$3.$ Although seven years is the average life for physiotherapy equipment, Boothe knows that due to changing technology this life can vary substantially. Compute the IRR to one decimal place if the life of the equipment were $($a$)$ five years and $($b$)$ nine years, rather than seven years. $($Hint: Use Microsoft Excel to calculate the discount factor$($s$).)($Do not round intermediate calculations and round your final answers to the nearest whole number.$)$

$4.$ Boothe is unsure about the estimated $$70,000$ annual cash inflow from the room. She thinks that the actual cash inflow could be as much as $15\%$ greater or less than this figure.

a$.$ Assume that the actual cash inflow each year is $15\%$ greater than estimated. Recompute the IRR to one decimal place using the seven$-$year life. $($Hint: Use Microsoft Excel to calculate the discount factor$($s$).)($Do not round intermediate calculations and round your final answers to the nearest whole number.$)$

b$.$ Assume that the actual cash inflow each year is $15\%$ less than estimated. Recompute the IRR to one decimal place using the seven$-$year life. $($Hint: Use Microsoft Excel to calculate the discount factor$($s$).)($Do not round intermediate calculations and round your final answers to the nearest whole number.$)$

$5.$ Refer to the original data. Assume that the equipment is purchased and that the room is opened for use. However, due to an increasing number of physiotherapists in the area, the clinic is able to generate only $$60,000$ per year in net cash receipts from the new room. At the end of five years, the clinic closes the room and sells the equipment to a company for a cash price of $$120,000.$ Compute the IRR to one decimal place that the clinic earned on its investment over the five$-$year period. $($Hint: Use Microsoft Excel to calculate the discount factor$($s$).$ A useful way to proceed is to find the discount rate that will cause the net present value of the investment to be equal to$,$ or near, zero$).($Do not round intermediate calculations and round your final answers to the nearest whole number.$)$