# Exercise-13: Accounting rate of return (ARR) with uneven cash flows

Learning objective:
This exercise illustrates the computation of accounting rate of return (ARR) when a projects cash flows are uneven.

A project requiring an initial cost of \$650,000 is expected to generate the following cash flows over its 6-years life:

The project does not require any cash expenses. Depreciation is to be provided using a general straight line method. According to firm’s accounting policies, the salvage value is treated as the reduction in depreciable basis.

Required: Compute the project’s accounting rate of return (ARR) from above information.

## Solution:

### Step 1 – Computation of annual depreciation expenses:

(Cost – salvage value)/life of the asset
= (\$650,000 – \$20,000)/6
= \$10,5000

### Step 2 – Computation of average incremental annual income:

Average income = (45,000 + 115,000 + 195,000 + 145,000 + 75,000 + 7,000)/6
= \$97,000

### Step 3 – Computation of accounting rate of return (ARR):

#### If initial investment is used as denominator:

Accounting rate of return = Incremental accounting income/Initial investment
= \$97,000/\$650,000
= 14.92%

#### If average investment is used as denominator:

Accounting rate of return = Incremental accounting income/Average investment
= \$97,000/\$335,000*
= 28.96%

*Average investment in project:
(\$650,000 + \$20,000)/2
= \$335,000

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