Sentry Company is contemplating the purchase of a new high$-$speed grinder to replace the existing grinder. The existing grinder was purchased $2$ years ago at an installed cost of $$60,000$; it is being depreciated under MACRS using a $5-$year recovery period. The existing grinder is expected to have a usable life of $5$ more years

$($hint: start depreciation expense in year $3$ since the existing grinder was purchased two years ago.$)$

The new grinder costs $$105,000$ and requires $$5,000$ of installation costs; it has a $5-$year usable life and would be depreciated under MACRS using a $5-$year recovery period.

The existing grinder can currently be sold for $$70,000$ without incurring any removal or cleanup costs. To support the increased business resulting from the purchase of the new grinder, the following would increase by respective amounts: accounts receivable by $$40,000,$ inventories by $$30,000,$ and accounts payable by $$58,000.$ At the end of $5$ years, the existing grinder is expected to have a market value of zero; the new grinder would be sold to net $$29,000$ after removal and cleanup costs and before taxes. The firm pays $40$ percent taxes on both ordinary income and capital gains.

The estimated profits before depreciation and taxes over the $5$ year for both the new and existing grinder are shown in the following table:

EBITDA

Year New Grinder Existing Grinder

$1$ $$43,000$ $$26,000$

$243,00024,000$

$343,00022,000$

$443,00020,000$

$543,00018,000$

a$.)$ Calculate the initial investment associated with the replacement of the existing grinder by the new one.

b$.)$ Determine the incremental operating cash inflows associated with the proposed grinder replacement.

c$.)$ Determine the terminal cash flow expected at the end of year $5$ from the proposed grinder replacement.

d$.)$ Depict on a time line the relevant cash flows associated with the proposed grinder replacement decision.

e$.)$ Calculate Payback, IRR, NPV assuming cost of capital of $12\%$ and MIRR assuming a reinvestment rate of $12\%.$

f$.)$ Explain the difference between Modified Internal Rate of Return $($MIRR$)$ and IRR.

g$)$ State and explain your recommendation on proposed capital expenditure.