Question
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(Straight Line Depreciation) A new machine cost $100,000, and will increase inventory by $10,000, A/R by...
(Straight Line Depreciation) A new machine cost $100,000, and will increase inventory by $10,000, A/R by $15,000, and A/P by $5,000. This machine will reduce our expenses by $18,000 per year. The machine will be depreciated to a zero book value in 10 years, but could be sold for $12,000 at the end of 10 years. The marginal tax rate is 35%, and the cost of capital is 12%. Calculate the payback, NPV, IRR, and PI.
Solutions
Expert Solution
Step 1: Calculate depreciation schedule:
| Depreciation Schedule | ||||
| Year | Opening Balance | Investment | Depreciation | Closing balance |
| - | 100000-12000= 88,000.00 | 88,000.00 | ||
| 1.00 | 88,000.00 | 88000/10= 8,800.00 | 79,200.00 | |
| 2.00 | 79,200.00 | 8,800.00 | 70,400.00 | |
| 3.00 | 70,400.00 | 8,800.00 | 61,600.00 | |
| 4.00 | 61,600.00 | 8,800.00 | 52,800.00 | |
| 5.00 | 52,800.00 | 8,800.00 | 44,000.00 | |
| 6.00 | 44,000.00 | 8,800.00 | 35,200.00 | |
| 7.00 | 35,200.00 | 8,800.00 | 26,400.00 | |
| 8.00 | 26,400.00 | 8,800.00 | 17,600.00 | |
| 9.00 | 17,600.00 | 8,800.00 | 8,800.00 | |
| 10.00 | 8,800.00 | 8,800.00 | - | |
Step 2: Calculate annual CF:
| CF calculation | |||
| Year | Remarks | 1 to 9 | 10.00 |
| Annual Benefit | Given | 18000 | 18000 |
| Depreciation | as per schedule | 8,800.00 | 8800 |
| EBIT | Annual Benefit-Depreciation | 9,200.00 | 9,200.00 |
| Tax | 0.35 x EBIT | 3,220.00 | 3,220.00 |
| NI | EBIT-Tax | 5980 | 5980 |
| Depreciation | Added back being a non cash expense | 8800 | 8800 |
| CF | 14780 | 14780 | |
| Wcinv Recovery | increase in inventory+ increase in AR -increase in AP | 20000 | |
| Salvage value | sale value of investment | 12000 | |
| Tax on profit of sale | 0.35x12000 (as equipment is completely depreciated, entire salvage value is profit) | 4200 | |
| Total CF | Wcinv Recovery+Salvage value-Tax on profit of sale | 14780 | 52580 |
Step 3: Calculate NPV & PI
| Year | CF | Discount factor | Discounted CF | ||||
| 0 | -1,20,000.00 | 1/(1+0.12)^0 | = | 1 | 1*-120000 | = | -120000 |
| 1 | 14780 | 1/(1+0.12)^1 | = | 0.892857143 | 0.892857142857143*14780 | = | 13196.42857 |
| 2 | 14780 | 1/(1+0.12)^2 | = | 0.797193878 | 0.79719387755102*14780 | = | 11782.52551 |
| 3 | 14780 | 1/(1+0.12)^3 | = | 0.711780248 | 0.711780247813411*14780 | = | 10520.11206 |
| 4 | 14780 | 1/(1+0.12)^4 | = | 0.635518078 | 0.635518078404831*14780 | = | 9392.957199 |
| 5 | 14780 | 1/(1+0.12)^5 | = | 0.567426856 | 0.567426855718599*14780 | = | 8386.568928 |
| 6 | 14780 | 1/(1+0.12)^6 | = | 0.506631121 | 0.506631121177321*14780 | = | 7488.007971 |
| 7 | 14780 | 1/(1+0.12)^7 | = | 0.452349215 | 0.452349215336893*14780 | = | 6685.721403 |
| 8 | 14780 | 1/(1+0.12)^8 | = | 0.403883228 | 0.403883227979369*14780 | = | 5969.39411 |
| 9 | 14780 | 1/(1+0.12)^9 | = | 0.360610025 | 0.36061002498158*14780 | = | 5329.816169 |
| 10 | 42580 | 1/(1+0.12)^10 | = | 0.321973237 | 0.321973236590696*42580 | = | 13709.62041 |
| NPV = sum of discounted CF | = | -27538.8477 | |||||
| PI = NPV/initial investment | = | -0.23 | |||||
Step 4: Calculate IRR, the rate at which NPV = 0 (Using either hit and trial or excel goal seek function)
| Year | CF | Discount factor | Discounted CF | ||||
| 0 | -1,20,000.00 | 1/(1+0.0666779932462238)^0 | = | 1 | 1*-120000 | = | -120000 |
| 1 | 14780 | 1/(1+0.0666779932462238)^1 | = | 0.937490045 | 0.937490045104144*14780 | = | 13856.10287 |
| 2 | 14780 | 1/(1+0.0666779932462238)^2 | = | 0.878887585 | 0.87888758466937*14780 | = | 12989.9585 |
| 3 | 14780 | 1/(1+0.0666779932462238)^3 | = | 0.823948361 | 0.823948361393159*14780 | = | 12177.95678 |
| 4 | 14780 | 1/(1+0.0666779932462238)^4 | = | 0.772443386 | 0.772443386485958*14780 | = | 11416.71325 |
| 5 | 14780 | 1/(1+0.0666779932462238)^5 | = | 0.724157985 | 0.724157985237119*14780 | = | 10703.05502 |
| 6 | 14780 | 1/(1+0.0666779932462238)^6 | = | 0.678890902 | 0.678890902242472*14780 | = | 10034.00754 |
| 7 | 14780 | 1/(1+0.0666779932462238)^7 | = | 0.636453463 | 0.636453462564088*14780 | = | 9406.782177 |
| 8 | 14780 | 1/(1+0.0666779932462238)^8 | = | 0.596668785 | 0.596668785325896*14780 | = | 8818.764647 |
| 9 | 14780 | 1/(1+0.0666779932462238)^9 | = | 0.559371046 | 0.559371046467409*14780 | = | 8267.504067 |
| 10 | 42580 | 1/(1+0.0666779932462238)^10 | = | 0.524404788 | 0.524404787582683*42580 | = | 22329.15586 |
| NPV | = | 0.000704527 | |||||
IRR comes to 6.6677993%
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