Question

What is the internal rate of return for the following:

(A) an initial outlay of $11,000 resulting in a single cash inflow of $25,648 in 11 years.

(B) an initial outlay of $9500 resulting in a cash inflow of $1912 at the end of each year for the next 8 years.

(C) an initial outlay of $10,500 resulting in a cash inflow of $1800 at the end of year 1, $4900 at the end of your 2 and $8400 at the end of year 3.

Answer 1

The answers are (I have given answers in 4 decimal places as well as 2 decimal places):

	A	B	C
IRR (4 decimal places)	7.9999%	11.9944%	16.3490%
IRR (2 decimal places)	8.00%	11.99%	16.35%

Calculations and explanations:

(a): Let the IRR be x%. Thus -11,000 + 25,648/(1+x)^11 = 0

or 25,648/(1+x)^11 = 11,000

or (1+x)^11 = 2.331636

or 1+x = 1.07999999

or x = 7.9999%

(b): Let the IRR be x%. Thus present value of $1912 for 8 years = 9500 under the IRR presmise.

so 1912/(1+x) + 1912/(1+x)^2 + 1912/(1+x)^3.......+1912/(1+x)^8 = 9500

Solving we get x = 11.9944% (11.99%).

Alternatively IRR function of excel can be used.

(c): Here let the IRR be "x"%. Thus 10500 = 1800/(1+x) + 4900/(1+x)^2 + 8400/(1+x)^3

Solving we get x = 16.3490% (or 16.35%)

We can use IRR function in excel.