Question

An investment of $10,000 has an investment/inflow ratio of 6.2 and a useful life of12 years. What are the annual cash inflow and internal rate of return?

Answer 1

Answer:

Annual cash flow =  $1, 613

Internal rate of return = 12%

Explanation:

The internal rate of return ( I.R.R) is the discount rate that makes the present value of cash inflows to be equal to the present value of cash inflow.

The investment to inflow ratio = Investment

                                                       Annual cash inflow

                                              6.2 = 10,000

                                                          y

                          6.2 × y = 10,000

                                   y = 10,000/6.2

                                       = 1,613

Annual cash inflow = $1,613

The internal rate of return,for this question, is the discount rate that equates  the present value (PV) of $1, 613 for 12 years to 10,000

Present Value of Annuity = Annual cash flow × Annuity factor

10,000 =    1 612.9  ×  6.2.

Note that the annuity factor is given as  6.2

To determine the rate that produces an annuity factor of 6.2, we use the Present Value of Annuity table.

Using the table,

We locate 12 under column labeled " n " - i.e no of periods, we look up for the figure 6.2 in the row opposite 12. The closest figure found is 6. 1944. Finally, we look up ( look upward )to find the rate that produces this figure, and it is 12%.

Note : Using the table, the intersection of 12% and 12 years gives the annuity factor 6.2

Annual cash flow =  $1, 613

Internal rate of return = 12%