ROIC is defined as a rate$-$of$-$return measure of how effectively a project utilizes the funds invested in it$,$ that is the funds remain internal to the project. The ROIC rate, which has a symbol of i$$ is determined using an approach called the net$-$investment procedure.

It involves developing a series of future worth $($F$)$ relations moving forward $1$ year at a time. In those years, if the net balance of the project cash flows is positive $($extra funds generated by the project$),$ the funds are invested at a rate called investment rate ii$.$ When the net balance is negative, ROIC is used.

The following method is used to determine ROIC and the viability of the project.

STEP $1$ Develop a series of future worth relations by setting up the following relation for each year t $($t $=1,2,3,....,$ n years$)$

Ft $=$ Ft$-1(1+$k$)+$ NCFt

Where Ft $=$ Future worth in year t based on previous year and time value of money

NCFt $=$ Net cash flow in year t

k $=$ ii if Ft$-1>0$ or i$$ if Ft$-1<0$

STEP $2-$ Set the Fn $=0$ to obtain ROIC for a given investment rate.

STEP $3$ If ROIC $>=$ MARR $($project is economically justified$),$ otherwise it is not justified.

Given the description above, determine the ROIC for the given cash$-$flow. MARR $=9\%,$ investment rate ii $=12\%$ per year

Year $0123$

NCF $+2000-500-8100+6800$

$($a$)$ Solution by Hand

$($b$)$ Optional $$ Solution using excel sheet $($Not graded$).$