Question

Kinky Copies may buy a high-volume copier. The machine costs $100,000 and this cost can be fully depreciated immediately. Kinky anticipates that the machine can actually be sold in 5 years for $30,000. The machine will save $20,000 a year in labor costs but will require an increase in working capital, mainly paper supplies, of $10,000. The firm’s tax rate is 21%, and the discount rate is 8%. What is the NPV of the project?

Using an elaborate spreadsheet based on guidance from my textbook, I calculated that NPV is 41,959.91. Am I on the right track?

Answer 1

Year 0 Cash flow              
Cost of machine.........    -$100,000          
Investment in Working capital   -10000          
Depreciation tax benefit              
(100000*21%)   $21,000          
___________________________________              
Total Cash flow at year 0    -$89,000          
___________________________________              
              
Cash flow from Year 1 to 5              
Year              
Incremental Savings   20000          
less: tax @21%   -4200          
___________________________________              
Free Cash flow   15800          
___________________________________              
              
Terminal inflow year 5              
Salvage value   30000          
less: tax@21%   -6300          
Working capital recovery   10000          
___________________________________              
   33700          
___________________________________              
              
              
NPV is sum of present value of all cash flows.              
Present value of cash flows = cash flows * PVF              
              
PVF formula = 1/(1+Discount rate)^period              
For year 1, PVF = 1/(1+8%)^1=   0.9259259259          
For year 2, PVF = 1/(1+8%)^2=   0.8573388203          
and so on.              
              
              
Calcultion of NPV              
Year   Free cash flow   PVF @8%   PV = Cash flow * PVF  
0   -$89,000   1   -89,000.00  
1   15800   0.9259259259   14,629.63  
2   15800   0.8573388203   13,545.95  
3   15800   0.793832241   12,542.55  
4   15800   0.7350298528   11,613.47  
5   15800   0.680583197   10,753.21  
5   33700   0.680583197   22,935.65  
              
              
NpV = sum of all free cash flows=           -2,979.53  
              
Note: Depreciation is deducted at time of purchase. so tax benefit at 21% will be allowed on year 0 only. Afterwards no Depreciation tax benefit will be received.              
(2) Depreciation is non cash expenditure. it is not real cash expenses.               
(3) Working capital will be recovered at year end.       

       

You have done something mistake. Actual NPV is -$2979.53

To calculate in Spreadsheet, put values of year 5 in total. Then apply NPV function given below in image: