Question

Question 3.1 - Break Even Analysis

Paul, a recent mechanical engineering graduate of Lakehead University plans to start a composite metal fabrication business called Superior Composites Limited. He came on this idea through a product design competition while in his undergraduate degree program.  

Paul plans to open the business in Thunder Bay, Ontario, in an unused warehouse space found on the former Global Sticks property east of the city. He has already obtained orders for his composite metal product from across North America, but his most important client will be the local Bombardier light transit manufacturing facility.

Composite metals are steel alloys that use graphite and other materials like fiberglass to produce light, yet very strong products that are in high demand by auto, mass transit and aircraft manufacturers. They offer the potential to produce products that are strong, flexible, light but yet corrosion resistant.

Superior Composite’s product consist of sheets of the metal composite that are the size of a standard piece of plywood. Superior Composites contracts a manufacturer to produce these sheets and then uses stamping and other CNC-driven laser machines to cut out pieces customer’s require in their manufacturing business.

For sales estimating purposes Paul will assume a set selling price for each sheet of composite material regardless of the complexity of the cutout designs required by the customer.   He makes this assumption since the CNC machine is simply programmed and cutting is done without much difference in time to complete each project. Paul assumes he will sell each sheet of metal composite for $5,250.   Each sheet will require $625 worth of steel, $112 of other materials, and $210 in energy costs.   Estimated direct labour costs per sheet are $215.

Superior Composites requires start up capital of $1,500,000. The startup capital will be used to purchase and install $1,000,000 in manufacturing equipment and $500,000 for working capital (cash and raw inventory). Paul has already raised $500,000 from himself, friends and family (sweat equity and love money) and has gone on-line through the Lakehead University Engineering Alumni Association and used ‘crowd funding’ to raise a further $500,000 by selling shares in the company at $100 each.  The remaining

$500,000 will be borrowed in the form of a 10-year fixed rate commercial loan from TD Commercial at a stated annual rate of interest of 3.67% compounded annually with annual payments.

   

Superior Composites will not have to spend much in the form of advertising. Demand for the product has come primarily from personal sales calls, and because of the product features, it essentially ‘sells itself.’

Nevertheless, there are numerous other costs associated with running this business including monthly lease costs for the warehouse of $8,450, and monthly lease costs for office space provided by the Innovation Centre of $1,250.

The firm will have a full-time accountant, full-time sales manager, and Paul will work full-time in the business overseeing manufacturing, shipping and receiving.   These salaried positions together with employment benefits will amount to $440,000 annually.

Other annual costs include:
External auditor costs		$31,000
Communication costs (website, equipment, line charges)		27,500
Depreciation (CCA) in the first year of operations		200,000
Other fixed operating costs            Interest expense – to be calculated on the fixed rate 10-year loan		370,000

Given the orders received for the product to date, Paul has made the following estimate for first year annual sales on a per unit basis as follows:

Probability	Unit Sales
20%	350
30%	450
30%	550
20%	650

In five years time, Paul estimates that unit sales will eventually grow to, and stabilize at 1,000 units annually.

Superior Composites Limited will be incorporated in Ontario and will face a tax rate of 11.5% on active business income.

Required:

1. Determine expected unit sales as well as the standard deviation of unit sales for the first year of operation of Superior Composites Limited.
2. Determine the first year loan payment for 3.67% 10-year $500,000 fixed rate commercial loan assuming annual loan payments made at the end of each year. (Annual, not monthly loan payments.)
3. Prepare a loan amortization schedule to determine the annual loan payment and the first year interest expense on the loan. (You will also need this schedule to estimate the interest expense in the fifth year in a later question).
4. Identify Superior Composites fixed costs and estimate total annual fixed costs for the proposed business. (Treat the first year loan payment (principal plus interest) as a fixed cost for the purposes of determining a break even point).
5. Determine Superior Composites variable cost per unit, as well as the unit contribution margin.
6. Using forecasts for total annual fixed costs and unit contribution margin for the first year, determine the annual breakeven point for this proposed operation in numbers of units produced and in sales dollars. (Demonstrate the formula, steps in solution and the result using MS Equation.)
7. What is the probably that the proposed venture as given, will break even in its first year of operation. Remember, once you have calculated the ‘Z’ value you will use the Values of the Standard Normal Distribution Function to estimate the probability of breaking even.   (You will use expected first year annual sales, standard deviation, and then determine the Z value given the sales breakeven point, to calculate the probability of breaking even.) (Demonstrate the formula, steps in solution and the result using MS Equation.)
8. A new venture like this is very risky, and Paul estimates that such a business would have a ‘justified’ beta coefficient of 1.9.     Assume the risk-free rate of return is 2% and the market premium for risk is 7%. What rate of return should a shareholder in Paul’s venture require, given the justified beta coefficient? (Demonstrate the formula, steps in solution and the result using MS Equation.)
1. Assume the firm is started and after five years, unit sales grow to 1,000 units annually as predicted. At 1,000 unit sales, forecast the firm’s annual profit and return on equity.   (Prepare a forma income statement for the fifth year of operation to predict net profit and measure return on equity. Remember that loan payments are not an expense, only the interest portion of the loan payment is an expense.)  
10. Compare the forecast Return on Equity for year five with the investor’s required rate of return assuming the risk-free rate remains at 2%; the market premium for risk at 6%; and the firm’s beta coefficient is 1.9.   (Is the prospective profitability of this firm in year five, sufficient given the capital investment involved?   Should Paul proceed to implement his business based on the forecasts he has used?) (Again, remember that when preparing pro forma income statements, only the interest portion of a loan payment is treated as an expense.)

Answer 1

a)

Unit Sales	Probability	Expected Unit sales	x-mean	Square of Deviation	variance = P*(X-mean)2
350.00	20%	70	-150.00	22500	4500
450.00	30%	135	-50.00	2500	750
550.00	30%	165	50.00	2500	750
650.00	20%	130	150.00	22500	4500
		500			10500
		Expected unit sales = 500 units Standard deviation is the square root of variance	102.47

b) Loan repayment for first year

Principal repayment = 50000

Interest repayment =3.67%*500000 =18350

Total amount = 68350

c)

	Repayment Schedule
	Year	Principal outstanding	Interest Accrued	Principal repayment	Repayment amount	Balance outstanding
	1	500000	18350	50000	68350	450000
	2	450000	16515	50000	66515	400000
	3	400000	14680	50000	64680	350000
	4	350000	12845	50000	62845	300000
	5	300000	11010	50000	61010	250000
	6	250000	9175	50001	59175	200000
	7	200000	7340	50002	57340	150000
	8	150000	5505	50003	55505	100000
	9	100000	3670	50004	53670	50000
	10	50000	1835	50005	51835	0

d)

Employee benefits	440000
Lease costs - warehouse	101400
Lease cost - office	15000
External auditor costs	31,000
Communication costs (website, equipment, line charges)	27500
Depreciation (CCA) in the first year of operations	200000
Other fixed operating costs	370000
Interest expense	18350
Principal repayment of loan	50000
Total annual Fixed Costs	1253250

e)

Direct materials
Steel	625
Other materials	112
Energy costs	210
Labour cost	215
Total Variable costs	1162
Selling price	5250
Contribution margin	4088

f)

	Breakeven point = A/B
	In Number of units
A	Fixed costs	1253250
B	Contribution per unit	4088
	BEP in units	306.57
	Rounded up to	307 units
	In Dollars
A	Fixed costs	1253250
B	PV Ratio = Contribution / Selling price	0.78
	BEP in units	$               16,09,482.02