To evaluate the investment opportunity, we will calculate the Net Present Value (NPV) and the Internal Rate of Return (IRR) to guide the decision-making process. Here's the approach:

1. NPV Calculation:

The formula for NPV is:

$\text{NPV} = \sum \left( \frac{C_t}{(1 + r)^t} \right) - C_0$

Where:

• $C_t$ = future cash flow at time $t$ (in this case, $930,000 at $t = 14$)
• $r$ = cost of capital (30% or 0.30)
• $C_0$ = initial investment ($290,000)
• $t$ = time period (14 years)

We will calculate the present value of the future cash flow and subtract the initial investment.

2. IRR Calculation:

The IRR is the discount rate that makes the NPV of the investment equal to zero. The formula for IRR is:

$\text{NPV} = 0 = \frac{C_{14}}{(1 + \text{IRR})^{14}} - C_0$

Solving for IRR will give us the rate of return at which the project breaks even.

3. Maximum Allowable Deviation:

The IRR also tells us the maximum deviation allowable in the cost of capital estimate. If the cost of capital is below the IRR, the project will still have a positive NPV, and if it exceeds the IRR, the project should be rejected.

Let's now calculate both NPV and IRR.### Results:

1. NPV Calculation:

   • The NPV of the investment opportunity is −$266,380.21. Since the NPV is negative, this suggests that the investment will result in a loss based on the current cost of capital (30%).

2. IRR Calculation:

   • The Internal Rate of Return (IRR) is approximately 8.68%. This is the rate at which the NPV becomes zero.

Decision:

• Since your cost of capital is 30%, which is much higher than the IRR (8.68%), you should not undertake this investment opportunity.
• Maximum allowable deviation in the cost of capital: If the cost of capital is above the IRR (8.68%), the investment will have a negative NPV. Therefore, the cost of capital can only be lower than 8.68% for this investment to be worthwhile.

Would you like further details on any part of the calculation or the concepts?

Related Questions:

1. How is the cost of capital estimated for an investment?
2. What is the significance of NPV in investment decisions?
3. How can a negative NPV impact long-term financial planning?
4. Why does the IRR differ from the cost of capital in risky investments?
5. What factors influence the IRR of a project?

Tip:

The higher the risk of an investment, the higher the required rate of return (cost of capital) to compensate for that risk.