Question

For the cash flow series below, calculate the external rate of return, using the return on invested capital approach with an investment rate of 14% per year.
Year Cash Flow, $
0 .......... 3000
1 .......... –2000
2 .......... 1000
3 ......... –6000
4 .......... 3800

Answer 1

Answer:

15.04%

Explanation:

When calculating the external rate of return, any excess cash flows are supposed to earn the MARR. It is used when there are multiple IRRs.

Year      Cash Flow

0             $3,000      

1             -$2,000       discounted at Year 0 = -$2,000/1.14 = -$1,754.39

2            $1,000        

3           -$6,000        discounted at Year 0 = -$6,000/1.14³ = -$4,049.83

4            $3,800      

total                         discounted at Year 0 = -$5,804.22

now we calculate the future value of our cash inflows:

Year      Cash Flow

0             $3,000      FV at end of Year 4 = $3,000 x 1.14⁴ = $5,066.88

2            $1,000          FV at end of Year 4 = $1,000 x 1.14² = $1,299.60

4            $3,800       FV at end of Year 4 = $3,800

total                         future value at end of Year 4 = $10,166.48

now we have the following equation:

-$5,804.22 x (1 + i)⁴ = $10,166.48

(1 + i)⁴ = $10,166.48 / -$5,804.22 = -1.751567

⁴√(1 + i) = ⁴√-1.751567

1 + i = 1.1504

i = 0.1504 = 15.04%