ISE 460
Fall 2006
FINAL
12/07/06 Solution
Problem No. 1
A project requires substantial working capital. Inventory and deferred payments from customers
are the major contributors. The length of the project is five years. The company uses an MARR of
20%. It is estimated that the working capital requirement is
$100,000 per year and rises with
inflation, year zero being the base. The financial analyst is estimating a minimum inflation rate of
3% with a probability of occurrence of 70%. The same analyst thinks that there is a 30% chance of
the inflation being 6% per year. What is the expected value of the present cost of the working
capital? (10 points)
We need to calculate the NPV separately under each of the two estimates of inflation.
Then get the expected value of each and add them.
Page 1
Initial Working capital
100,000
$
Initial Working capital
100,000
$
Length of project
5 years
Length of project
5 years
Inflation rate
3%
Inflation rate
3%
MARR
20%
MARR
20%
0
1
2
3
4
5
0
1
2
3
4
5
Capital
(100,000)
(3,000)
(6,090)
(9,273)
(12,551)
14,986
Capital
(100,000)
(3,000)
(6,090)
(9,273)
(12,551)
130,914
NPV
(112,125)
NPV
(65,537)
Initial Working capital
100,000
$
Initial Working capital
100,000
$
Length of project
5 years
Length of project
5 years
Inflation rate
6%
Inflation rate
6%
MARR
20%
MARR
20%
0
1
2
3
4
5
0
1
2
3
4
5
Capital
(100,000)
(6,000)
(12,360)
(19,102)
(26,248)
47,782
Capital
(100,000)
(6,000)
(12,360)
(19,102)
(26,248)
163,709
NPV
(118,093)
NPV
(71,504)
Inflation rate
NPV
Probability
expected value
Inflation ratNPV
Probability expected value
3%
(112,125)
70%
(78,488)
3%
(65,537)
70%
(45,876)
6%
(118,093)
30%
(35,428)
6%
(71,504)
30%
(21,451)
Combined
(113,916)
Combined
(67,327)
Year
Year
Year
Year
Alternate
Alternate
Initial Working capital
100,000
$
Initial Working capital
100,000
$
Length of project
5 years
Length of project
5 years
Inflation rate
3%
Inflation rate
3%
MARR
20%
MARR
20%
0
1
2
3
4
5
0
1
2
3
4
5
Capital
(100,000)
(103,000)
(106,090)
(109,273)
(112,551)
414,986
Capital
(100,000)
(103,000)
(106,090)
(109,273)
(112,551)
530,914
NPV
(210,248)
NPV
(163,659)
Initial Working capital
100,000
$
Initial Working capital
100,000
$
Length of project
5 years
Length of project
5 years
Inflation rate
6%
Inflation rate
6%
MARR
20%
MARR
20%
0
1
2
3
4
5
0
1
2
3
4
5
Capital
(100,000)
(106,000)
(112,360)
(119,102)
(126,248)
447,782
Capital
(100,000)
(106,000)