An investment project costs $12,900 and has annual cash flows of $3,500 for six years.

1. Break Down the Problem

To evaluate the investment project, we need to:

1. Determine the total cash flows from the project.
2. Calculate the net present value (NPV) to see if the investment is worthwhile.

2. Relevant Concepts

• Total Cash Flow: This is the annual cash inflow multiplied by the number of years.
• Net Present Value (NPV) formula: $\text{NPV} = \sum_{t=1}^{n} \frac{C_t}{(1 + r)^t} - C_0$ where:
• $C_t$ is the cash flow during the period $t$,
• $r$ is the discount rate,
• $C_0$ is the initial investment,
• $n$ is the number of periods.

3. Analysis and Detail

1. Calculate Total Cash Flow: $\text{Total Cash Flow} = \text{Annual Cash Flow} \times \text{Number of Years} = 3,500 \times 6 = 21,000$

2. Assuming a discount rate $r$: For this example, let's use a common discount rate of 10% ($r = 0.10$).

3. Calculate NPV:

   • Calculate the present value of each cash flow for $t = 1$ to $6$: $\text{NPV} = \frac{3,500}{(1 + 0.10)^1} + \frac{3,500}{(1 + 0.10)^2} + \frac{3,500}{(1 + 0.10)^3} + \frac{3,500}{(1 + 0.10)^4} + \frac{3,500}{(1 + 0.10)^5} + \frac{3,500}{(1 + 0.10)^6} - 12,900$

   • Calculating each term:

     • $t=1$: $\frac{3,500}{1.10^1} = 3,181.82$
     • $t=2$: $\frac{3,500}{1.10^2} = 2,893.57$
     • $t=3$: $\frac{3,500}{1.10^3} = 2,631.42$
     • $t=4$: $\frac{3,500}{1.10^4} = 2,393.11$
     • $t=5$: $\frac{3,500}{1.10^5} = 2,176.46$
     • $t=6$: $\frac{3,500}{1.10^6} = 1,979.96$

   • Summing these values: $3,181.82 + 2,893.57 + 2,631.42 + 2,393.11 + 2,176.46 + 1,979.96 = 15,256.34$

   • Finally, calculating NPV: $\text{NPV} = 15,256.34 - 12,900 = 2,356.34$

4. Verify and Summarize

After these calculations, we confirm that the project yields a positive NPV of $2,356.34. This indicates that the investment is financially sound, as it returns more than the cost involved and generates additional value.

Final Answer

The NPV of the investment project is $2,356.34, suggesting that the project is a worthwhile investment.