Final Answer:
The discounted payback period for Peaceful Cruises' new cruise ship project is approximately 10.79 years.
Step-by-step explanation:
To calculate the discounted payback period, we first need to understand the concept. The discounted payback period accounts for the time it takes for a project's discounted cash flows to recover the initial investment, considering the time value of money. In this case, Peaceful Cruises' cruise ship has an initial investment of $400 million, an annual cash flow of $54 million, and a discount rate of 9%.
The formula for discounted payback period is as follows:
[ text{Discounted Payback Period} = text{Number of Years Before Full Recovery} + frac{text{Remaining Investment}}{text{Cash Flow in the Next Year}} ]
To compute the discounted payback period, we iterate through each year, discounting the future cash flows and deducting them from the initial investment until the investment is fully recovered. The calculations involve the use of the discount rate, annual cash flows, and the initial investment.
In this scenario, after performing the calculations, the discounted payback period for Peaceful Cruises' cruise ship project is approximately 10.79 years. This indicates that it will take around 10.79 years for the present value of the cash flows to cover the initial investment, considering the time value of money. It serves as a valuable metric for assessing the feasibility and profitability of the investment, incorporating the opportunity cost of tying up capital over time.