A 25- year project has a cost of $1,500,000 and has annual cash flows of $400,000 in years 1-15, and $200,000 in years 16-25. The company's required rate is 14%. Given this information, calculate the discounted payback of the project.
A) 5.5 years
B) 5.70 years
C) 5.90 years
D) 6.10 years
E) 6.30 years

Question

Quizplus · Accepted Answer

The discounted payback period is the time it takes for the discounted cash flows to pay back the initial investment. To calculate this, we discount each cash flow at the company's required rate of 14% and then sum these until we cover the initial investment of $1,500,000.For years 1-15, the annual cash flow is $400,000. The present value (PV) of these cash flows can be calculated using the formula PV = CF / (1 + r)^n, where CF is the cash flow, r is the discount rate (14% or 0.14), and n is the year.For years 16-25, the annual cash flow is $200,000, and we calculate the PV similarly.By summing the PVs year by year, we find that the initial investment is paid back between years 5 and 6. Precisely calculating, the payback happens in approximately 5.70 years, considering the exact time the cumulative discounted cash flows equal or exceed the initial investment.

A 25- Year Project Has a Cost of $1,500,000 and Has