Question

1. Determine the IRR of the following. (Hint: If you use the financial calculator app, there is an IRR and NPV calculator option). A) Define IRR. Provide an example of how companies may use it. B) An initial investment of $10,750 resulting in a free cash flow of $3,500 at the end of year 1, $2,000 at the end of year 2, and $7,000 at the end of year 3. C) An initial investment of $5,000 resulting in a SINGLE free cash flow of $38,077 after 10 years. D) An initial investment of $12,000 resulting in a free cash flow of $7,000 at the end of year 1 through 5 and $8,000 at the end of year 6.

Answer 1

1. Internal rate of return (IRR) is the interest rate at which the net present value of all the cash flows from an investment equal zero.

The formula for IRR if cash flows are at the end of year

0 = CF0 + CF1/ (1+IRR) ^1 + CF2/ (1+IRR) ^2+ CF3/ (1+IRR) ^3 + CF4/ (1+IRR) ^4 …… CFn/ (1+IRR) ^n

Where CF0, CF1, CF2, CF3, CF4….CFn are the cash flows for the respective periods 0, 1, 2, 3, 4 …. N

Companies use IRR calculations to check the viability of their projects. If IRR is more than the required rate of return then the projects are acceptable.

2. Internal rate of return (IRR) calculation:

Year	Cash Flow
0	-$10,750
1	$3,500
2	$2,000
3	$7,000
IRR	6.92%

Year	Cash Flow
0	-$5,000
1	$0
2	$0
3	$0
4	$0
5	$0
6	$0
7	$0
8	$0
9	$0
10	$38,077
IRR	22.51%

Year	Cash Flow
0	-$12,000
1	$7,000
2	$7,000
3	$7,000
4	$7,000
5	$7,000
6	$8,000
IRR	54.36%

Formulas used in IRR calculation in excel

1 Year Year 2 0 3 1 4 2 5 3 6 IRR Cash Flow - 10750 3500 2000 7000 =IRR(B2:35) Cash Flow - 12000 7000 7000 7000 7000 7000 8000 =IRR(E2:E8) 8 Year 90 10 1 Cash Flow -5000 IRR 11 2 12 3 13 4 14 5 15 6 16 7 이이이이이이이이이 17 8 18 9 19 10 20 IRR 38077 =IRR(B9:B19) 21