Transcript Rate of Return Analysis

Multiple Rates of Return
Problem
Lecture No. 26
Chapter 7
Contemporary Engineering Economics
Copyright © 2006
Contemporary Engineering Economics, 4th
edition, © 2007
Net Investment Test



What it is: A process to determine whether or not a
firm borrows money from a project during the
investment period.
How to test: A project is said to be a net investment
when the project balances computed at the project’s
i* values, PB(i*)n, are either less than or equal to
zero throughout the life of the investment.
Meaning: The investment is net in the sense that the
firm does not overdraw on its return any point and
hence is not indebted to the project
Contemporary Engineering Economics, 4th
edition, © 2007
Pure Investment



Definition: An investment in which a firm
never borrows money from the project.
How to Determine: If the project passes the
net investment test, it is a pure investment.
Relationship: A simple investment is always a
pure investment.
Contemporary Engineering Economics, 4th
edition, © 2007
Mixed Investment



Definition: An investment in which a firm
borrows money from the project during the
investment period
How to determine: If a project fails the net
investment test, it is a mixed investment.
Relationship: If a project is a mixed
investment, it is a nonsimple investment.
(However, we can’t say that a nonsimple
investment is also a mixed investment.)
Contemporary Engineering Economics, 4th
edition, © 2007
Example 7.6 Pure versus Mixed
Investments
Project Cash Flows
n
0
1
2
3
i*
A
B
-$1,000
1,000
2,000
1,500
33.64%
-$1,000
1,600
-300
-200
21.95%
C
-$1,000
500
-500
2,000
29.95%
Contemporary Engineering Economics, 4th
edition, © 2007
D
-$1,000
3,900
-5,030
2,145
(10%,30%
,50%)
Sample Calculation – Net Investment
Test (Project B)
Use 21.95% as an interest rate to find the project balances
PB(21.95%)0  $1000
PB(21.95%)1  $1000(1  0.2195)  $1600 $380.5
PB(21.95%)2  $380.5(1  0.2195)  $300  $164.02
PB(21.95%)3  $164.02(1  0.2195)  $200  0
(-, +, +, 0)  Mixed investment
Contemporary Engineering Economics, 4th
edition, © 2007
Net investment test (Example 7.6)
Contemporary Engineering Economics, 4th
edition, © 2007
Multiple Rates of Return Problem
$2,300
$1,000
$1,320
• Find the rate(s) of return:
$2,300 $1,320
PW (i)  $1,000 

1 i
(1  i)2
0
Contemporary Engineering Economics, 4th
edition, © 2007
Analytical Solution:
1
Let x 
. Then,
1 i
$2,300 $1,320
PW (i )  $1,000 

(1  i )
(1  i ) 2
 $1,000  $2,300 x  $1,320 x 2
0
Solving for x yields,
x  10 / 11 or x  10 / 12
Solving for i yields
i  10% or 20%
Contemporary Engineering Economics, 4th
edition, © 2007
PW Plot for a Nonsimple Investment
with Multiple Rates of Return
Contemporary Engineering Economics, 4th
edition, © 2007
Fail the Net Investment Test
Use either i* =20% or 10%
n=0
n=1
n=2
Beg. Balance
Interest Charged
Payment
-$1,000
-$1,000
-$200
+$2,300
+$1,100
+$220
-$1,320
Ending Balance
-$1,000
+$1,100
$0
Cash borrowed (released) from the project is assumed to
earn the same interest rate through external investment
as money that remains internally invested
a mixed
investment
Contemporary Engineering Economics, 4th
edition, © 2007
Conceptual Issue:
Can the firm be able to invest the money released from the
project at 20% externally in Period 1?
• If the firm’s MARR is exactly 20%, the answer is “yes”,
because it represents the rate at which the firm can always
invest the money in its investment pool. Then, the 20% is
also true IRR for the project.
.
• Suppose the firm’s MARR is 15% instead of 20%. The
assumption used in calculating i* is no longer valid. In
order to calculate i*, we assumed that all cash released from the
project can be invested at the i* instead of MARR.
• Conclusion: Neither 10% nor 20% is a true IRR.
Contemporary Engineering Economics, 4th
edition, © 2007
How to Proceed:
• If you encounter multiple rates of return,
abandon the IRR analysis and use the PW
criterion.
If NPW criterion is used at MARR = 15%
PW(15%) =
-$1,000 + $2,300 (P/F, 15%, 1)
- $1,320 (P/F, 15%, 2 )
= $1.89 > 0
Accept the investment
• If you want to find the true rate of return (or return on
invested capital) to the project, follow the procedure
outlined in Section 7.3.4.
Contemporary Engineering Economics, 4th
edition, © 2007