Question

An analyst has the following projected free cash flows for an investment: Year 1: $125,050; Year 2: $137,650; Year 3 to15: $150,000 a year; Year 16 to 20: $200,000 a year.

The investment is expected to have a terminal value of $500,000 at the end of Year 20.

If the analyst has estimated a present value of $3 millions for the investment, what is the discount rate that she/he has used in calculations.

A. % 1.37

B. % 1.78

C. % 2.12

D. % 3.25

Answer 1

B   1.78%

lets construc the cash flows given into a table, as given in the question

the 20th year CF wil be 700,000 = 200,000     +   500,000(terminal value)

lets find the NPV at any random rate- lets say 3 % For the above cash flows in excel using the NPV function as shown below:

the excel formulas are

as seen above, the NPV is at cell B24, based on the rate input at B23

but the NPV isnot equal to our given npv of 3million. so lets set the IRR which will yield an NPV of 3m using goal seek

lets use Goal seek function, to make our target NPV at B24 =   3,000,000, by changing the value in cell B23- which is our IRR rate

we enter the use goal seek as shown below

when we press enter- the NPV value changes to 3000000   and changing the IRR to 0.017873346 as shown below

so we got the desired IRR = 0.01787 X100    =1.78%