The valuation method that shows the project’s impact on the value of the firm is net present value (NPV). To calculate NPV, we need to determine the initial investment outlay, the operating cash flows, and the terminal year cash flows. Then, we discount the cash flows at the WACC. The calculations are as follows:
Step 1: Initial Investment Outlay:
= cost of new machine + proceeds/loss from old machine + change in net working capital (NWC)
= -$90,000 + $30,000 - $6,800 + $5,000 = -$61,800 (cash outflow)
Details of calculation:
· Cost of new lathe = $90,000 outflow
· Sale of Old Machine:
o Sales price = $30,000 inflow
o Tax/tax credit: $6,800 outflow
§ = (Sales price – book value)*(tax rate) = (30,000 – 13,000)*0.4
· Change in NWC = $5,000 inflow
o DNWC = D current assets - D current liabilities = 20,000 – 25,000 = -5,000 (a decrease in working capital is a source of funds)
Step 2: Operating Cash Flows (years 1-4): Given as $16,800 inflow
Step 3: Terminal Value:
= year 5 cash flow + return/use of NWC + proceeds/loss from disposal of new machine + tax/tax credit
= $16,800 - $5,000 + $15,000 + $1,920 = $28,720 inflow
Details of calculation:
· Year 5 cash flow (given) = $16,800 inflow
· Working capital (reverse 5,000 initial inflow) = $5,000 outflow
· Sale of New Lathe:
o Sales price = $15,000 inflow
o Tax/tax credit: $1,920 inflow
§ = (Sales price – book value)*(tax rate)
§ Here, the Book value = Purchase price – depreciated amount. Using MACRS we have depreciated 78% of the value, or have 22% remaining. 0.22 * 90,000 = 19,800
§ Tax effect = (15,000 – 19,800)*(0.4) = -1,920, or a tax credit
Step 4: Calculate NPV:
NPV = -$61,800 + ($16,800 / 1.131) + ($16,800 / 1.132) +($16,800 / 1.133) +($16,800 / 1.134) +($28,720 / 1.135) = $3,759.
Since the NPV is positive, Patch Grove should replace the old lathe with the new one, because the new lathe will increase the firm’s value by the amount of the NPV, or $3,759.
You may also solve this problem quickly by using the cash flow (CF) key on your calculator.
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Calculating NPVA with the HP12C® |
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Key Strokes |
Explanation |
Display |
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[f]→[FIN]→[f]→[REG] |
Clear Memory Registers |
0.00000 |
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[f]→[5] |
Display 5 decimals – you only need to do this once. |
0.00000 |
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61,800→[CHS]→[g]→[CF0] |
Initial Cash Outlay |
-61,800.00000 |
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16,800→[g]→[CFj] |
Period 1 Cash flow |
16,800.00000 |
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4→[g]→[Nj] |
Cash Flow Occurs for 4 periods |
4.00000 |
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28,720→[g]→[CFj] |
Period 5 Cash flow |
28,720.00000 |
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13→[i] |
WACC |
13.00000 |
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[f]→[NPV] |
Calculate NPV |
3,759.18363 |
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Calculating NPVA with the TI Business Analyst II Plus→ |
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Key Strokes |
Explanation |
Display |
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[2nd]→[Format]→[5]→[ENTER] |
Display 5 decimals – you only need to do this once. |
DEC= 5.00000 |
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[CF]→[2nd]→[CLR WORK] |
Clear Memory Registers |
CF0 = 0.00000 |
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61,800®[+/-]→[ENTER] |
Initial Cash Outlay |
CF0 = -61,800.00000 |
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[↓]→16,800→[ENTER] |
Period 1 Cash Flow |
C01 = 16,800.00000 |
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[↓] 4 [ENTER] |
Frequency of Cash Flow 1 |
F01 = 4.00000 |
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[↓]→28,720→[ENTER] |
Period 2 Cash Flow |
C02 = 28,720.00000 |
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[↓] |
Frequency of Cash Flow 2 |
F02 = 1.00000 |
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[NPV]→13→[ENTER] |
WACC |
I = 13.00000 |
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[↓]→[CPT] |
Calculate NPV |
NPV = 3,759.18363 |
