Question

Present Value of Ordinary Annuity Period/Rate 5% 6% 7% 8% 9% 10 7.7217 7.3601 7.0236 6.7101 6.4177 11 8.3064 7.8869 7.4987 7.1390 6.8052 12 8.8633 8.3838 7.9427 7.5361 7.1607 13 9.3936 8.8527 8.3577 7.9038 7.4869 Knowledge Check 01 Clean Tel, Inc. is considering investing in an 11-year project with annual cash inflows of $1,000,000. These cash inflows have an initial investment of $7,139,000. At what discount rate would this present value be the same as the initial investment

Answer 1

Answer:

The discount rate of 8% for 11 year period provides the present value of annual cash flows to be equal to the initial investment.

Explanation:

Using the table of present value of annuity provided, we can check the rate and time period which is return the present value of cash flows from the project to be equal to initial Investment.

We are told that the Project's life is expected to be 11 Years. Thus using the 11 year period from the table we can see the following rates,

11 Year Period

Rate = 5%  ,  Annuity Factor = 8.3064  

Rate = 6%  ,  Annuity Factor = 7.8869

Rate = 7%  ,  Annuity Factor = 7.4987

Rate = 8%  ,  Annuity Factor = 7.1390

Rate = 9%  ,  Annuity Factor =  6.8052

We know that the annual cash flows from the project is $1,000,000 and we know the Initial Outlay is $7,139,000.

Multiplying the annual cash flow from the above annuity factors for each rate we can see which rate provides the present value of annual cash flows to be equal to initial outlay.

Rate = 5%  ,  Present value = 8.3064 *  1000000    = $8,306,400  

Rate = 6%  ,  Annuity Factor = 7.8869 *  1000000    = $7,886,900

Rate = 7%  ,  Annuity Factor = 7.4987 *  1000000    = $7,498,700

Rate = 8%  ,  Annuity Factor = 7.1390 *  1000000    = $7,139,000

Rate = 9%  ,  Annuity Factor =  6.8052 *  1000000    = $6,805,200

From the above calculation we can see that the rate of 8% provides the present value of annual cash flows to be equal to the initial investment.