A project with a 3-year life has the following probability distributions for possible end of year cash flows in each of the next three years: Using an interest rate of 8 percent, find the expected present value of these uncertain cash flows.(Hint: Find the expected cash flow in each year, then evaluate those cash flows.)

Question

A project with a 3-year life has the following probability distributions for possible end of year cash flows in each of the next three years:  Using an interest rate of 8 percent, find the expected present value of these uncertain cash flows.(Hint: Find the expected cash flow in each year, then evaluate those cash flows.)

Quizplus · Accepted Answer

To find the expected present value of the uncertain cash flows, we need to find the expected cash flow in each year first.
Year 1:
Expected cash flow = (0.20 x R1,000) + (0.50 x R1,500) + (0.30 x R2,000) = R1,550
Present value of year 1 cash flow = R1,550 / (1.08^1) = R1,435.19
Year 2:
Expected cash flow = (0.40 x R1,500) + (0.50 x R1,700) + (0.10 x R2,200) = R1,595
Present value of year 2 cash flow = R1,595 / (1.08^2) = R1,365.96
Year 3:
Expected cash flow = (0.30 x R1,800) + (0.40 x R2,100) + (0.30 x R2,500) = R2,070
Present value of year 3 cash flow = R2,070 / (1.08^3) = R1,736.88

Expected present value of uncertain cash flows = Present value of year 1 cash flow + Present value of year 2 cash flow + Present value of year 3 cash flow
= R1,435.19 + R1,365.96 + R1,736.88
= R4,538.03

So, the expected present value of the uncertain cash flows is R1,347.61.
The best choice is E.

A Project with a 3-Year Life Has the Following Probability