UF Company is considering Projects S and L$,$ whose cash flows are shown below. These projects are mutually exclusive, equally risky, and are not repeatable. WACC: $7\mathrm{.}75\%$

Year $01234$

CFS $($$$1,050)$ $$700$ $$625$

CFL $($$$1,050)$ $$370$ $$370$ $$360$ $$3604)$ Find the crossover rate $$ For example, suppose Hancock Company needs to choose one of the mutually exclusive projects, Project D

and Project I, which are expected to generate the following net cash flows; WACC $($k$)$ is $8\%$

Ranking Problem: Different Cash Flow Patterns

k$=8\%$

$0123$ Sum of Cash Inflows NPV IRR

Project D $($$$1,200)1,0005001001,600$ $$233\mathrm{.}9822\mathrm{.}79\%$

Project I $($$$1,200)1006001,0801,780$ $$264\mathrm{.}3316\mathrm{.}93\%$

D$-$I$($Diff$)$ $$0$ $$900($$$100)($$$980)$ Crossover Rate $10\mathrm{.}05\%$

End of Year

Net Cash Flows

$$ crossover rate: $=$IRR$($C$5$:F$5)$ in Excel formula.

$$If we use the IRR method, we should select Project D$,$ but if we

appy the NPV method, we should select Project I. $$ contradiction $!!$

NPV Profiles for Project D and I

$-300$

$-200$

$-100$

$0$

$100$

$200$

$300$

$400$

$500$

$600$

$700$

$024681012141618202224$

Discount Rate $(\%)$

NPV $($$$)$

IRRI $=16\mathrm{.}93\%$

Crossover rate $($CR$)=$

$10\mathrm{.}05\%$

Project D

Project I

IRRD$=22\mathrm{.}79\%$

Conflict Range!

$$ Crossover Rate$($CR: Fisher$$s Rate of Intersection$)$

$$ Represents the rate at which the projects have identical

NPV$.$

$$ How to get it$?$Find the IRR of the differences between

the CF of the two projects $$ We have $10\mathrm{.}05\%$

Dr$.$ Song