Solved problem on future worth method - 3
Solved problem on future worth method - 3
The
cash flow diagram of two alternatives shown in figure 1 and figure 2.
Figure 1
Figure 2
Evaluate the alternatives based on future
worth method at i = 10%, compounded annually and select the best one.
Given data
Method
= Future worth method - revenue dominated cash flow
i
= 10%
Alternative 1
P
= ₹. 7,00,000
R1
= ₹. 50,000
R2
= ₹. 1,00,000
R3
= ₹. 1,50,000
R4=
₹. 2,00,000
R5
= ₹. 2,50,000
R6
= ₹. 3,00,000
A1
= ₹. 50,000
G
= ₹. 50,000
n
= 6 years
S
= ₹.0
Alternative 2
P
= ₹. 9,00,000
R1
= ₹. 60,000
R2
= ₹. 1,20,000
R3
= ₹. 1,80,000
R4=
₹. 2,40,000
R5
= ₹. 3,00,000
R6
= ₹. 3,60,000 ₹
A1
= ₹. 60,000
G
= ₹. 60,000
n
= 6 years
S
= ₹.0
Formula used
Here
revenue on all years is in an incremental order. So need to convert it into
annual equal amount.
A
= A1 + G (A/G, i, n)
FW(i)
= -P (F/P, i, n) + A (F/A, i, n) + S
Solution
Alternative 1
A = 50,000 + 50,000 (A/G, 10%, 6)
= 50,000 + 50,000 (2.2236)
= 50,000 + 1,11,180
A = ₹.
1,61,180
FW(10%)1 = - 7,00,000 (F/P, 10%, 6) + 1,61,180
(F/A, 10%, 6) + 0
= - 7,00,000 (1.949)+ 1,61,180
(7.716)
= - 13,64,300 + 12,43,664.88
FW(10%)1 = ₹. -1,20,635.12
Alternative 2
A = 60,000 + 60,000 (A/G, 10%, 6)
= 60,000 + 60,000 (2.2236)
= 60,000 + 1,33,416
A = ₹.
1,93,416
FW(10%)2 = - 9,00,000 (F/P, 10%, 6) + 1,93,416
(F/A, 10%, 6) + 0
= - 9,00,000 (1.949) + 1,93,416
(7.716)
= - 17,54,100 + 14,92,397.856
FW(10%)2 = ₹ -2,61,702.144
Result
In future worth
method revenue dominated cash flow, the alternative which has maximum future
worth amount is the best alternative. Therefore alternative 1 is the best
alternative. (Note: Here both the alternative is given negative result. So both
can be rejected.)
