# What is the accounting break-even quantity?

**FNCE 370v8: Assignment 3**

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

There are 12 questions in this assignment. The break-down of marks for each question is presented in the table below. Please show all your work as this will help the marker give you part marks as well as serve as a good study aid as you prepare for the Final Examination.

Question |
Marks Available |
Reference |

1 | 3 | Lesson 7 |

2 | 10 | Lesson 7 |

3 | 7 | Lesson 7 |

4 | 10 | Lesson 7 |

5 | 4 | Lesson 8 |

6 | 10 | Lesson 8 |

7 | 10 | Lesson 8 |

8 | 10 | Lesson 8 |

9 | 4 | Lesson 9 |

10 | 10 | Lesson 9 |

11 | 12 | Lesson 9 |

12 | 10 | Lesson 9 |

Total |
100 |

1. Define mutually exclusive investment decisions, and give an example of this type of decision. (**3 marks**)

**I would define mutually exclusive investment decisions in which the acceptance of a project precludes the acceptance of one or more alternative projects.**

2. Consider the following cash flow [-100, + 230, -132]. We want to decide under what range of discount rate this is an advantageous investment. But noting the change in sign, we conclude IRR is not a suitable instrument. (**10 marks**)

a. Write the expression for NPV using the unknown r as discount rate.

b. Write this expression as a function of [1/(1+r)].

NPV =

c. Show that the expression in (b) as a quadratic equation. Look this up if necessary.

d. Solve the quadratic equation for its two roots.

e. Prepare a table of NPV vs. r for r= 0,10,20,40,100%.

f. Draw the graph of NVP vs. r.

g. Under what range of r values is this an acceptable investment?

h. Noting that NPV increases then declines as r grows from 0 to 40%, determine at what level of r NPV is a maximum (recall that d(NPV)/ds = 0, where NPV is a maximum). If you have sufficient background, solve this using calculus. If not, graphically find the top of the NPV hill (where slope = 0).

What is the maximum value of NPV? (There is one bonus point for the correct answer using calculus).

3. Consider the following information for projects A and B, which are mutually exclusive.

(**7 marks**)

Year |
Project A |
Project B |
Note |

0 | -100,000 | -120,000 | A – B = -100,000 – (-120,000) = +20,000 |

1 | 31,250 | 0 | 31 250 |

2 | 31,250 | 0 | 31 250 |

3 | 31,250 | 0 | 31 250 |

4 | 31,250 | 0 | 31 250 |

5 | 31,250 | 200,000 | -168 750 |

a. At what discount rate will the two projects have the same net present value?

If the two projects have the same NPV, then NPVA NPVB = 0.

Therefore, we have to calculate the IRR where NPV of the new project will be equal to zero.

By calculating the IRR of the new project we find that the IRR will be 26.78%

Therefore IRR of the project will be 26.78% where the NPVA – NPVB =0

IRR

= 26.78%

b. At the discount rate of 10%, which is the better project?

P.V @10%

1

0.909

0.826

0.751

0.683

0.621

Total P.V =

Total P.V ( A) -100 000 Total P.V ( B) -120 000

28406.25

0

25812.5

0

23468.75

0

21343.75

0

19406.25

124200

18437.5

4200

At the discount rate of 10% project A is the better project because the NPVA is higher than the NPVB

(Hint 1: If the two projects have the same NPV, then NPV_{A} – NPV_{B} = 0. You can subtract line by line.)

(Hint 2: If the difference in initial investment comes out positive and your financial calculator is programmed to accept negative PV, adjust the FV accordingly.)

4. Canadian Classics manufactures parts for classic automobiles. The CFO is considering the purchase of a two-ton press, which will allow the firm to stamp auto fenders. The equipment costs $250,000. The project is expected to produce after-tax cash flows of $80,000 per year. Liquidating the equipment will net the firm $10,000 in cash at the end of five years. The firm requires a 15% rate of return on all investments. The firm’s tax rate is 38%. Ignore the effects of CCA. (**10 marks**)

a. What is the payback period for the proposed investment?

**3.03 Years**

b. What would happen to the payback period if the sale of the equipment at the end of five years nets the firm $200,000, rather than $10,000?

**There will be no change in the Payback period because the sale of the equipment takes place at the end of the 5th year and therefore not making any change in the payback period.**

c. What is the project’s discounted payback period?

**Exactly 4.481 years.**

d. What is the project’s net present value?

**$23 210**

e. What is the project’s profitability index?

**1.09**

f. What is the project’s internal rate of return?

**19% **

5. (**4 marks**)

a. Why is it important to consider additions to net working capital in developing cash flows?

**It is important to consider additions to net working capital because every capital project needs additional working capital to finance the increase in the level of activity. The increase in working capital requirement arises due to the need of maintain higher inventories, accounts receivable etc. At the expiry of the project the working capital will be released and therefore be treated as cash inflows.**

** **

b. What is the effect of an increase in net working capital on a project’s operating cash flow?

**The effect of increase in net working capital on a project’s operating cash flow is that it will increase the cash inflows.**

** **

c. What normally happens to the additions to net working capital as the project winds down?

**When the projects winds down the inventories of the project will be sold out and the accounts receivable will be collected. All these activities will free up the additions which will be made in the working capital in the beginning of the capital .Therefore the working capital which is invested in the beginning of the year will be released at the end of the year.**

6. Given the following cash flows for two mutually exclusive projects (A and B), which project should be chosen?

Assume that the required rate of return of both projects is 11%.

