To solve this, we will calculate the Net Present Value (NPV) of the cash flows for both scenarios with discount rates of 6.9% and 2.9%. The formula for NPV is:

$NPV = \sum \frac{CF_t}{(1 + r)^t} - \text{Initial Investment}$

where:

• $CF_t$ is the cash flow at time $t$,
• $r$ is the discount rate (cost of capital),
• $t$ is the time in years.

Given:

• Initial Investment = $11,300 (at $t = 0$)
• Cash flows = $565 at $t = 1$, $1,695 at $t = 2$, and $11,300 at $t = 10$

Let's calculate the NPV for both discount rates.

Part (a): NPV with a 6.9% Discount Rate

1. NPV Calculation: $NPV = \frac{565}{(1 + 0.069)^1} + \frac{1695}{(1 + 0.069)^2} + \frac{11300}{(1 + 0.069)^{10}} - 11300$

2. Decision: If the NPV is positive, the investment is worthwhile.

Part (b): NPV with a 2.9% Discount Rate

1. NPV Calculation: $NPV = \frac{565}{(1 + 0.029)^1} + \frac{1695}{(1 + 0.029)^2} + \frac{11300}{(1 + 0.029)^{10}} - 11300$

2. Decision: Again, if the NPV is positive, the investment is worthwhile.

Let’s calculate these values.### Results:

1. NPV with 6.9% Discount Rate: -$3,489.91

   • Decision: Since the NPV is negative, this investment is not recommended at a 6.9% discount rate.

2. NPV with 2.9% Discount Rate: -$659.78

   • Decision: The NPV is still negative at a 2.9% discount rate, so the investment is not recommended even with the lower cost of capital.

Would you like a breakdown of the calculations or have further questions?

Additional Questions:

1. How would changing the initial investment affect the NPV?
2. What if the final cash flow at $t = 10$ increased or decreased by 10%?
3. How sensitive is the NPV to different discount rates?
4. Could increasing intermediate cash flows (e.g., at $t = 1$ or $t = 2$) improve the investment decision?
5. How would the NPV change if the investment period extended beyond ten years?

Tip:

A negative NPV indicates that the present value of cash inflows is insufficient to cover the initial investment cost at the given discount rate.