To calculate the Net Present Value (NPV) and the payback period for the investment project, we can follow these steps:

1. Calculate NPV

The NPV formula in Excel is: $\text{NPV} = \text{Cash Flows} / (1 + r)^t$ Where:

• $r$ is the discount rate (8% or 0.08)
• $t$ is the year

Given cash inflows are:

• Year 1: $910
• Year 2: $1,050
• Year 3: $3,000
• Year 4: $3,300
• Year 5: $4,700

The investment outlay (initial cash flow) is $8,260, which we subtract from the calculated NPV.

In Excel, the formula will look like:

excelCopy code
=NPV(0.08, 910, 1050, 3000, 3300, 4700) - 8260

Calculating NPV:

1. Calculate the present values of cash inflows:

   • Year 1: $\frac{910}{(1+0.08)^1} = \frac{910}{1.08} \approx 842.59$
   • Year 2: $\frac{1050}{(1+0.08)^2} = \frac{1050}{1.1664} \approx 900.63$
   • Year 3: $\frac{3000}{(1+0.08)^3} = \frac{3000}{1.259712} \approx 2385.14$
   • Year 4: $\frac{3300}{(1+0.08)^4} = \frac{3300}{1.360488} \approx 2420.89$
   • Year 5: $\frac{4700}{(1+0.08)^5} = \frac{4700}{1.469328} \approx 3195.53$

2. Sum of present values: $842.59 + 900.63 + 2385.14 + 2420.89 + 3195.53 \approx 10644.87$

3. Calculate NPV: $NPV = 10644.87 - 8260 \approx 2384.87$

2. Calculate Payback Period

To estimate the payback period, we need to determine how long it takes to recover the initial investment of $8,260 from the cash inflows. Assuming cash inflows occur evenly throughout the year, we first calculate the average annual cash inflow:

Total Cash Inflows: $910 + 1050 + 3000 + 3300 + 4700 = 12960$

Average Annual Cash Inflow: $\text{Average} = \frac{12960}{5} = 2592$

Payback Period:

• Year 0: Cumulative Cash Flow = -8260
• Year 1: Cumulative Cash Flow = -8260 + 2592 = -5668
• Year 2: Cumulative Cash Flow = -5668 + 2592 = -3076
• Year 3: Cumulative Cash Flow = -3076 + 2592 = -484
• Year 4: Cumulative Cash Flow = -484 + 2592 = 2108

At the end of Year 3, we are still short, but at the beginning of Year 4, we exceed our investment.

To find the exact payback period, we can calculate the fraction of Year 4 needed: $\text{Amount remaining} = 484$ $\text{Cash inflow in Year 4} = 3300$ $\text{Fraction of Year 4} = \frac{484}{3300} \approx 0.146$

Thus, the payback period is: $3 + 0.146 \approx 3.15 \text{ years}$

Summary of Results

• NPV: Approximately $2,384.87
• Payback Period: Approximately 3.15 years

Would you like any further details or clarifications on these calculations? Here are some related questions you might find interesting:

1. How does changing the discount rate affect the NPV?
2. What are the limitations of using NPV for investment decisions?
3. How can you calculate the Internal Rate of Return (IRR) for this project?
4. What is the significance of the payback period in capital budgeting?
5. How would you evaluate a project with irregular cash flows?

Tip: Always consider the risk factors associated with projected cash flows when making investment decisions.