In: Accounting
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.
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 |