Developing Capacity Alternatives Reported By: Donnalyn S. Boncodin

Developing Capacity Alternatives Design flexibility into systems. Take a “big picture” approach to capacity changes Prepare to deal with capacity “chunks” Attempt to smooth out capacity requirements Identify the optimal operating level

Evaluating Alternatives Cost-Volume (Break-Even) Analysis Financial Analysis Decision Theory – is a helpful tool for financial comparison of alternatives under conditions of either risk or uncertainty. Queuing Analysis – Often useful for designing service systems.

Evaluating Alternatives Figure 5.3 Production units have an optimal rate of output for minimal cost. Minimum cost Average cost per unit Rate of output Minimum average cost per unit

Evaluating Alternatives Figure 5.4 Minimum cost & optimal operating rate are functions of size of production unit. Small plant Average cost per unit Medium plant Large plant Output rate

Cost-Volume Relationships Cost-Volume (Break-Even) Analysis – focuses on relationships between cost, revenue and volume of output. Total Cost = Fixed Cost + Variable Cost x Q units Fixed Costs – are those that tend to remain constant regardless of volume of output. Variable Costs – vary directly with volume of output.

Cost-Volume Relationships Figure 6.5a Amount ($) Q (volume in units) Total cost = VC + FC Total variable cost (VC) Fixed cost (FC)

Cost-Volume Relationships Figure 5.5b Amount ($) Q (volume in units) Total revenue B. Total Revenue increases linearly with output.

Cost-Volume Relationships Figure 5.5c Amount ($) Q (volume in units) BEP units Profit Total revenue Total cost C. Profit = TR - TC

Assumptions of Cost-Volume Analysis One product is involved Everything produced can be sold Variable cost per unit is the same regardless of volume Fixed costs do not change with volume Revenue per unit constant with volume Revenue per unit exceeds variable cost per unit

Cost-Volume Relationships Formula: Profit = Total Revenue – Total Cost = Revenue per unit x Q – (Fixed Cost + (Variable Cost x Q) Volume = Specified Profit + Fixed Cost Revenue per unit – Variable Cost QBEP = Fixed Cost Revenue per Unit – Variable Cost per Unit

Cost-Volume Relationships Example: Old-Fashioned Berry Pies, Ltd. Currently operates a single bakery but is now considering a second location in a new shopping mall. The owner estimates that fixed cost would be $3,000 per week and that labor and materials to produce pies at that location will be 60 cents pe pie. Pies will be sold for $1.60 each. What number of pies be sold in order to break-even? What profit (or loss) would there be on sales of 10,000 pies in one week? What volume would be required in order to realize a profit of $12,000?

Cost-Volume Relationships Solution: 1. FC = $3,000, VC = $ 0.60 per unit, Rev = $1.60 per unit QBEP = FC = $ 3,000 = 3,000 pies / week Rev - VC $1.60 - $0.60 2. Profit = Rev x Q – (FC + (VC x Q)) = $1.60(10,000) – ($3,000 + ( $0.60 x 10,000)) = $7,000 3. Volume = SP + FC = $12,000 + $3,000 = 15,000 pies Rev - VC $1.60 - $0.60

Financial Analysis Cash Flow - the difference between cash received from sales and other sources, and cash outflow for labor, material, overhead, and taxes. Present Value - the sum, in current value, of all future cash flows of an investment proposal.

Financial Analysis Methods: Payback – widely used method that focuses on the length of time it will take for an investment to return to its original cost. Present Value Method – summarizes the initial cost of an investment, its estimated annual cash flows, and any expected salvage value of an investment in a single value called the equivalent interest rate, taking into account the time value of money. Internal Rate of Return (IRR) – summarizes the initial cost, expected annual cash flows, and estimated future salvage value of an investment proposal in an equivalent interest rate.

Payback Period Analysis Example: Determine the payback period for each of the follow in proposals given their estimated cash flows. Assume each requires an initial investment of $40,000. Year A B C 1 $10,000 $20,000 $1,000 2 10,000 20,000 5,000 3 10,000 2,000 10,000 4 10,000 1,000 20,000 5 10,000 100 40,000 6 10,000 0 80,000

Payback Period Analysis Solution: Calculate the cumulative cash flows for each alternative, and note when the cumulative amount equals the original investment. Year A B C 1 $10,000 $20,000 $1,000 2 20,000 40,000 6,000 3 30,000 42,000 16,000 4 40,000 36,000 5 76,000 Thus, A’s payback period is exactly four years. B’s is exactly two years and C’s is between four and five years. Alternative B is the most attractive, and C is the least.

Net Present Value Net present value = Present value of - Initial Cost future cash flows Example 1: ( Annual cash flows are all the same amount.) Determine the net present value of a proposal that has an economic life of nine years, an initial cost of $30,000, and an annual cash flow of $10,000. The firm’s cost of capital is 12%. Solution: n = 9, A = $10,000, Initial Cost = $30,000 and i=12% Find annuity factor : 5.328 Find the present value of cash flows: $10,000(5.328) = $53,280. Determine the net present value: $53,280 - $30,000 = $23,280.

Net Present Value Example 2: ( Annual cash flows are not all the same amount.) A newspaper is considering two investment proposals for new piece of equipment. Proposal A has an initial cost of $2,000, and proposal B has an initial cost of $1,000. Given the following cash flow information and the firm’s cost of capital of 10%, determine which proposal has the higher present value. Cash Flows Year Proposal A Proposal B 1 $1,000 $2,000 2 2,000 1,000 3 3,000 800 4 100

Net Present Value Solution: Find the present value of cash flows   Proposal A Proposal B Year Cash Flow x PVF = PV 1 1,000.00 0.909 909.00 $2,000 0.91 1,818.00 2 2,000.00 0.826 1,652.00 0.83 826.00 3 3,000.00 0.751 2,253.00 800.00 0.75 600.80 4 100.00 0.68 68.30 $4,814 $3,313.10

Net Present Value Solution: 2. Subtract the Initial Investments to find the present value of each investments. Proposal A: $4,814 - $2,000 = $2,814 Proposal B: $3,313 - $1,000 = $2,313 Hence, proposal A has a higher present value.

Internal Rate of Return PVA = Initial investment = I Annual Cash Flows A Example: An automatic bottlecapping machine requires an initial investment of $9,000. During its estimated useful life of 11 years, it will provide an annual cash flow of $1,800. At the end of 11 years, the machine will have no salvage value. Determine the internal rate of return. Solution: I = $9,000, A= $1,800, n = 11 years, I = $9,000 = 5.00 A 1,800 Referring to Table for n= 11, we find PVA = 5.029 for i=16% and PVA = 4.656 for i=18%. Since the computed value is approximately 5.029 we conclude that the IRR is approximately 16%.