Question

An investment has an initial cost of $3.2 million. This investment will be depreciated by $900,000 a year over the 3-year life of the project. Should this project be accepted based on the average accounting rate of return (AAR) if the required rate is 10.5 percent? Why or why not?

years----------------net income

1------------------------ 211700

2 -----------------------186400

3---------------------- 165500

Answer 1

Solution:

The Average accounting return is calculated using the formula

= Average Net Income / Average Investment

Calculation of Average Net Income:

As per the Information given in the question we have

Net Income Year 1 : $ 211,700

Net Income Year 2 : $ 186,400

Net Income Year 3 : $ 165,500

No. of years = 3

Thus Average Net income = ( Sum of Net Income earned from Year 1 to Year 3 ) / No. of years

= ( $ 211,700 + $ 186,400 + $ 165,500 ) / 3

= $ 563,600 / 3

= $ 187,866.6667

Thus the Average Net Income = $ 187,866.6667

Calculation of Book value of the end of Year 3:

As per the information given in the question we have

Initial Cost = $ 3,200,000

Depreciation per year = $ 900,000

No. of years = 3

Total depreciation for 3 years = $ 900,000 * 3 = $ 2,700,000

Thus the Book value at the end of Year 3 = Initial cost – Total depreciation for 3 years

= $ 3,200,000 - $ 2,700,000

= $ 500,000

Thus the Book value at the end of Year 3 = $ 500,000

Calculation of Average Investment:

Average Investment = ( Initial Book value + Book value at end of Year 3 ) / 2

= ( $ 3,200,000 + $ 500,000 )/ 2

= $ 3,700,000 / 2

= $ 1,850,000

Applying the above values in the Average accounting rate of return formula we have:

The Average Accounting Return = Average Net Income / Average Investment

= $ 187,866.6667 / $ 1,850,000

= 0.1015

= 10.15 %

Thus the Average accounting rate of return = 10.15 %

The required rate of return = 10.50 %

A project should be accepted only if the Average accounting rate of return is greater than or equal to the required rate of return.

Since the average accounting rate of return at 10.15 % is less than the required rate of return of 10.50%, the project should not be accepted.