a project will provide annual cash inflows of $4,171, $5,700, and $8,000 at the end of each year for the next three years, respectively. what is the present value of these cash flows, given a 9% discount rate. 

To calculate the present value (PV) of these cash flows, we need to discount each cash flow to the present using the given 9% discount rate. The formula for calculating the present value of a future cash flow is:

\[
PV = \dfrac{C}{(1 + r)^t}
\]

Where:
- $ PV $ is the present value
- $ C $ is the future cash flow
- $ r $ is the discount rate (9% or 0.09)
- $ t $ is the number of years into the future the cash flow is received

### Let's calculate the present value for each year separately:

1. **Year 1 cash flow** ($ C_1 = 4,171 $):
\[
PV_1 = \dfrac{4,171}{(1 + 0.09)^1} = \dfrac{4,171}{1.09} = 3,826.61
\]

2. **Year 2 cash flow** ($ C_2 = 5,700 $):
\[
PV_2 = \dfrac{5,700}{(1 + 0.09)^2} = \dfrac{5,700}{(1.09)^2} = \dfrac{5,700}{1.1881} = 4,796.37
\]

3. **Year 3 cash flow** ($ C_3 = 8,000 $):
\[
PV_3 = \dfrac{8,000}{(1 + 0.09)^3} = \dfrac{8,000}{(1.09)^3} = \dfrac{8,000}{1.29503} = 6,175.28
\]

### Now, sum the present values of each cash flow to get the total present value:

\[
PV_{total} = PV_1 + PV_2 + PV_3 = 3,826.61 + 4,796.37 + 6,175.28 = 14,798.26
\]

So, the total present value of the cash flows is approximately **$14,798.26**.

Would you like more details or have any questions?

### Related questions:
1. What is the impact of increasing the discount rate on the present value?
2. How would the present value change if the cash inflows were received at the beginning of each year instead?
3. How would you calculate the present value if the cash flows were uneven and spread over more years?
4. How can this present value calculation be extended to include additional cash inflows or expenses in the future?
5. How does the concept of present value apply to capital budgeting decisions?

### Tip: 
Remember, the higher the discount rate, the lower the present value of future cash flows will be.

A project will provide annual cash inflows of $4,171, $5,700, and $8,000 at the end of each year for the next three years, respectively. What is the present value of these cash flows, given a 9% discount rate?

Learn how to calculate the present value of future cash inflows for a project providing $4,171, $5,700, and $8,000 annually over the next three years, using a 9% discount rate. The detailed solution covers financial concepts like discounting and the time value of money, suitable for finance students or advanced math learners.

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