5. The management of Dewey, Cheatham & Howe, a private hospital is considering a

Question

5. The management of Dewey, Cheatham & Howe, a private hospital is considering automating some back office functions. This would replace five personnel that currently cover three shifts per day, 365 days per year. Each person earns $35,000 per year. Company-paid benefits and overhead are 45% of wages. Money costs (use this as MARR) 8%. Combined federal and state taxes total 40%. Annual property taxes and maintenance are 2.5% and 4 % of the investment cost, respectively. Depreciation is 15-year straight-line (i.e. 1/15 * investment cost). Disregarding inflation, how large an investment in the automation project can be economically justified?

Use Excel to solve this problem.

Explanation / Answer

Answer: $1178816 Calculation and explanations: At the maximum investment cost the NPV will be Zero with 8% MARR. The PV of the after tax inflows and outflows are calculated below: 1) Annual after tax savings in personnel cost = 5*(35000+35000*45%)*(1-0.40) = 152250 PV of after tax savings in personnel cost = 152250*(1.08^15-1)/(0.08*1.08^15) = 1303181 2) Tax shield on depreciation = (C/15)*0.40 where C = The initial investment required. PV of tax shield on depreciation= (C/15)*0.40*PVIFA(8,15) = (C/15)*0.40*8.5595 = C*0.2283 3) After tax annual property taxes and maintenance cost = C*6.5%*0.60 PV of annual property taxes and maintenance cost = C*6.5%*0.60*8.5595 = C*0.3338 4) Equating the PV of the above three items with the cost of investment to get 0 NPV, we have C = 1303181+C*0.2283-C*0.3338 Solving for C 1.1055*C = 1303181 1178816 C = 1303181/1.1055 = $1178816 (Answer) CHECK for 0 NPV: PV of after tax savings in personnel cost = 152250*(1.08^15-1)/(0.08*1.08^15) = 1303181 PV of tax shield on depreciation = (1178816/15)*0.40*8.5595 = 269069 PV of taxes and maintenance cost = 1178816*6.5%*0.60*8.5595 = 393513 Initial investment 1178816 NPV -80 Almost 0 Difference due to rounding off

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