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Capital Budgeting

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The process of determining and selecting the most profitable long-term (>1 year) projects. Firm ’ s capital budgeting decisions define its strategic plan. Projects : mutually exclusive vs. independent. Tools ; Break even point, Payback period, Discounted-payback, NPV, and IRR

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Break even point The amount of production units which make zero profit to the firm. It implies that total revenue is equal to total cost. Profit = Total Revenue - Total Cost Break even when profit = 0, hence; Total Revenue = Fixed cost + Variable cost

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(P) (X 0 ) = FC + (VC) (X 0 ) ; therefore, whenP > VC whereX 0 = Break even point (units) P = Sale Price ($ per unit) FC = Fixed Cost ($) VC = Variable Cost ($) Break even point X 0 = FC (P – VC) units $ Revenue Total Cost Fixed Cost

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Break even point Example; In order to operate a coffee shop, Joe need to have $9,000 for initial fixed-cost. The variable cost is $4 per cup. He will sell his coffee for $7 each cup. How many coffee cups needed to be sold for break-even? If he want $3,000 profit, how many additional cups he need to sell? Solution; Profit = Revenue – Total cost Break-even when profit = 0 ; 0 = ($7)(X 0 ) – [ $9,000 + ($4)(X 0 ) ] X 0 = 3,000 cups What if profit = $3,000 ; $3,000 = ($7)(X) – [ $9,000 + ($4)(X) ] X = 4,000 cups He need to sell additional 1,000 cups after he get break-even in order to make $3,000 profit. (Notice; the units produced after get break- even generate the pure profit from theirs margin multiply by units.

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Payback period The number of years required to recover the original cost of investment Payback will occur when the cumulative net cash flow equals zero Decision rule: The shorter the payback is the better one. To decide which project to be accepted, benchmark payback period is needed. If project ’ s payback equal or less than benchmark ’ s payback, accept the project If project ’ s payback more than benchmark ’ s payback, reject the project

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Payback period Example; given the benchmark payback period is 4 years. If A and B are independent, accept both of them. If A and B are mutually exclusive, A would be accepted over B.

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Discounted payback period An improvement over the payback period by consider the time value of money. Example (continued); given the firm ’ s cost of capital = 10%

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Net present value (NPV) Given the flaws in the payback methods of only ranking projects, NPV provide the specific amount of dollar for project evaluations. Decision rule: For independent projects, if NPV > 0, then accept the project. If NPV < 0, then reject the project. For mutually exclusive projects, choose the one with the highest NPV subject to the condition that the NPV is 0 or greater.

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Net present value (NPV) Example (continued); NPV A NPV B

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Internal rate of return (IRR) The rate of return which provides NPV equal to zero. The rate of return which bring inflow ’ s present value equal to outflow ’ s present value. Decision rule: Benchmark rate,usually firm ’ s cost of capital, is required as the minimum rate that the firm will accept for a given project. For independent projects, if IRR > Cost of Capital, then accept the project. If IRR < Cost of Capital, then reject the project. For mutually exclusive projects, the projects are ranked on the basis of their IRRs.

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Internal rate of return (IRR) Example (continued); the firm ’ s cost of capital = 10% Project A ; 2,000 = 1,000/(1+IRR A ) /(1+IRR A ) /(1+IRR A ) /(1+IRR A ) 4 Trial and error give IRR A = 14.5% Project B ; 2,000 = 200/(1+IRR B ) /(1+IRR B ) /(1+IRR B ) 3 + 1,200/(1+IRR B ) 4 Trial and error give IRR B = 11.8% If A and B are independent, accept both because their IRR more than 10%, which is the cost of capital If A and B are mutually exclusive, then A would be ranked higher than B since IRR A > IRR B and both are more than cost of capital.

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Comparison of NPV and IRR Some conflicting decisions may occur between the two methods. NPV method is the better.

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Comparison of NPV and IRR Cost of Capital NPV Crossover Rate = 7.2 % IRR B = 11.8% IRR A = 14.5% There are two reasons that the NPV profiles intersect. 1. The projects have different sizes, or 2. The projects have different lives.

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Comparison of NPV and IRR For independent projects, IRR and NPV methods always give the same accept or reject decision.

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Comparison of NPV and IRR For mutually exclusive projects, the IRR and NPV methods sometimes give the different decision.

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Comparison of NPV and IRR The NPV method is better, since NPV is the one that selects the project that maximizes shareholders ’ wealth Mathematically, the NPV method assumes the reinvestment rate of the cash flows is the cost of capital, while the IRR method assumes the reinvestment rate to be the IRR. In conclusion, the NPV method is considered to bet the best method since it leads to conceptually correct capital budgeting decisions.

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