10.8 - Gene and Linda Voiland School of Chemical Engineering ...

ChE 450
Chemical Process Design and Analysis I
Fall, 2012
Washington State University
Voiland School of Chemical Engineering
and Bioengineering
Richard L. Zollars
Problem 10.8, Turton, Bailie, Whiting and Schaewitz
The projected costs for a new plant are given below (all numbers are in $10 6 ):
Land cost = $7.5
Fixed Capital Investment = $210 ($60 at end year 1, $39.60 at end of year 2, and $20.40
at end of year 3)
Working Capital = $35 (at start-up)
Start-up at end of year 3
Revenue from sales = $52
Cost of Manufacturing (without depreciation) = $18
Tax Rate = 40%
Depreciation Method = Current MACRS over 5 years
Length of time over which profitability is to be assessed = 10 years after start-up
Internal rate of return = 9.5% p.a.
For this project, do the following:
a. Draw a cumulative (nondiscounted) after-tax cash flow diagram
b. From part (a), calculate the following non-discounted profitability criteria for the project:
(i) Cumulative cash position and cumulative cash ratio
(ii) Payback period
(iii) Rate of return on investment
c. Draw a cumulative (discounted) after-tax cash flow diagram.
d. From part (c), calculate the following discounted profitability criteria for the project:
(i) Net present value and net present value ratio
(ii) Discounted payback period
(iii) Discounted cash flow rate of return (DCFROR)
SOLUTION
a. The easiest way to approach this is to use Excel. The results are shown below. The
cumulative, non-discounted cash flow diagram is shown on the following page.
b. (i) The cumulative cash position is the final cumulative project value at the end of year
13. So the cumulative cash position (CCP) is $132 million. The cumulative cash
ratio (CCR) is
(ii) To find the pay back period (PBP) you need to find the point where the cumulative
cash flow is greater than its lowest point by the FCI. In this case, at year 3 the net
cash flow is -162.5 million. Since the FCI was $120 million you need to find the year
when the cumulative cash flow was -$162.5 million + $120 million = -$42.5 million.

Year Land FCI Working Revenue Deprec (DDB) Deprec (SL) Deprec (MACRS) FCI - Sum(D) Taxes Cash Flow Discounted Cum. Cash Cum. Cash Disc Interest Rate
0 0 0 0 0 0 0.095
0 7.5 -7.5 -7.5 -7.5 -7.5
1 60 -60 -54.79452055 -67.5 -62.29452055
2 39.6 -39.6 -33.0268343 -107.1 -95.32135485
3 20.4 -20.4 -15.53773857 -127.5 -110.8590934
3 35 -35 -26.6578848 -162.5 -137.5169782
4 34 24 24 96 4 30 20.8672288 -132.5 -116.6497494
5 34 38.4 21.33333333 38.4 57.6 -1.76 35.76 22.71574131 -96.74 -93.9340081
6 34 23.04 16.45714286 23.04 34.56 4.384 29.616 17.18073291 -67.124 -76.75327519
7 34 13.824 13.824 13.824 20.736 8.0704 25.9296 13.73716083 -41.1944 -63.01611436
8 34 13.824 13.824 6.912 8.0704 25.9296 12.54535236 -15.2648 -50.470762
9 34 6.912 6.912 10.8352 23.1648 10.23532135 7.9 -40.23544065
10 34 13.6 20.4 8.231689409 28.3 -32.00375124
11 34 13.6 20.4 7.517524575 48.7 -24.48622666
12 34 13.6 20.4 6.865319246 69.1 -17.62090742
13 34 13.6 20.4 6.269697942 89.5 -11.35120948
13 42.5 13.06187071 132 1.710661237

Project Value ($million)
150
Cumulative Non-Discounted Cash Flow
100
50
0
0 2 4 6 8 10 12 14
-50
-100
-150
-200
Years

From the Excel spreadsheet the cumulative (non-discounted) cash flow at year 7
is -$41.2 million. Interpolating gives year 6.95. But the start-up occurred in year 3 so
the payback period is 6.95 – 3 = 3.95 years.
(iii)To find the rate of return on investment (ROROI) take the slope of a straight line
from the start-up cash position to the final cash position minus working capital and
land (but with the salvage value, in this zero). At start-up (year 3) the cumulative
cash position is -162.5 million. At the end (year 13) the cash position is $132 million
minus working capital ($35million) and land ($7.5 million). Thus the slope is
( ) ( )
Then
c. The cumulative discounted cash flow diagram is shown on the following page.
d. (i) The net present value (NPV) is read directly from the cumulative CFD as
$1.71 million. The net present value ratio (NPVR) then is
(ii) The discounted payback period (DPBP) is found just like the PBP except now using
discounted values. The discounted FCI is 60/(1.095) + 39.6/(1.095) 2 + 20.4/(1.095) 3
= $103.3 million. At start-up the discounted cash position was -137.5 million. Thus
you need to find the time when the cumulative cash flow reached -137.5 + 103.3
= -34.2 million. This occurred between years 9 and 10. Interpolating gives year 9.73
years. The start-up was in year 3 so the DPBP is 9.73 – 3 = 6.73 years.
(iii)The discounted cash flow rate of return (DCFROR) is the rate of return that gives a
cumulative cash value of zero at the end of the project. Since an interest rate of 9.5%
p.a. gives a positive value at the end of the project we know that the DCFROR must
be higher. You could try adjusting the value of the interest rate upwards until the
cumulative cash position becomes 0 or use the Solver utility in Excel. Using Solver
gives a DCFROR of 9.73% p.a.

Project Value ($millions)
20
Cumulative Cash Flow (Discounted)
0
0 2 4 6 8 10 12 14
-20
-40
-60
-80
-100
-120
-140
-160
Years