A machine currently in use was originally purchased last year (one year ago) for $20,000. It is being depreciated using the straight-line method over a four-year period. A new machine can be purchased for $26,000 plus a $5,000 delivery and installation charge. The new machine will be depreciated using the straight-line method over a five-year period.
If the new machine is acquired, the investment in accounts receivables is expected to rise by $2,500, the inventory investment will increase by $1,000, and accounts payable will increase by $1,500. Net working capital is expected to increase each year at the same percentage as sales (revenue) over the life of the project.
Revenue is expected to be $7,500 per year with the old machine. Revenue with the new machine is expected to be $12,000 in year 1 and increase at the rate of 1 percent per year for year 2, 2 percent per year for years 3 - 4, and 3 percent per year for year 5.
Incremental operating costs associated with the new machine are expected to $1,000 in year 1 and increase by 1% per year over the life of the machine. At the end of four years, the old machine was expected to have a salvage value of zero, but it can be sold today for $12,000 before taxes. The new machine is expected to have a salvage value of $1,000 at the end of its life. The firm’s tax rate is 40 percent and the risk-adjusted discount rate is 12 percent.
PLEASE SHOW ALL WORK
1. Calculate the after-tax, incremental cash flows in year 0 to 5.
2. Calculate payback.
3. Calculate net present value.
4. Calculate internal rate of return.
1.)
| Purchase Value of new Asset | 26000 | ||||
| Installation Charges | 5000 | ||||
| Total Value | 31000 | ||||
| Less: After tax Cash from old machine | |||||
| Book Value of Asset now = 20000 - ((20000-0)/5) | 15000 | ||||
| Sale proceeds | 12000 | ||||
| loss on sale of asset | 3000 | ||||
| Net Investment in New Asset = 31000 - 12000 | 19000 | ||||
| Investment in WC | |||||
| Increase in receivables | 2500 | ||||
| Increase in Inventory | 1000 | ||||
| Increase in Payables | 1500 | ||||
| Net Investment in WC | 2000 | ||||
| Total cash flow in year 0 | 21000 | ||||
| New Depreciation = (Value of asset - salvage value)/ no.life of Asset | 6000 | ||||
| Old Depreciation for 3 years | 5000 | ||||
| Incemental Depreciation = | 1000 | ||||
| Tax savings on loss 40% of 3000 benefit will be at year end = 1200 is to be deducted from tax at year 1 so tax at year 1 = (2500 x 40%) - 1200 | |||||
| Terminal Cash flow = additional Net working capital recouped + salvage value after 5 years | |||||
| years | Year1 | Year2 | Year3 | Year4 | Year5 |
| New revenue | 12,000.00 | 12,120.00 | 12,362.40 | 12,609.65 | 12,987.94 |
| Old revenue | 7500 | 7500 | 7500 | 7500 | 7500 |
| Incremental Revenue | 4,500.00 | 4,620.00 | 4,862.40 | 5,109.65 | 5,487.94 |
| (-)Incremental operating Cost | 1,000.00 | 1,010.00 | 1,020.10 | 1,030.30 | 1,040.60 |
| (-) Incremental Depreciation | 1,000.00 | 1,000.00 | 1,000.00 | 6,000.00 | 6,000.00 |
| Incremental PBT | 2,500.00 | 2,610.00 | 2,842.30 | -1,920.65 | -1,552.67 |
| Tax@ 40% | -200.00 | 1,044.00 | 1,136.92 | -768.26 | -621.07 |
| Incremental PAT | 2,700.00 | 1,566.00 | 1,705.38 | -1,152.39 | -931.60 |
| Add: Incremental Depreciation | 1,000.00 | 1,000.00 | 1,000.00 | 6,000.00 | 6,000.00 |
| Investment in additional NWC | -20.00 | -39.60 | -38.81 | -57.05 | |
| Annual Cashflow After tax | 3,680.00 | 2,526.40 | 2,666.57 | 4,790.56 | 8,223.86 |
| Add: terminal Cash flow |
3,155.46 |
||||
Annual cash flow at year5 is inclusive of Terminal cash flow
2.)
| Annual Cashflow After tax | 3,680.00 | 2,526.40 | 2,666.57 | 4,790.56 | 8,223.86 |
| years | 1 | 2 | 3 | 4 | 5 |
| Cumulative Cash flow | 3,680.00 | 6,206.40 | 8,872.97 | 13,663.53 | 21,887.39 |
| Payback period | 4 years 7 months and 24 days | 5,336.47 | |||
| 4 years + months | 7.786810973 | ||||
| 4 years + 7 months +Days | 23.604 | ||||
| No. of years before crossing invest ment by cumulative annual cashflow | 4 | ||||
| Amount remained for crossing invest ment by cumulative annual cashflow at year 4 = 19000-13663.53=5336.47 | |||||
Payback period =No. of years before crossing invest ment by cumulative annual cashflow +( Amount remained for crossing invest ment by cumulative annual cashflow at year 4/ annual cash flow in year 5) x 365
3.)
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4.) IRR = LR +(NPV @LR/(NPV@ LR-NPV@HR))(HR-LR)
| Annual Cashflow After tax | 3,680.00 | 2,526.40 | 2,666.57 | 4,790.56 | 8,223.86 |
| Discount factor@5% = HR | 0.952380952 | 0.907029478 | 0.863837599 | 0.822702475 | 0.783526166 |
| Present value | 3,504.76 | 2,291.52 | 2,303.49 | 3,941.21 | 6,443.61 |
| Total Present value | 18,484.58 | ||||
| Investment at year0 | 19000 | ||||
| NPV | -515.42 | ||||
| Annual Cashflow After tax | 3,680.00 | 2,526.40 | 2,666.57 | 4,790.56 | 8,223.86 |
| Discount factor@3% = LR | 0.970873786 | 0.942595909 | 0.915141659 | 0.888487048 | 0.862608784 |
| Present value | 3,572.82 | 2,381.37 | 2,440.29 | 4,256.35 | 7,093.97 |
| Total Present value | 19,744.80 | ||||
| Investment at year0 | 19,000 | ||||
| NPV | 744.80 |
Substitute values in formula , we will get 6.18%
.
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