(Hint: Use EAC.) (**10 marks**)

Year\Project |
A |
B |

0 | -$1,000,000 | -$850,000 |

1 | 300,000 | 187,500 |

2 | 300,000 | 187,500 |

3 | 300,000 | 187,500 |

4 | 300,000 | 187,500 |

5 | 300,000 | 187,500 |

6 | 187,500 | |

7 | 187,500 | |

8 | 187,500 |

Year\Project | A | B | PV A | PV B |

0 | -$1,000,000 | -$850,000 | ||

1 |
300,000 | 187,500 | $270,270.27 | $168,918.9 |

2 | 300,000 | 187,500 | $243,486.73 | $152,179.2 |

3 |
300,000 | 187,500 | $219,357.41 | $137,098.3 |

4 | 300,000 | 187,500 | $197,619.29 | $123,512.0 |

5 | 300,000 | 187,500 | $178,035.40 | $111,272.1 |

6 | 187,500 | $100,245.1 | ||

7 | 187,500 | $90,310.95 | ||

8 | 187,500 | $81,361.22 | ||

$1,108,769.11 | $964,898.0 | |||

NPV | $108,769.11 | $114,898.0 |

I would choose Project B as the NPV is higher than Project A’s.

7. A firm is considering bidding on a project to produce eight widgets per year for the next four years. In order to complete the project, the firm must lease facilities for $30,000 per year, purchase equipment that costs $100,000, as well as pay labour and material costs of $19,000 per unit produced. The equipment can be depreciated at the Class 8 CCA rate of 20%. At the end of the fourth year, it can be sold for $10,000, and the asset class will remain open after the disposal of the equipment. In addition, net working capital will increase by $50,000 if the project is undertaken, but these can be recovered at the end of the project. The company’s tax rate is 40%.

What is the minimum bid per widget if the firm requires 18% return on its investment? (**10 marks**)

8. You are evaluating a project for Ultimate Inc. The project produces chew-resistant doghouses. You estimate the sales price of these doghouses to be $500 and sales volume to be 2,500 units per year over the project’s three-year life. Variable costs amount to $300 per unit and fixed costs (not including depreciation) are $150,000 per year. The project requires an initial investment of $250,000 and this will be depreciated on a straight-line basis to zero over the three-year project life. There will be an initial net working capital investment of $90,000 (t_{0}) and two further investments of $90,000 at the beginning of each year thereafter. The full amount of working capital will be recovered at the end of the project’s life (i.e., $270,000 at t_{3}). The tax rate is 35% and the required return on the project is 15%. (**10 marks**)

- What is the EBIT for the project in the first year?

- What is the operating cash flow for the project in year 2?

- Suppose the actual market value of the initial investment at the end of year 3 is $50,000. What is the effect of the $50,000 salvage value on year 2 cash flows?

- What is the NPV of this project?

9. Describe how the inclusion of a strategic option can affect setting a bid price.

(**4 marks**)

10.A project requires an initial investment of $10,000, straight-line depreciable to zero over four years. The discount rate is 10%. The firm’s tax bracket is 34%, and they receive a tax credit for negative earnings in the year in which the loss occurs. Additional information for variables with forecast error is shown below: (**10 marks**)

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Item |
Base Case |
Lower Bound |
Upper Bound |

Unit Sales | 3,000 | 2,750 | 3,250 |

Price/Unit | $14 | $13 | $16 |

Variable cost/unit | $9 | $10 | $8 |

Fixed costs | $9,000 | $10,000 | $8,500 |

- What is the base case NPV for the project?

- What is the worst case NPV for the project?

- What is the best case NPV for the project?

- Suppose you want to conduct a sensitivity analysis for the possible changes from the base case in unit sales. What is the IRR when the sales level equals 3,250 units?

- Suppose you are interested in the project’s sensitivity to unit price. What is the NPV for the base case at a price of $13 per unit?

- What is the base case accounting break-even point?

- What is the base case cash break-even point?

- What is the base case financial break-even point? Ignore taxes.

11.A firm is considering the purchase of equipment which will cost $3 million. This equipment will last for 10 years, at the end of which it can be sold for $800,000. The CCA rate for this asset class is 30%, and the firm expects to have other assets in this asset class at the end of year 10. This equipment is expected to increase before-tax operating cash flows by $750,000 per year. However, in order to put the equipment to use, an additional $150,000 will need to be invested in net working capital initially (i.e., at t=0). The required rate of return is 16% and the firm’s marginal tax rate is 35%.

(**12 marks**)

a. Should the firm purchase this equipment?

b. Suppose that to arrive at the before-tax operating cash flows in part (a), we have used the following estimates:

Fixed costs = $120,000

Variable costs = 60% of sales

What is the Net Present Value of the new equipment if, in the best-case scenario, we estimate that fixed costs could be lower by 20% and sales revenues could be higher by 25%?

c. Given the information in (a), and assuming that fixed costs are $120,000 and variables costs are 60% of sales, what is the sales level at which Net Present Value equals zero? (In other words, what is the financial break-even sales level?)

12.A project has the following estimated data: price = $65 per unit; variable costs = $33 per unit; fixed costs = $4,000; required return = 16%; initial investment = $9,000;

life = three years.

Ignore the effect of taxes and assume straight-line depreciation to zero. (**10 marks**)

- What is the accounting break-even quantity?

- What is the cash break-even quantity?

- What is the financial break-even quantity?

- What is the degree of operating leverage at the financial break-even level of output?