Rate of Return Method
RATE OF RETURN METHOD
The
rate of return of a cash flow pattern is the rate of interest at which the
present worth of the cash flow reduces to zero.
The
rate of return for each alternative is computed.
The
alternative which has the highest rate of return is selected as the best
alternative.
A generalized cash flow diagram to
demonstrate the rate of return method of comparison is presented in Fig.
 |
| Revenue dominated cash flow diagram |
Here,
P
= Initial investment
Rj
= Revenue at the end of the ‘j’th year
i
= Interest rate compounded annually
S
= Salvage value at the end of ‘n’th year
First step:
The
present worth amount of the above cash flow diagram for some interest rate i is
PW(i) = -P + R1[1/(1 + i)1]
+ R2[1/(1 + i)2] + ... + Rj[1/(1 + i) j] + Rn[1/(1 + i)n]
+ S[1/(1 + i)n]
The above equation can be simplified
as,
PW(i) = -P + R1 (P/F, i, 1) + R2
(P/F, i, 2) + . . . + Rj (P/F, i, J) + Rn (P/F, i, n) + S (P/F, i, n)
Incase if revenue is equal for all the
given years (R1 = R2 = … = Rj = Rn = A) then the above formula is rewritten as,
PW(i) = -P + A (P/A, i, n) + S
(P/F, i, n)
Second step:
The
above equation is evaluated for different values of i, until the present worth
changes from positive to negative.
Third step:
Then
the value of i is obtained using the following formula
Where,
i = Rate of
return interest
ij+1
= interest rate where present worth changes from positive to negative
ij
= interest rate before ij+1
PW(ij)
= present worth at ij
PW(ij+1) =
present worth at ij+1
