Assume compound interest unless otherwise stated. Must be solved with factors and$/$or Excel PV$,$ FV$,$ PMT$,$ NPER, or interest rate functions; you may not use NPV$.$

Formulation $($including factors$)/$ calculations must be shown. For each problem, include a cash flow diagram. If Excel is used for calculations, include the Excel formula$($s$)$ used.

a$.$ A new process costs $$140,000$ to install at time $0$ and $$60,000$ at time $1.$ It will then save the company $$50k$ per

year for years $2-10.$ Equipment in the process will require turnarounds $($maintenance events$)$ in year $5($costing $$25k)$

and year $9($costing $$35k).$ At $14\%$ interest, what is the equivalent present worth of this project? Also, at this interest

rate, is the project worth doing? $($explain why or why not$)$

b$.$ A automotive manufacturer has a $4-$year $($now to end of year $4)$ fixed price contract with a supplier for parts

costing $$3m$ per year. Once the contract ends, the cost is expected to rise at $4\%$ per year through year $10.$ Find the

equivalent $P$ and A for these cashflows at $i=10\%.$

c$.$ A investment costs $$13,000$ at time $0$ to implement, but will return $$4,000$ at end of year $1,$$$6,000$ at end of year

$2,$ and $$19,000$ at end of year $5.$ What is the rate of return on this investment? $($hint: use IRR function in Excel$)$