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In: Finance
The Rustic Welt Company is proposing to replace its old welt-making machinery with more modern equipment....
The Rustic Welt Company is proposing to replace its old welt-making machinery with more modern equipment. The new equipment costs $10.8 million (the existing equipment has zero salvage value). The attraction of the new machinery is that it is expected to cut manufacturing costs from their current level of $9.80 a welt to $5.80. However, as the following table shows, there is some uncertainty about both the future sales and the performance of the new machinery: Pessimistic Expected Optimistic Sales (million welts) 2.2 2.3 2.5 Manufacturing cost ($ per welt) 7.80 5.80 4.80 Life of new machinery (years) 11 14 17 Conduct a sensitivity analysis of the replacement decision assuming a discount rate of 8%. Rustic does not pay taxes. Calculate the NPV.
Solutions
Expert Solution
| IC | Initial Cash Flow in million dollars | ($10.80) | ||||||||||
| A | Current Cost per Welt | $9.80 | $9.80 | $9.80 | $9.80 | $9.80 | $9.80 | $9.80 | $9.80 | $9.80 | ||
| B | New Cost per welt | $7.80 | $5.80 | $4.80 | $7.80 | $5.80 | $4.80 | $7.80 | $5.80 | $4.80 | ||
| C=A-B | Saving per welt | $2.00 | $4.00 | $5.00 | $2.00 | $4.00 | $5.00 | $2.00 | $4.00 | $5.00 | ||
| Sales in million welt | 2.2 | 2.2 | 2.2 | 2.3 | 2.3 | 2.3 | 2.5 | 2.5 | 2.5 | |||
| Annual Savings in Million dollar | $4.40 | $8.80 | $11.00 | $4.60 | $9.20 | $11.50 | $5.00 | $10.00 | $12.50 | |||
| CALCULATION OF PRESENT VALUE OF SAVINGS | ||||||||||||
| FOR LIFE OF NEW MACHINERY =11 YEARS | ||||||||||||
| AT VARIOUS LEVEL OF ANNUAL SAVINGS | ||||||||||||
| Rate | Discount Rate | 8% | 8% | 8% | 8% | 8% | 8% | 8% | 8% | 8% | ||
| Nper | Number of Years of Savings=Life of new machinery | 11 | 11 | 11 | 11 | 11 | 11 | 11 | 11 | 11 | ||
| Pmt | Annual Savings(Million dollars) | $4.40 | $8.80 | $11.00 | $4.60 | $9.20 | $11.50 | $5.00 | $10.00 | $12.50 | ||
| PV | Present Value of Annual Savings(Million dollars) | $31.41 | $62.82 | $78.53 | $32.84 | $65.68 | $82.10 | $35.69 | $71.39 | $89.24 | ||
| (Using PV function of excel) | ||||||||||||
| NPV=PV+IC | Net Present Value (PV-$10.8 million) ($ million) | $20.61 | $52.02 | $67.73 | $22.04 | $54.88 | $71.30 | $24.89 | $60.59 | $78.44 | ||
| CALCULATION OF PRESENT VALUE OF SAVINGS | ||||||||||||
| FOR LIFE OF NEW MACHINERY =14 YEARS | ||||||||||||
| AT VARIOUS LEVEL OF ANNUAL SAVINGS | ||||||||||||
| Rate | Discount Rate | 8% | 8% | 8% | 8% | 8% | 8% | 8% | 8% | 8% | ||
| Nper | Number of Years of Savings=Life of new machinery | 14 | 14 | 14 | 14 | 14 | 14 | 14 | 14 | 14 | ||
| Pmt | Annual Savings(Million dollars) | $4.40 | $8.80 | $11.00 | $4.60 | $9.20 | $11.50 | $5.00 | $10.00 | $12.50 | ||
| PV | Present Value of Annual Savings(Million dollars) | $36.27 | $72.55 | $90.69 | $37.92 | $75.85 | $94.81 | $41.22 | $82.44 | $103.05 | ||
| (Using PV function of excel) | ||||||||||||
| NPV=PV+IC | Net Present Value (PV-$10.8 million) ($ million) | $25.47 | $61.75 | $79.89 | $27.12 | $65.05 | $84.01 | $30.42 | $71.64 | $92.25 | ||
| CALCULATION OF PRESENT VALUE OF SAVINGS | ||||||||||||
| FOR LIFE OF NEW MACHINERY =17 YEARS | ||||||||||||
| AT VARIOUS LEVEL OF ANNUAL SAVINGS | ||||||||||||
| Rate | Discount Rate | 8% | 8% | 8% | 8% | 8% | 8% | 8% | 8% | 8% | ||
| Nper | Number of Years of Savings=Life of new machinery | 17 | 17 | 17 | 17 | 17 | 17 | 17 | 17 | 17 | ||
| Pmt | Annual Savings(Million dollars) | $4.40 | $8.80 | $11.00 | $4.60 | $9.20 | $11.50 | $5.00 | $10.00 | $12.50 | ||
| PV | Present Value of Annual Savings(Million dollars) | $40.14 | $80.27 | $100.34 | $41.96 | $83.92 | $104.90 | $45.61 | $91.22 | $114.02 | ||
| (Using PV function of excel) | ||||||||||||
| NPV=PV+IC | Net Present Value (PV-$10.8 million) ($ million) | $29.34 | $69.47 | $89.54 | $31.16 | $73.12 | $94.10 | $34.81 | $80.42 | $103.22 | ||
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