Question $1$ Non$-$Linear Taxes and Value Added by Risk Management

Case $1$: A firm purchases a capital asset $($for example production equipment$)$ at a cost of $$1$ billion $($Initial

capital expenditure that will be used for five years straight line depreciated with zero remaining value$)$

which generates an income $($after COGS and other expenses$)$ stream over a five$-$year period of either

$$132$ million. With probability $\frac{1}{2}$ firm incurs liability claims

$$532$ million. With probability $\frac{1}{2}$ firm does not incur liability claims

Assume the income streams with the probability in each year remains the same. $($The actual realization may

not the same$).$ Depreciation is straight$-$line $($i$.$e$.,$ equal installments over $5$ years$)$ and the tax rate shield from

depreciation is $200$ million per year. Assume the tax rate is $34\%$ for all levels of income. $($Note if the net

income zero or negative, the tax liability is zero as well. Also, negative net income does not necessarily

mean negative cash flows$).$ The discount rate is assumed to be $6\%.$ Please show how risk management can

add values to firm through reduction of expected tax payments.

Step $1$: Please determine the expected net cash flow from year $0($today$)$ to year $5.$

A$)$ To get the expected net cash flow, you need first to determine the EBT $($Earning before Tax$),$ which

is the income $($after COGS and other expenses$)$ minus depreciation, in each scenario in each year. Note

based on the assumption each year's potential income stream are the same, the EBT of each scenario in

each year also are the same. You just need write down for one year.

B$)$ Then apply the tax rate to determine the taxes payment in each scenario. $($You just need write

down one year$)$

C$)$ Then determine the net cash flow $($which is "income $($after COGS and other expenses$)-$ tax

payment"$)$ in each scenario and fill the following table.