Solve $1$d$,2$d$,3$d$,4$d$.$

$1$a$.$ Annuity EQ: Payback period $=$ Cost $/$ Annual cash flow

$1$b$.$ Rule: Accept the project if the $PP$ the cutoff period.

$1$c$.$ EX: Evaluate a project costing $$25,000$ and returning $$10,000$ annually for three years using the PP method and a $3-$year cutoff period. $PP=$$$25,\frac{000}{\text{\$}}10,000=2\mathrm{.}5$ years ACCEPT

$1$d$.$ Problem: Evaluate a project costing $$10,000$ and returning $$6000$ annually for two years using the PP method and a $1\mathrm{.}5-$year cutoff period.

$2$a$.$ Mixed$-$stream EQ: Payback period $=$ Last year before recovery $+($Shortfall $/$ Next year's cash flow$)$

$2$b$.$ Rule: Accept the project if the $PP$ the cutoff period.

$2$c$.$ EX: Evaluate a project costing $$25,000$ and returning $$12,000,$$$10,000$ and $$8000$ in years $1-3$ using the PP method and a $2-$year cutoff period. $PP=2+$$$\frac{3000}{\text{\$}}8000=2\mathrm{.}38$ REJECT

$2$d$.$ Evaluate a project costing $$10,000$ and returning $$5000,$$$4000$ and $$3000$ over years $1-3$ using the PP method and a $2\mathrm{.}5-$year cutoff period.

$3$a$.$ EQ: Discounted payback period $=$ Same as $"2$a$"$ after the inflows are discounted

$3$b$.$ Rule: Accept the project if the DPP $$ the cutoff period.

$3$c$.$ EX: Evaluate a project costing $$15,000$ and returning $$8000$ and $$10,000$ in years $1$ and $2$ using the DPP method, a $7\%$ discount rate and a $2-$year cutoff. DPP $=1+$$$\frac{7523}{\text{\$}}8734=1\mathrm{.}86,$ ACCEPT

$3$d$.$ Problem: Reevaluate the project in $"2$ d$"$ using the DPP method, an $8\%$ discount rate and a $2\mathrm{.}5-$year cutoff period.

$4$a$.EQ$ : Net present value $=PV$ of inflows $-$ Cost

$4$b$.$ Rule: Accept the project if the NPV $>$$$0.$

$4$c$.$ EX: Reevaluate the project in $"1c"$ using the NPV method and a $10\%$ discount rate.

$NPV=$$$24,869-$$$25,000=-$$$131,$ REJECT

$4$d$.$ Reevaluate the project in $"2d"$ using the NPV method and a $12\%$ discount rate.