Your firm is considering an investment that will cost $920,000 today.The investment will produce cash flows of $450,000 in year 1,$270,000 in years 2 through 4,and $200,000 in year 5.The discount rate that your firm uses for projects of this type is 11.25%.What is the investment's equivalent annual annuity?
A) $52,377
B) $42,923
C) $41,387
D) $40,399

Question

Quizplus · Accepted Answer

The equivalent annual annuity is the equal annual cash flow that would have the same present value as the investment's actual cash flows. To calculate the equivalent annual annuity, we can use the following formula:Equivalent annual annuity = Present value of cash flows / Present value factorThe present value of the cash flows is the sum of the present values of each individual cash flow. The present value factor is the sum of the present value factors for each year.The present value of the cash flows is:$450,000 / (1 + 0.1125)^1 + $270,000 / (1 + 0.1125)^2 + $270,000 / (1 + 0.1125)^3 + $270,000 / (1 + 0.1125)^4 + $200,000 / (1 + 0.1125)^5 = $1,238,765.23The present value factor is:1 / (1 + 0.1125)^1 + 1 / (1 + 0.1125)^2 + 1 / (1 + 0.1125)^3 + 1 / (1 + 0.1125)^4 + 1 / (1 + 0.1125)^5 = 3.60477The equivalent annual annuity is:$1,238,765.23 / 3.60477 = $52,377.00Therefore, the investment's equivalent annual annuity is $52,377.

Your Firm Is Considering an Investment That Will Cost $920,000