# Replacement Decision

Decision regarding replacement of an existing asset with another is based on the net present value and internal rate of return of the incremental cash flows, i.e. the difference between periodic net cash flows if the existing asset is kept and the periodic net cash flows if the asset is replaced.

In capital budgeting and engineering economics, the existing asset is called the defender and the asset which is proposed to replace the defender is called the challenger. Estimation of incremental cash flows for such replacement analysis involves calculation of net cash flows of the defender, net cash flows of the challenger and then finding the difference in cash flows for both the assets.

## Technique

Calculating periodic cash flows of existing asset is straight forward. Since the existing asset is already purchased, the initial investment outlay is zero and the periodic net cash flows are calculated based on the following formula:

Net cash flows = (revenue – operating expenses – depreciation) * (1 – tax rate) + depreciation

If the asset is replaced, it involves investment is the new asset and sale or disposal of the existing asset. Disposal of exiting asset has some income tax implications which need to be reflected in the calculation of initial investment as follows:

Initial investment after replacement = cost of new asset - sale proceeds of old asset +/- tax on disposal

Tax on disposed asset = (sale proceeds of old assets – book value of old asset) * tax rate

As evident from the equation above, if the old asset is sold at an amount higher than its book value, the company bears a related tax cost which is added to the initial investment. Similarly, if the sale proceeds are lower than the book value of the asset sold, there is a resulting tax shield which is subtracted from sum of cost of new asset and sale proceeds of the old asset.

## Example

M1-BUS operates buses on different inter-city routes. The management is considering upgrading its fleet of 50 standard buses (purchased at $8 million) which has a book value of $3 million. It expects to sell the existing fleet for $4 million and purchase a new fleet at a cost of $12 million. The existing revenue of the fleet is $4 million per annum which is expected to rise by 25% per annum if the new fleet is introduced. The existing operating cost of the fleet is $2 million which is expected to drop by 30% after up-gradation.

Determine if replacement is a good idea if the company’s weighted average cost of capital is 10% and the analysis period is 8 years. The company pays taxes at the rate of 33% and it charges depreciation on straight line basis.

__Solution__

In analysing whether to replace the fleet or not, we need to work out the net cash flows of the existing fleet and net cash flows after the replacement and then finding the difference between both to arrive at the incremental cash flows. The incremental cash flows are then used to calculate net present value and/or internal rate of return.

**Existing fleet**

Capital investment = 0

Revenue = $4 million

Operating cost = $2 million

Annual depreciation = $8 million/8 = $1 million

Periodic net cash flows = (revenue – operating cost – depreciation) * (1 – tax rate) + depreciation

Periodic net cash flows = ($4 million - $2 million - $1 million) * (1 – 33%) + $1 million = $1.67 million

**Replaced fleet**

Cost of new fleet = $12 million

Sale proceeds of old fleet = $4 million

Book value of old fleet = $3 million

Tax on sale of old fleet = ($4 million - $3 million) * 33% = $0.33 million

Net initial investment = $12 million – $4 million + $0.33 million) = $8.33 million

New revenue = $4 million * 1.25 = $5 million

New operating cost = $2 million * (1 – 10%) = $1.8 million

Depreciation expense on new fleet = $12 million/8 = $1.5 million

Periodic net cash flows = ($5 million - $1.8 million - $1.5 million) * (1 – 33%) + $1.5 million = $2.64 million

**Incremental cash flows**

Incremental cash flows at time 0 = net investment after replacement – net investment before replacement

Incremental cash flows at time 0 = $8.33 million – 0 = $8.33 million

Incremental cash flows in Year 1 to 8 = net annual cash flows after replacement – net annual cash flows before replacement

Incremental cash flows in Year 1 to 8 = $2.64 million - $1.67 million = $0.97 million

Calculating net present value and IRR:

NPV = PV factor for 8 years at 10% * incremental cash flows (Year 1-8) – incremental initial investment

NPV = 5.335 * $0.97 million – $8.33 million

NPV = -$3.15 million

IRR = -2%

Since the net present value is negative and IRR is way below the hurdle rate, it is not feasible to replace the fleet at this stage.

Written by Obaidullah Jan, ACA, CFAhire me at