Risk$-$adjusted discount rates$$Basic Country Wallpapers is considering investing in one of three mutually exclusive projects, E$,$ F$,$ and G$.$ The firm$$s cost of capital, r$,$ is $10\%,$ and the risk$-$free rate, RF$,$ is $2\%.$

The firm has gathered the basic cash flow and risk index data for each project as shown in the following table.

Project $($j$)$

E

F

G

Initial Investment $($CF$0)$

$-$$$15,000$

$-$$$11,000$

$-$$$19,000$

Year $($t$)$

Cash Inflows

$1$

$$6,000$

$$6,000$

$$4,000$

$2$

$6,000$

$4,000$

$6,000$

$3$

$6,000$

$5,000$

$8,000$

$4$

$6,000$

$2\mathrm{.}000$

$12,000$

Risk index $($RIj$)$

$1\mathrm{.}80$

$1\mathrm{.}00$

$0\mathrm{.}60$

Find the net present value $($NPV$)$ of each project using the firm$$s cost of capital. Which project is preferred in this situation?

The firm uses the following equation to determine the risk$-$adjusted discount rate, RADR, for each project j: RADRj$=$Rf $+[$RIj x $($r$-$Rf$)]$

Where: Rf$=$risk free rate of return

RIj$=$risk index for project j

r$=$cost of capital

Substitute each project$$s risk index into this equation to determine its RADR.

Use the RADR for each project to determine its risk$-$adjusted NPV$.$ Which project is preferable in this situation?

Compare and discuss your finding in part a and c$.$ Which project do you recommend that the firm accept?