Calculate the initial outlay, annual cash flows, WACC, NPV, IRR, PI, and payback

Question

Calculate the initial outlay, annual cash flows, WACC, NPV, IRR, PI, and payback period for the following proposed project. Determine whether the company should consider the project. The Marble Arch Company is considering replacing a manual production process with a machine. The manual process requires three relatively unskilled workers and a supervisor. Each worker makes $17,500 a year and the supervisor earns $24,500. The new machine can be run with only one skilled operator who will earn $41,000. Payroll taxes and employee benefits are an additional third of all wages and salaries. The machine costs $140,000 to buy and $10,000 to install. It will be depreciated on a straight line basis for five years. The project life is 6 years and the machine is expected to have zero salvage value by the end of the project. A service contract covers all maintenance of the proposed new machine for $5,000 a year. The machine's output will be virtually indistinguishable from that of the manual process in both quality and quantity. There are no other operating differences between the manual and the machine processes. The company just paid a dividend of $3.10 per share to its stockholders. The company has been growing at an annual 10 year moving average 6 percent and investors expect the company to continue to grow at the same rate indefinitely into the future. The current market price for the firm's common stock is $53 per share. The company has no preferred stock. The company's bonds have an annual coupon rate of 5.5%, paid semiannually. The bonds will mature in 7 years and currently sell for $835. The firm's tax rate is 40 percent. The company's equity multiplier is 1.62 and the company wants to maintain its current capital structure.

Explanation / Answer

INITIAL OUTLAY: cost of the machine 140000 installation costs 10000 Total initial cost 150000 ANNUAL CASH FLOWS: savings in wages and salaries {(17500*3+24500)+1/3rd for addl costs} 102667 less: cost of one skilled operator (41000+1/3rd) 54667 net savings in wages and salaries 48000 maintenance costs 5000 depreciation (150000/6) 25000 increase in profit before tax 18000 tax @ 40% 7200 incremental profit after tax 10800 add: depreciation 25000 annual cash flows after tax 35800 WACC: cost of equity - Ke =[(3.1*1.06)/53] + 0.06 = 0.122 = 12.2% cost of debt - Kd = the value of 'r' (semi annual rate) from the following equation: 835 = 1000*pvif(r,14) + 27.5*0.6*pvifa(r,14) discounting with 4% pv = 1000*0.5775 + 16.5*10.5631 = 577.5 + 174.29 = 751.79 discounting with 3% pv = 1000*66.11 + 16.5*11.2961 = 661.1 + 186.39 = 847.49 exact half yearly rate = 3 + 12.49/95.7 = 3.13 Annual rate 3.13*2 = 6.26% Equity multiplier = total assets/equity =1.62 equity = 1, debt = 0.62 WACC = 12.2*1/1.62 + 6.26*0.62/1.62 = 9.93% NPV: PV of annual cash inflows = 35800*pvifa(9.93,6) = 35800*4.3642 = 156238 Less: Initial investment 150000 NPV 6238 IRR: 35800*pvifa(r,6) = 150000 pvifa(r,6) = 150000/35800 = 4.1899 interest factor for 11% = 4.2305 for 12% = 4.1114 so IRR = 12 - 785/1191 = 11.34% PI: PV of cash inflows/initial investment = 156238/150000 = 1.04 Payback: Initial investment/annual cash flows = 150000/35800 = 4.2 years

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