Find the present value of the cash flow shown below if interest rate (𝑖) is 10% per year. Year Cash 1 2000 2 5000 3 0 4 -2000 5 3000
Question
Find the present value of the cash flow shown below if interest rate (𝑖) is 10% per year. Year Cash 1 2000 2 5000 3 0 4 -2000 5 3000
Solution
The present value (PV) of a future cash flow is calculated using the formula:
PV = CF / (1 + i)^n
where:
- CF is the cash flow
- i is the interest rate
- n is the number of periods
Let's calculate the present value for each year:
- For year 1: PV = 2000 / (1 + 0.10)^1 = 1818.18
- For year 2: PV = 5000 / (1 + 0.10)^2 = 4132.23
- For year 3: PV = 0 / (1 + 0.10)^3 = 0
- For year 4: PV = -2000 / (1 + 0.10)^4 = -1369.86
- For year 5: PV = 3000 / (1 + 0.10)^5 = 1862.74
Now, add up all these present values to get the total present value of the cash flow:
Total PV = 1818.18 + 4132.23 + 0 - 1369.86 + 1862.74 = 6443.29
So, the present value of the cash flow is approximately 6443.29.
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