Your division is considering two projects with the following cash flows $($in millions$)$:

$0123$

$|----------------------|--------------------------|-----------------------------|$

Project A $-$ $$25$ $$5$ $$10$ $$17$

Project B $-$ $$20$ $$10$ $$9$ $$6$

What are the projects$$ NPVs assuming the WACC is $5\%?10\%?15.\%?$

What are the projects' IRRs at each of these WACCS?

If the WACC was $5\%$ and A and B were mutually exclusive, which project would you choose? What if the WACC was $10\%?15\%?($Hint: The crossover rate is $7\mathrm{.}8\%)$

Solution

Expert$-$verified

WACC.B $5\%$

$3\mathrm{.}5240$

$6-163$

$9\mathrm{.}0100$

$210$

$5.18$:$0$

$4,6846$

$3$ $$17$

$29,5166$

S$\mathrm{.}6000$

$3,5166$

ToelPv

$,0000$

$9\mathrm{.}0698$

loy

nmildions

$090954$Sn Mlutons

PV

$45\mathrm{.}866360$

$210$ $$9$

$1,6360$

$6\mathrm{.}8049$

$3.3450$

O $657$sI$\mathrm{.}1775$

$.0865|134959$

$35\mathrm{.}000$m $|$SD$0000$

$-$$$\backslash \backslash ,9135|0\mathrm{.}55$W

Px $(12-$l$0)$

Reloy. o$,$s$616$

$5160\mathrm{.}4629$

T$.$ouys

TRR$..10\%+1,11\%$

IKK$-11-11\%$

$11,11\%$

$0\mathrm{.}9091$ $$996968.-696$o

$|0\mathrm{.}8269|3743$Z$610756/($CO

& $8698$

t$\mathrm{.}036$

$0\mathrm{.}5541$

$5\%$

$10\%$

$|5\%$

$$3\mathrm{.}5166$

$0\mathrm{.}5816$

$-$$ $1\mathrm{.}9135$

IRR fir Prject B $-13\mathrm{.}26\%$

$(11-11\%>5$ x$)$

O$-$S$816)$

$($$$1,0364$ Vs

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Step $1$

NPV $=\backslash$sum$\_\{$t$=0\}^\{$n$\}\backslash$frac$\{$CF$\_$t$\}\{(1+$ r$)^$t$\}$

Explanation:

Net Present Value $($NPV$)$ is calculated by summing the present values of all cash flows $($CF$)$ from time $0$ to n$,$ discounted back at the required rate of return, r$.$

Step $2$

Step $3$

Step $4$

Step $5$

Step $6$

Answer

Calculate NPV for both projects at $5\%,10\%,$ and $15\%$ WACC. The project with the higher NPV at each WACC should be chosen if they are mutually exclusive. Calculate IRR for both projects to determine their profitability.

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