An investment you purchased today for $60,000 will pay $20,000 in 1 year and $25,000,$30,000,$35,000 and finally $110,000 at the end of each of the next years respectively. If interest rates are 9.0% (per year). What is the Net present value of this investment? A) $65,082.71 B) $38,156.06 C) $28,042.51 D) $98,843.46 E) $51,964.27
To calculate the net present value (NPV) of this investment, we need to discount the future cash flows to their present value using the interest rate of 9.0%.
The formula to calculate the present value (PV) of a future cash flow is:
PV = CF / (1 + r)^n
Where CF is the future cash flow, r is the interest rate, and n is the number of years.
For the cash flows given:
PV1 = $20,000 / (1 + 0.09)^1 = $20,000 / 1.09^1 ≈ $18,348.62
PV2 = $25,000 / (1 + 0.09)^2 = $25,000 / 1.09^2 ≈ $20,726.40
PV3 = $30,000 / (1 + 0.09)^3 = $30,000 / 1.09^3 ≈ $23,193.89
PV4 = $35,000 / (1 + 0.09)^4 = $35,000 / 1.09^4 ≈ $25,746.60
PV5 = $110,000 / (1 + 0.09)^5 = $110,000 / 1.09^5 ≈ $70,115.30
To calculate the NPV, we subtract the initial investment of $60,000 from the sum of the present values of the future cash flows:
NPV = PV1 + PV2 + PV3 + PV4 + PV5 - Initial Investment
NPV = $18,348.62 + $20,726.40 + $23,193.89 + $25,746.60 + $70,115.30 - $60,000
NPV ≈ $98,330.81
Therefore, the correct option is D) $98,330.81 (rounded to the nearest cent).
To calculate the net present value (NPV) of the investment, we need to discount all future cash flows to their present values and then subtract the initial investment.
Step 1: Calculate the present value of each cash flow:
PV = CF / (1 + r)^n
Where:
PV = Present value
CF = Cash flow
r = Interest rate
n = Number of periods
For the first cash flow of $20,000 after 1 year:
PV1 = $20,000 / (1 + 0.09)^1 = $20,000 / 1.09 = $18,348.62
For the second cash flow of $25,000 after 2 years:
PV2 = $25,000 / (1 + 0.09)^2 = $25,000 / 1.1881 = $21,042.51
For the third cash flow of $30,000 after 3 years:
PV3 = $30,000 / (1 + 0.09)^3 = $30,000 / 1.2950 = $23,165.38
For the fourth cash flow of $35,000 after 4 years:
PV4 = $35,000 / (1 + 0.09)^4 = $35,000 / 1.4116 = $24,805.07
For the fifth and final cash flow of $110,000 after 5 years:
PV5 = $110,000 / (1 + 0.09)^5 = $110,000 / 1.5386 = $71,793.96
Step 2: Calculate the net present value (NPV):
NPV = PV1 + PV2 + PV3 + PV4 + PV5 - Initial Investment
The initial investment is $60,000.
NPV = $18,348.62 + $21,042.51 + $23,165.38 + $24,805.07 + $71,793.96 - $60,000 = $99,156.54
Therefore, the net present value (NPV) of this investment is $99,156.54.
None of the provided answer options match exactly with $99,156.54, but the closest option is D) $98,843.46.