An asset under your management, with an estimated design life of $16$ years, cost $11,000,000$ to purchase and install. It has a revenue stream of $$2,700,000$ per year for each full year of operation.

Costs of operation and maintenance of this asset are as follows:

$$750,000$ per year for Years $1$ to $5$ of the life of the asset

$$850,000$ per year for Years $6$ to $11$ of the life of the asset

$$1,000,000$ per year for years $12$ to $14$ of the life of the asset

$$1,200,000$ for years $15$ and $16$ of the life of the asset.

As the asset is currently $15$ years old, and there is a lead time of twelve months for ordering and installing a new asset, or undertaking rehabilitation, a decision needs to be made soon with respect to the best option for its ongoing use. Condition monitoring information confirms that the asset is nearing the end of its design life and should be replaced once that life is reached.

The replacement process $($which commences when the asset has reached the end of its design life of $16$ years$)$ will take about six months. While the old asset will remain partially in service over the replacement period, revenue during the year in which the replacement is being undertaken $($Year $1$ of the replacement asset's life$)$ will reduce to $$1,900,000.$

The residual $($scrap$)$ value of the replaced asset is $$3,000,000.$ It will cost $$1,100,000$ to remove the asset from service when it is replaced.

Alternatively, the asset can be rehabilitated and upgraded at the end of $16$ years of service. The opportunity will be taken to improve the technology of the asset and to enhance the capacity of the asset. This process is expected to cost $$14,000,000$ and be completed within one year, during which the old asset will continue to remain in reduced service. The upgraded asset is then expected to last for $16$ years from the commencement of the rehabilitation process$).$

Costs of operation and maintenance of the rehabilitated and upgraded asset are expected to be as follows:

$$500,000$ for Year $1$ of the life of the upgraded asset $($i$.$e$.,$ the year in which rehabilitation takes, as there will still be some maintenance required for the existing asset, which will remain partially in service during this period$)$

$$1,200,000$ per year for Years $2$ to $7$ of the life of the upgraded asset

$$1,350,000$ per year for Years $8$ and $9$ of the life of the upgraded asset

$$1,800,000$ per year for Years $10$ to $16$ of the life of the upgraded asset.

The upgraded asset is expected to have a revenue stream of $$3,700,000$ per year, except in Year $1,$ when the upgrade process takes place.

The complexities of the rehabilitation and upgrading process mean that while the asset will continue to operate during the upgrade, there will be considerable service reduction during the rehabilitation and upgrading process. This revenue is expected to be $$1,700,000$ only, applicable to the first year of operation of the rehabilitated and upgraded asset only.

At the end of the life $(16$ years$)$ of the rehabilitated and upgraded asset, it must be replaced by a completely new asset. The costs incurred for this replacement are expected to be incurred by the new asset and are therefore not to be considered in the analysis process.

Funds are available for whatever option is selected.

Money costs $8\mathrm{.}0\%$ per annum. Assume zero inflation.

Your task

$($a$)$ Using at least two methods of comparing alternatives, including net present value, calculate the best option between replacing and rehabilitating this asset.

$($b$)$ Comment on your answer. Include in your comments an assessment of the advantages and disadvantages of each method you use to compare alternatives.

$($c$)$ Conduct a sensitivity analysis using different values of the discount rate, using the discount rates of $3\%$ per annum, $7\mathrm{.}5\%$ per annum, $12\%$ per annum and at least one $(1)$ other discount rate.

$($d$)$ Determine the discount rate at which the choice between replacement and rehabilitation of the asset after its life of $16$ years would be indifferent.

$($e$)$ Draw your results on a graph showing net present value of each of the two options $($replacement and rehabilitation$).$