You are considering investing in a start up company. The founder asked you for ​$290 comma 000 today and you expect to get $ 930 comma 000 in 14 years. Given the riskiness of the investment​ opportunity, your cost of capital is 30 %. What is the NPV of the investment​ opportunity? Should you undertake the investment​ opportunity? Calculate the IRR and use it to determine the maximum deviation allowable in the cost of capital estimate to leave the decision unchanged.

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.

You are considering investing in a start up company. The founder asked you for $290,000 today and you expect to get $930,000 in 14 years. Given the riskiness of the investment opportunity, your cost of capital is 30%. What is the NPV of the investment opportunity? Should you undertake the investment opportunity? Calculate the IRR and use it to determine the maximum deviation allowable in the cost of capital estimate to leave the decision unchanged.

Explore the NPV and IRR calculations for a startup investment opportunity. With a $290,000 upfront cost and an expected return of $930,000 in 14 years, learn whether this investment is worthwhile given a 30% cost of capital. Detailed analysis includes NPV (-$266,380.21) and IRR (8.68%).

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