What is the approximate annual rate of return on an investment with...

 

What is the approximate annual rate of return on an investment with an initial cash outlay of $ 10 000 and net cash inflows of $ 2770 per year for 5 years ?

The approximate annual rate of return = 11.94%

Step-by-step explanation

The annual rate of return is the rate that discounts expected cash flows to the level of the initial investment.

The rate is also referred to as IRR.

To calculate the annual rate of return, we use both the interpolation method and the trial and error methods.

IRR = A + {P/ (P + N)} * (B - A)

Where;

A - Rate that gives a positive NPV

B - Rate that gives a negative NPV

P - Positive NPV

N - Negative NPV

NPV = C * {1 - (1 + r) ^{- n}}/ r - initial cost

Where;

C - Expected cash flows

r - Annual rate of return

n - Time

Try r = 9%

NPV = 2,770 * {1 - (1.09) ^{- 5}}/ 0.09 - 10,000

         = 2,770 * 3.8897 - 10,000

        = $774.33

Try r = 12%

NPV = 2,770 * {1 - (1.12) ^{- 5}}/ 0.12 - 10,000

         = 2,770 * 3.6048 - 10,000

        = - $14.77

Annual rate of return = 9% + {774.33/ (774.33 + 14.77)} * (12 - 9) %

                = 9% + 0.981282 * 3%

                = 11.94%

The approximate annual rate of return = 11.94%