Question

Raymobile Motors is considering the purchase of a new production machine for 350,000. The purchase of this machine will result in an increase in earnings before interest and taxes of $120,000 per year. To operate this machine​ properly, workers would have to go through a brief training session that would cost $27,000 after tax. In​ addition, it would cost $4,000 after tax to install this machine correctly. ​ Also, because this machine is extremely​ efficient, its purchase would necessitate an increase in inventory of $32,000. This machine has an expected life of 10 ​years, after which it will have no salvage value. Assume simplified​ straight-line depreciation, that this machine is being depreciated down to​ zero, a 32 percent marginal tax​ rate, and a required rate of return of 14 percent.

a.  What is the initial outlay associated with this​ project?

b.  What are the annual​ after-tax cash flows associated with this project for years 1-9​?

c.  What is the terminal cash flow in year 10?

​(that is, the annual​ after-tax cash flow in year 10 plus any additional cash flows associated with termination of the​ project)?

d.  Should this machine be​ purchased?

Answer 1

a) Purchase price of a new production machine Employees training cost Machine installation charges Increase in working capital (inventory) Initial outlay associated with this project $350,000 $27,000 $4,000 $32,000 -$413,000 b) Increase in earnings before interest and taxes Less: Annual depreciation expense Before-tax increase in annual earnings Less: Taxes at 32% After-tax increase in annual earnings Add: Depreciation expense (Non-cash expense) Annual after-tax cash flows for years 1-9 $120,000 -$35,400 [($350000 + $4000) / 10 years] $84,600 $27,072 [$84600 x 32%] $57,528 $35,400 $92,928 c) Annual after-tax cash flows for year-10 Add: Working capital recovery at the end Add: Machine's salvage value at the end Terminal cash flow in year 10 $92,928 [Ref: Part-(b) $32,000 [Inventory investment] $0 $124,928

d) 14% 10 Cost of capital, RATE Machine's economic life, NPER Annual after-tax cash flows, PMT Working capital recovered at the end, FV Annual cash flow type, TYPE Present value of future cash flows Less: Initial outlay associated with this project Net Present Value (NPV) $92,928 [Ref: Part-(b)] $32,000 [Ref: Part-(c)] 0 = 0 if occurs at the end of each year; 1 if occurs at the beginning of each year. $493,355 [Ref: NOTE] $413,000 (Ref: Part-(a)] $80,355 CONCLUSION: Positive NPV implies that the cash outflows associated with this project are recovered even after considering time value of money before expiry of project's economic life. As this project's NPV is positive, this machine should be purchased. NOTE:

Present value of future cash flows is calculated using EXCEL FUNCTION PV(rate,nper,pmt,fv,type) where rate=14%; nper=10; pmt=-92928; fv=-32000; type=0; Here, value for pmt & fv are negative as they denote cash inflows; type = 0 because cash flows occur at the end of each year only. A 1 Cost of capital, RATE 2 Machine's economic life, NPER 3 Annual after-tax cash flows, PMT 4 Working capital recovered at the end, FV 5 Annual cash flow type, TYPE 6 Present value of future cash flows 7 Less: Initial outlay associated with this project 8 Net Present Value (NPV) 14% 10 $92,928 [Ref: Part-(b)] $32,000 (Ref: Part-(c)] 0 = 0 if occurs at the end of each year; 1 if occurs at the beginning of each year. =PV(B1,B2,-B3,-B4,B5) [Ref: NOTE] -$413,000 (Ref: Part-(a)] =SUM(B6:37)