Solve the problem given in Example 5.2 by E.R.R. method.
Chapter 5
Q. 5.10
Step-by-Step
Verified Solution
Step 1: The cash flow diagram for the given problem is shown in Fig. 5.2.
Step 2: Since a specific value of e is not given take e = M.A.R.R. = 10\%.
Step 3: All cash outflows (negative cash flows/expenditures) are discounted to period 0 (the present) at e\% in the following manner:
=₹1,05,815.4+₹30,000\left(3.7908\right)
=₹2,19,539.4
Step 4: All cash inflows (positive cash flows/receipts) are compounded to period n (the future) at e\% in the following manner:
=₹53,000\left(6.1051\right)+₹30,000
=₹3,53,570.3
Step 5: The result of this step is given as:
₹2,19,539.4=₹3,53,570.3Step 6: The L.H.S. of the equation given at Step 5 represents present worth whereas its R.H.S. represents future worth. Therefore, the two sides cannot be equal. Introduce the factor \left(F/P,i^{\prime}\% ,n\right) on to the L.H.S. to bring a balance between two sides of equation in the following manner:
₹2,19,539.4\left(F/P,i^{\prime}\% ,5\right)=₹3,53,570.3Step 7: The equation given at Step 6 is solved as:
₹2,19,539.4\left(F/P,i^{\prime}\% ,5\right)=₹3,53,570.3\left(F/P,i^{\prime}\% ,5\right)=₹3,53,570.3/₹2,19,539.4
\left(F/P,i^{\prime}\% ,5\right)=1.61
\left(1+i^{\prime}\right)^{5}=1.61
1+i^{\prime}=1.0999
i^{\prime}=1.0999-1=0.0999=9.99\% which is almost equal to 10\%.
Since the value of i^{\prime}\% = 9.99\% = M.A.R.R. = 10\%, the investment in the project is economically barely justified.
