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Fed letal altah Q\mathbf{Q} Cf aving Singhr Ropecira. O=\mathrm{O}= □\square ...
Aug 8, 2024
Solution by Steps
step 1
To determine the initial investment associated with the purchase of the new machines, we need to calculate the cash flows for the existing machines over the next four years. The cash flow for each year is given by the formula: Cash Flow=Revenue−Expenses \text{Cash Flow} = \text{Revenue} - \text{Expenses}
step 2
Calculating the cash flows for each year:
- Year 1: 500000−380000=120000 500000 - 380000 = 120000 - Year 2: 620000−520000=100000 620000 - 520000 = 100000 - Year 3: 680000−600000=80000 680000 - 600000 = 80000 - Year 4: 720000−650000=70000 720000 - 650000 = 70000
step 3
The operating cash inflows for the existing machines over the four years are: 120000,100000,80000,70000 120000, 100000, 80000, 70000
step 4
Next, we calculate the operating cash inflows for the new machines, which will increase revenue by 25% 25\% and expenses by 10% 10\% . The new revenue and expenses are calculated as follows:
- New Revenue: 500000×1.25=625000 500000 \times 1.25 = 625000 , 620000×1.25=775000 620000 \times 1.25 = 775000 , 680000×1.25=850000 680000 \times 1.25 = 850000 , 720000×1.25=900000 720000 \times 1.25 = 900000 - New Expenses: 380000×1.10=418000 380000 \times 1.10 = 418000 , 520000×1.10=572000 520000 \times 1.10 = 572000 , 600000×1.10=660000 600000 \times 1.10 = 660000 , 650000×1.10=715000 650000 \times 1.10 = 715000
step 5
Now, we calculate the cash flows for the new machines:
- Year 1: 625000−418000=207000 625000 - 418000 = 207000 - Year 2: 775000−572000=203000 775000 - 572000 = 203000 - Year 3: 850000−660000=190000 850000 - 660000 = 190000 - Year 4: 900000−715000=185000 900000 - 715000 = 185000
step 6
The operating cash inflows for the new machines over the four years are: 207000,203000,190000,185000 207000, 203000, 190000, 185000
step 7
To find the incremental cash flows for the project, we subtract the cash flows of the existing machines from the cash flows of the new machines:
- Year 1: 207000−120000=87000 207000 - 120000 = 87000 - Year 2: 203000−100000=103000 203000 - 100000 = 103000 - Year 3: 190000−80000=110000 190000 - 80000 = 110000 - Year 4: 185000−70000=115000 185000 - 70000 = 115000
step 8
The incremental cash flows for the project are: 87000,103000,110000,115000 87000, 103000, 110000, 115000
step 9
Finally, we calculate the Net Present Value (NPV) using the formula: NPV=∑CFt(1+r)t NPV = \sum \frac{CF_t}{(1 + r)^t} , where CFt CF_t is the cash flow at time t t and r r is the cost of capital (0.08)
step 10
Calculating the NPV:
NPV=87000(1+0.08)1+103000(1+0.08)2+110000(1+0.08)3+115000(1+0.08)4 NPV = \frac{87000}{(1 + 0.08)^1} + \frac{103000}{(1 + 0.08)^2} + \frac{110000}{(1 + 0.08)^3} + \frac{115000}{(1 + 0.08)^4} Calculating each term: - Year 1: 870001.08≈80555.56 \frac{87000}{1.08} \approx 80555.56 - Year 2: 1030001.1664≈88163.73 \frac{103000}{1.1664} \approx 88163.73 - Year 3: 1100001.259712≈87473.73 \frac{110000}{1.259712} \approx 87473.73 - Year 4: 1150001.36049≈84600.00 \frac{115000}{1.36049} \approx 84600.00
step 11
Summing these values gives: NPV≈80555.56+88163.73+87473.73+84600.00≈340793.02 NPV \approx 80555.56 + 88163.73 + 87473.73 + 84600.00 \approx 340793.02
Answer
The Net Present Value (NPV) for this project is approximately $340793.02.
Key Concept
The Net Present Value (NPV) is a method used to evaluate the profitability of an investment by comparing the present value of cash inflows to the present value of cash outflows.
Explanation
The NPV calculation incorporates the time value of money, allowing us to assess whether the projected cash flows from the new machines justify the initial investment. A positive NPV indicates that the project is expected to generate value.
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