Assume compound interest unless otherwise stated. Problems $1-13$ must be solved with factors and$/$or Excel PV$,$ FV$,$ PMT$,$ NPER, or interest rate functions; you may not use NPV for these problems.Formulation $($including factors$)/$ calculations must be shown for credit. For each problem, include a cash flow diagram. If Excel is used for calculations, include the Excel formula$($s$)$ used.

$11.$ A automotive manufacturer has a $4-$year $($now to end of year $4)$ fixed price contract with a supplier for parts costing $$3$m 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$=10\%.$

B$.$ 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$)$

C$.$ An improvement in a production line cost $$80,000$ to implement at time $0,$ but will return $$20,000/$ year in cost savings and new revenues. At $$18\%$ interest, how many years will it take until the improvement project breaks even?

D$.$ A project has a complex set of cash flows associated with it$,$ with the net cash flow each years as follows: time $0$: $-$$$80$k; time $1$:$$40$k; time $2$: $$200$k; time $3$: $-$$$100$k; time $4-6$: $-$$$110$k each year; time$7$: $$30$k; time $8$: $$500$k$.$ At i$=10\%,$ find the equivalent P for this project.