purchase price 550,000, period of useful 10 years, annual revenue 100,000,operating costs 32,000, depreciation 55,000 no income taxes can you show me how to get the answer I have an answer but not sure if it is correct
To calculate the net present value (NPV) of an investment, we need to determine the cash flows for each year, discount them to present value, and then sum them up.
1. Calculate the annual cash flows:
Revenue - Operating costs = Cash flow
$100,000 - $32,000 = $68,000
2. Calculate the depreciation expense for each year:
Depreciation expense = Purchase price / Useful life
$550,000 / 10 = $55,000
3. Determine the net cash flows for each year:
Cash flow - Depreciation expense = Net cash flow
$68,000 - $55,000 = $13,000
4. Discount the net cash flows to present value using an appropriate discount rate. Let's assume a discount rate of 10%.
Year 1:
Present value = Net cash flow / (1 + discount rate)^years
PV1 = $13,000 / (1 + 0.10)^1 = $11,818.18
Year 2:
PV2 = $13,000 / (1 + 0.10)^2 = $10,743.80
Year 3:
PV3 = $13,000 / (1 + 0.10)^3 = $9,767.09
Year 4:
PV4 = $13,000 / (1 + 0.10)^4 = $8,878.26
Year 5:
PV5 = $13,000 / (1 + 0.10)^5 = $8,068.42
Year 6:
PV6 = $13,000 / (1 + 0.10)^6 = $7,329.47
Year 7:
PV7 = $13,000 / (1 + 0.10)^7 = $6,654.06
Year 8:
PV8 = $13,000 / (1 + 0.10)^8 = $6,035.51
Year 9:
PV9 = $13,000 / (1 + 0.10)^9 = $5,467.74
Year 10:
PV10 = $13,000 / (1 + 0.10)^10 = $4,946.13
5. Sum up all the present values to get the net present value (NPV):
NPV = PV1 + PV2 + PV3 + PV4 + PV5 + PV6 + PV7 + PV8 + PV9 + PV10
NPV = $11,818.18 + $10,743.80 + $9,767.09 + $8,878.26 + $8,068.42 + $7,329.47 + $6,654.06 + $6,035.51 + $5,467.74 + $4,946.13
NPV = $79,768.66
So, the net present value of this investment is $79,768.66. If the NPV is positive, it suggests that the investment is worthwhile.