A 30 year project is estimated to cost $35 million dollars and provide annual cash flows of $5 per year in years 1-5; $4 million per year in years 6-20 and $2 million per year in years 21-30. If the company's required rate of return is 10%, determine the discounted payback for the project.
A) 15.90 years
B) 13.90 years
C) 11.90 years
D) 9.90 years
E) 7.90 years

Question

Quizplus · Accepted Answer

To determine the discounted payback period for the project, we need to calculate the present value (PV) of the cash flows at the company's required rate of return (10%) and then find out how many years it takes for these discounted cash flows to cover the initial investment of $35 million.Years 1-5: $5 million per year$$ PV = \sum_{t=1}^{5} \frac{5}{(1+0.10)^t} $$Years 6-20: $4 million per year$$ PV = \sum_{t=6}^{20} \frac{4}{(1+0.10)^t} $$Years 21-30: $2 million per year$$ PV = \sum_{t=21}^{30} \frac{2}{(1+0.10)^t} $$Calculating these sums gives us the total present value of the cash flows. By adding the discounted cash flows year by year, we find the year in which the cumulative discounted cash flows equal or exceed the initial investment of $35 million. Given the complexity of the calculation and without providing the detailed math here, the correct answer is based on the calculation that matches the options provided. The discounted payback period is the time it takes for the project to break even in net present value terms, not just in nominal terms. For this question, the correct answer is 15.90 years, which means it takes nearly 16 years for the discounted cash flows to cover the initial investment, considering the time value of money at a 10% discount rate.

A 30 Year Project Is Estimated to Cost $35 Million