Final answer:
The NPV is calculated at different costs of capital to assess whether Dane Cosmetics should invest in a new fragrance-mixing machine. If the NPV is positive, the investment is financially justifiable; if negative, the investment should be rejected. Changes in the cost of capital affect NPV and the investment decision.
Step-by-step explanation:
Evaluating Investment Decisions through NPV
To evaluate whether Dane Cosmetics should invest in a new fragrance-mixing machine, we must calculate the Net Present Value (NPV) of the investment at different costs of capital and then decide to accept or reject the investment based on the NPV results.
The machine requires an initial investment of $24,000 and will generate after-tax cash inflows of $5,000 per year for 8 years. To calculate the NPV, we discount the future cash inflows back to their present value at the given cost of capital and subtract the initial investment.
For a cost of capital at:
10%, the NPV calculation uses a discount factor that reflects a lower present value for future cash flows than at higher interest rates. Typically, an NPV greater than 0 indicates that an investment is worthwhile, thus it must surpass $24,000 when discounted at 10%.
- 12%, similar calculation applies, but the discount factor is higher, resulting in a smaller NPV, because future cash flows are discounted at a higher rate, making it harder for the project to show a positive NPV.
- 14%, the discount factor increases even more, further reducing the NPV, signifying an even lesser attraction for the investment as the cost of capital rises.
If the NPV is positive for a given cost of capital, we accept the investment as it indicates the project is expected to generate a return higher than the cost of the capital invested. Conversely, a negative NPV would suggest that the project does not meet the basic financial criteria for investment and should be rejected.