Final answer:
The discounted payback period is a financial metric used to determine the length of time it takes for an investment to recoup its initial cost in present value terms, considering the discounted cash flows. In this case, the initial investment for the new cruise ship is $400 million, and the annual cash flow for the next 10 years is $57 million. The discount rate is 5%.
Step-by-step explanation:
The discounted payback period is a financial metric used to determine the length of time it takes for an investment to recoup its initial cost in present value terms, considering the discounted cash flows. In this case, the initial investment for the new cruise ship is $400 million, and the annual cash flow for the next 10 years is $57 million. The discount rate is 5%.
To calculate the discounted payback period, we need to find the cumulative present value of the cash flows and determine the year in which the present value equals or exceeds the initial investment.
Using the discount rate of 5%, the present value of the cash flows for each year can be calculated using the formula PV = CF / (1 + r)^n, where PV is the present value, CF is the cash flow, r is the discount rate, and n is the year.
For example, to calculate the present value for the first year, PV = $57 million / (1 + 0.05)^1 = $54.29 million.
By summing the present values of the cash flows each year, we can determine the discounted payback period. Find the year in which the cumulative present value equals or exceeds the initial investment of $400 million. In this case, the discounted payback period is less than 10 years, so it will be less than the given time frame.
Hope this helps!