are accurate only to within ?15%; the marketing department’s price estimate is accurate only to within ?10%; and the engineering department’s net working capital estimate is accurate only to within ?5%. What is your worst-case scenario for this project? Your best-case scenario? (9 marks)

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