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Departement de science économique Department of Economics ENGINEERING ECONOMICS ECO 1192B Yellow Assignment #2: Breakeven Analysis C

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Departement de science économique

Department of Economics

ENGINEERING ECONOMICS

ECO 1192B

Yellow Assignment #2: Breakeven Analysis

C. Theoret Winter 2021

A. Assignment Instructions

1. Completing an unallocated assignment will result in a zero (0%) score.

2. You will submit your assignment #2 answers on Brightspace on April 1 between 7 and 7:30 pm (Ottawa, Ontario time).

3. Assignment answers submitted late or by other means will be rejected.

4. The sequence of assignment questions in this document will be maintained on April 1 (i.e., no question scrambling)

5. Where appropriate

• Four options will be provided for an assignment question.
• Options will consist of ranges of dollars, percentages etc. depending on the question.

6. Please consult Background Paper #25 on Brightspace for assistance or discuss specific issues during my weekly office hour.

Please note that this assignment has two sections:

• Section A: Toledo Company revenues, costs and profits
• Section B: Annual Equivalent Revenue Requirement (AER)

(You may wish to consult Background Paper #25 for Section B).

Section A: Toledo Company revenues, costs and profits

(Questions 1 to 13)

Toledo Company manufactures and sells medical equipment throughout

Canada. Its total revenue and cost functions are given below:

• Total revenue = 170Q-3.5Q'9

                                    (Q = equipment production)

• Total cost = 500+30Q-3Q²+Q³/3

1. Total fixed cost is

2. The lower (smaller) breakeven level in a production range from 0 to 50 units of equipment is

3. The higher (bigger) breakeven level in a production range from 0 to 50 units of equipment is

4. Total profits ($) are maximized at a production level of

5. Total variable costs at the profit maximizing production level are between

6. Total production costs at the profit maximizing production level are between

7. Total revenues at the profit maximizing production level are

8. Total profits at the profit maximizing production level are

9. At the profit-maximizing production level, the vertical distance between the total revenue and total cost curves is

10. The average variable cost (variable cost per unit) of equipment at the profit-maximizing production level is

11. The average (total) cost per unit produced at profit-maximizing production level is

12. The revenue per unit produced and sold at the profit-maximizing production level is

13. Profit per unit sold at the profit-maximizing production level (all production is sold) is

Section B: Annual Equivalent Revenue Requirement

(Questions 14 to 19)

Your decision to purchase a small business depends on the annual equivalent revenue (AER) required to meet all expenses (operating, taxes, return on capital, repayment of debt) given the values of parameters such as the inflation rate, the debt ratio, the return anticipated on your investment as shown in the following

Table.

iaf = r(idf)(1-t)+(1-r)[(1+ie)(1+if)-1]

Where

1. iaf = inflation-adjusted after-tax cost of debt and owner-provided capital

2. id = inflation-free before-tax cost of debt capital

3. idf = inflation-adjusted before-tax cost of debt capital

4. ie = cost of equity (owner) capital

5. if = inflation rate

6. r = debt ratio

7. t = tax rate

8. SV=Gross salvage value (i.e., SV before taxes)

9. NSV=SV adjusted for taxes on recaptured depreciation and capital gains (as required) where

NSV=SV- taxes on recaptured depreciation-taxes on capital gains (as required)

Use the following equation:

AER =AEOC+[P(A/P, iaf,N)-NSV(A/F,iaf,N)-t(AED)]/(1-t)

AEOC=annual equivalent operating expenses

AED = Annual Equivalent Depreciation

AER = pre-tax annual revenues required to meet annual expenses

Reminder: The net salvage value (NSV) is the after-tax salvage value (SV) for relevant income taxes (if any) due to capital gains, recaptured depreciation or terminal loss.

1. Initial Cost or Purchase Price ($)                                             500,000

2. Projected Salvage Value ($)                                                     50,000

3. Useful life (years)                                                                          5

4. Annual Operating Cost ($) at EOY1                                        60,000

14. Inflation rate (if)=0%; r=0%; t=0%; ie=8%. MARR (=iaf) for this business environment is

15. Inflation rate (if)=0%; r=0%; t=0%; ie=8%. The annual equivalent revenue (AER) for this business environment is

16. Inflation rate (if)=0%; t=0%; r=50%; id=12%; ie=8%. If you needed to borrow 50% of the required capital (i.e., 50% of $500,000), MARR (=iaf) for this business environment would be

17. Inflation rate (if)=0%; t=40%; r=50%; id=12%; ie=8%. If you borrowed 50% of the required capital, the AER (see formula above) would be

18. Inflation rate (if)=10%; t=40%; r=50%; id=12%; ie=8%; annual operating costs are fully responsive to the inflation rate. MARR (=iaf) for this business environment would be

19. Inflation rate (if)=10%; t=40%; r=50%; id=12%; ie=8%; annual operating costs are fully responsive to the inflation rate. AER for this business environment would be

Questions 20 and 22

Use the following equation:

AER =AEOC + [P(A/P,iaf,N)CTF-SV(A/F,iaf,N)CSV] / (1-t)

AEOC=annual equivalent operating expenses

AER = pre-tax annual revenues required to meet annual expenses

Note that, in the capital factor equation, SV must not be adjusted for neither recaptured depreciation nor capital gains.

The CSV factor automatically accounts for any depreciation recapturing. However, an additional term is needed to account for any after-tax capital gains (NCG) as shown in the following equation.

AER =AEOC + [P(A/P,iaf,N)CTF-SV(A/F,iaf,N)CSV

-NCG(A/F,iaf,N)] / (1-t)

5. Initial Cost or Purchase Price ($)                  500,000

6. Projected Salvage Value ($)                           50,000

7. Useful life(years)                                                  5

8. Annual Operating Cost ($) at EOY1              60,000

20. Inflation rate=10%; t=40%; r=60%; id=12%; ie=8%; annual operating costs are fully responsive to the inflation rate. Based on capital tax factor (CTF) approach (see equation in Table above), the AER for this business environment would be

21. Inflation rate=10%; t=40%; r=75%; id=12%; ie=8%; annual operating costs are fully responsive to the inflation rate. Based on capital tax factor (CTF) approach (see equation in Table above), the AER for this business environment would be

22. If the debt ratio (r) increases while all other parameter values remain constant, AER will [Decrease? Increase? Remain constant?