You are designing a new product and want to estimate the net present value of the first year of future sales. You think you could make your first sale a year from now, and would have$5000in revenue (sales) each month. For a nominal annual discount rate of10%, compounded monthly, the net present value of that first year of sales is [NPV]. Answer to the nearest whole dollar. Hint: first draw the cash flow diagram; the first arrow up should be att=13months and the last att=24months.
Question
You are designing a new product and want to estimate the net present value of the first year of future sales. You think you could make your first sale a year from now, and would have$5000in revenue (sales) each month. For a nominal annual discount rate of10%, compounded monthly, the net present value of that first year of sales is [NPV]. Answer to the nearest whole dollar. Hint: first draw the cash flow diagram; the first arrow up should be att=13months and the last att=24months.
Solution
To calculate the Net Present Value (NPV), we need to discount each future cash flow back to its present value and then sum them up. Here are the steps:
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Identify the cash flows: In this case, the cash flows are $5000 each month, starting from the 13th month to the 24th month.
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Identify the discount rate: The nominal annual discount rate is 10%, compounded monthly. This means the monthly discount rate is 10%/12 = 0.833%.
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Calculate the present value of each cash flow: The present value of a future cash flow can be calculated using the formula: PV = FV / (1 + r)^n, where FV is the future value, r is the discount rate, and n is the number of periods.
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Sum up the present values: The NPV is the sum of the present values of all future cash flows.
Let's calculate:
Month 13: PV = 4463 Month 14: PV = 4428 ... Month 24: PV = 3916
Adding these up, the NPV to the nearest whole dollar is $52,200.
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