Products
Rewards 
from HOLOOLY

We are determined to provide the latest solutions related to all subjects FREE of charge!

Please sign up to our reward program to support us in return and take advantage of the incredible listed offers.

Enjoy Limited offers, deals & Discounts by signing up to Holooly Rewards Program

HOLOOLY 
BUSINESS MANAGER

Advertise your business, and reach millions of students around the world.

HOLOOLY 
TABLES

All the data tables that you may search for.

HOLOOLY 
ARABIA

For Arabic Users, find a teacher/tutor in your City or country in the Middle East.

HOLOOLY 
TEXTBOOKS

Find the Source, Textbook, Solution Manual that you are looking for in 1 click.

HOLOOLY 
HELP DESK

Need Help? We got you covered.

Chapter 5

Q. 5.8

Solve the problem given in Example 5.2 by the I.R.R. method.

Step-by-Step

Verified Solution

Step 1: The cash flow diagram for the given problem is shown in Fig. 5.2.
Step 2: The P.W. of the net receipts at an interest rate of i^{\prime } is calculated as:

P.W.=₹53,000\left(P/A,i^{\prime}\% ,5\right)+₹30,000\left(P/F,i^{\prime}\% ,5\right)

Step 3: The P.W. of the net expenditures at an interest rate of i^{\prime } is calculated as:

P.W.=₹1,05,815.4+₹30,000\left(P/A,i^{\prime}\% ,5\right)

Step 4: The net present worth N.P.W. is obtained as:

N.P.W.=₹53,000\left(P/A,i^{\prime}\% ,5\right)+₹30,000\left(P/F,i^{\prime}\% ,5\right)-₹1,05,815.4-₹30,000\left(P/A,i^{\prime}\% ,5\right)

Step 5: 0 =₹53,000\left(P/A,i^{\prime}\% ,5\right)+₹30,000\left(P/F,i^{\prime}\% ,5\right)-₹1,05,815.4-₹30,000\left(P/A,i^{\prime}\% ,5\right)

The equation given at Step 5 normally involves trial-and-error calculations until the i^{\prime }\% is found. However, since we do not know the exact value of i^{\prime }\%, we will probably try a relatively low i^{\prime }\%, such as 5\%, and a relatively high i^{\prime }\%, such as 12\%.

At i^{\prime }\% = 5\%:

₹53,000\left(P/A,5\%,5\right)+₹30,000\left(P/F,5\%,5\right)-₹1,05,815.4-₹30,000\left(P/A,5\% ,5\right)

 

₹53,000\left(4.3295\right)+₹30,000\left(0.7835\right)-₹1,05,815.4-₹30,000\left(4.3295\right)=+₹17,268.1

At i^{\prime }\% = 12\%:

₹53,000\left(P/A,25\%,5\right)+₹30,000\left(P/F,25\%,5\right)-₹1,05,815.4-₹30,000\left(P/A,25\% ,5\right)

 

₹53,000\left(3.6048\right)+₹30,000\left(0.5674\right)-₹1,05,815.4-₹30,000\left(3.6048\right)=-₹5,883

Since we have both a positive and a negative P.W. of net cash flows, linear interpolation can be used as given below to find an approximate value of i^{\prime }\%

\frac{12\%-5\%}{₹17,268.1-\left(-₹5,883\right)}=\frac{i^{\prime }\%-5\%}{₹17,268.1-₹0}

 

i^{\prime}\%=5\%+\frac{₹17,268.1}{₹17,268.1-\left(-₹5,883\right)}\left(12\%-5\%\right)

i^{\prime }\% = 10.22\%, which is approximately equal to 10\%.

Step 6: Since the value of i^{\prime }\% = M.A.R.R., the investment in the project is economically barely justified.

Note: Let us check whether the value of N.P.W. at i^{\prime } = 10\% is 0.

N.P.W.=₹53,000\left(P/A,i^{\prime}\%,5\right)+₹30,000\left(P/F,i^{\prime}\%,5\right)-₹1,05,815.4-₹30,000\left(P/A,i^{\prime}\%,5\right)

At i^{\prime }\% = 10\%:

N.P.W.=₹53,000\left(P/A,10\%,5\right)+₹30,000\left(P/F,10\%,5\right)-₹1,05,815.4-₹30,000\left(P/A,10\%,5\right)

 

=₹53,000\left(3.7908\right)+₹30,000\left(0.6209\right)-₹1,05,815.4-₹30,000\left(3.7908\right)

 

N.P.W.=0

Thus i^{\prime } = 10\% which is equal to the given M.A.R.R. and therefore, the investment in the project is economically barely justified.