Rob Roy Corporation has been using its present facilities at its annual full capacity of $10,000$ units for the last $3$ years. Still, the company is unable to keep pace with continuing demand for the product that is estimated to be $25,000$ units annually. This demand level is expected to continue for at least another $4$ years. To expand manufacturing capacity and take advantage of the demand, Rob Roy must acquire equipment costing $$1,000,000.$ The equipment will double the current production quantity. This equipment has a useful life of $10$ years and can be sold for $$200,000$ at the end of year $4$ or $$30,000$ at the end of year $10.$ Analysis of current operating data provides the following information:

Per Unit

Sales price $ $236$

Variable costs:

Manufacturing $ $97$

Marketing $10$ $ $107$

Fixed costs:

Manufacturing $ $45$

Other $2570177$

Pretax operating income $ $59$

The fixed costs include depreciation expense of the current equipment. The new equipment will not change variable costs, but the firm will incur additional fixed manufacturing costs $($excluding depreciation on the new machine$)$ of $$250,000$ annually. The firm needs to spend an additional $$200,000$ in fixed marketing costs per year for additional sales. Rob Roy is in the $35\%$ tax bracket. Management has set a minimum rate of return of $20\mathrm{.}0\%$ after$-$tax for all capital investments. Assume, for simplicity, that MACRS depreciation rules do not apply.

$8.$ Management has decided to invest in the new equipment but is unsure of the reliability of some of the estimates and as such has asked some $$what$-$if$$ questions. Treat each of the following two cases independently.

a$.$ By how much can the unit variable cost for units produced by the new equipment increase and still justify the purchase of the equipment $($i$.$e$.,$ have the investment generate an after$-$tax IRR of exactly $14\%,$ its cost of capital$)?($Do not round intermediate calculations. Round your final answer to $2$ decimal places.$)($Hint: the present value annuity factor from Appendix C Table $2$ for $4$ years, $20\mathrm{.}00\%$ is $2\mathrm{.}589.)$

b$.$ The company is anticipating an increase in competition. Management believes that, in response, it will have to reduce the selling price of the product. By how much can the firm decrease the per$-$unit selling price $($for all units sold$)$ and still be able to justify the purchase of the new equipment? What percentage decrease in selling price does this represent? $($Round your answers to $2$ decimal places $($i$.$e$.0\mathrm{.}1234=12\mathrm{.}34\%).)$