Question

# Our refinery has a remaining life of 3 years, and is fully utilised processing 1.5 million...

Our refinery has a remaining life of 3 years, and is fully utilised processing 1.5 million barrels of crude oil per annum at a processing cost of \$10.00 real per barrel. By modifying the refinery at a cost of \$6 million we can reduce the processing cost to \$8.50 real per barrel. We can depreciate this capital cost fully on a straight line basis over the residual 3-year life of the operation. The corporate tax rate is 30%. Should we modify the plant if our real discount rate is 5% and we expect inflation to be 1.75%?

Annaul cost saving (\$M) = 1.5 x (10 - 8.5) = 1.5 x 1.5 = 2.25

Annual depreciation (\$M) = Cost / Life = 6/3 = 2

After-tax income (\$M) = (Cost saving - Depreciation) x (1 - Tax rate) = (2.25 - 2) x (1 - 0.3) = 0.25 x 0.7 = 0.175

After-tax cash flow (\$M) = After-tax income + Annual depreciation = 0.175 + 2 = 2.175

Nominal interest rate = Real rate + Inflation rate = 5% + 1.75% = 6.75%

So,

NPW (\$M) = - 6 + 2.175 x P/A(6.75%, 3) = - 6 + 2.175 x 2.6363** = - 6 + 5.73 = - 0.27

Since NPW < 0, we should not modify.

**P/A(6.75%, 3) = [1 - (1.0675)-3] / 0.0675 = (1 - 0.8220) / 0.0675 = 0.1780 / 0.0675 = 2.6363

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