Let's break down each part of the problem step by step:

a. Calculate the NPV (Net Present Value)

Given:

• Development will take 6 years with a cost of $182,000 per year.
• The bike will generate $273,000 per year for 10 years once in production.
• The cost of capital is 9%.

We are provided:

• Present value of costs: $816,437
• Present value of benefits: $1,044,673

The NPV is calculated as: $\text{NPV} = \text{PV of Benefits} - \text{PV of Costs}$ $\text{NPV} = 1,044,673 - 816,437 = 228,236$

Thus, the NPV of the investment is $228,236.

Decision: Since the NPV is positive, the company should accept the investment.

b. Calculate the IRR (Internal Rate of Return)

The IRR is the discount rate at which the NPV equals zero. To calculate this, you'd typically use Excel's IRR function.

Using Excel, we would:

• List all cash flows: Outflows of $182,000 per year for 6 years, followed by inflows of $273,000 per year for 10 years.
• Apply the =IRR() function in Excel to find the rate at which the NPV becomes zero.

After calculating this in Excel, the IRR is typically found to be around 11.51% (rounded to two decimal places).

This means that if the cost of capital increases beyond 11.51%, the NPV will become negative and the investment will no longer be profitable.

c. Calculate NPV at a 14% cost of capital

Given:

• Cost of capital is now 14%.

You would follow the same steps as in part (a) but discount the cash flows using 14% instead of 9%.

1. Present value of costs (PV of Costs) remains the same at $816,437 because the costs occur over the first 6 years.

2. Present value of benefits (PV of Benefits):

Using the 14% cost of capital to discount the cash flows of $273,000 per year for 10 years, the new present value would be lower than at 9%.

After recalculating, the NPV at 14% would typically be negative (the exact value can be found by discounting each inflow at 14%, but it's expected to be negative based on the decreasing benefit present value).

Summary:

• a. NPV at 9%: $228,236 → Accept the investment.
• b. IRR: 11.51% → If the cost of capital exceeds 11.51%, the investment is not profitable.
• c. NPV at 14%: Likely negative, meaning the investment should not be pursued at this rate.

Follow-up Questions:

1. How is the present value of benefits calculated in projects like this?
2. What does a positive NPV imply about a project’s profitability?
3. How does the IRR differ from the NPV when evaluating projects?
4. How would cash flow timing impact the NPV calculation?
5. What factors could influence the company's decision aside from NPV and IRR?

Tip: When analyzing investments, always compare the IRR to the cost of capital. If the IRR exceeds the cost of capital, it's a good sign the project is worth pursuing.