Final answer:
The discounted payback period for Peaceful Cruises' investment is calculated by discounting future cash flows at 11% and summing them until they equal the $150 million investment. This tells us how many years it will take for the investment to pay for itself in today's dollars.
Step-by-step explanation:
To calculate the discounted payback period for Peaceful Cruises' new cruise ship investment, we need to discount the future cash flows at the given rate and then determine how long it takes for the sum of these discounted cash flows to recoup the initial investment. With an initial investment of $150 million and an annual cash flow of $29 million over 10 years at a discount rate of 11%, we discount each annual cash flow using the formula for present value: PV = C / (1 + r)^t, where C is the cash flow, r is the discount rate, and t is the time period in years.
The discounted payback period is the time it takes for the sum of the discounted cash flows to equal the initial investment. To find this, we calculate the cumulative discounted cash flow for each year until it equals or exceeds the initial investment. Once the cumulative sum reaches $150 million, that year signifies the discounted payback period.