Introduction to Finance

Estimating Yearly Operating Cash Flows
Table LE17.7
summarizes the information 
known thus far. The initial outlay totals $170,000 in year zero, and salvage value is $12,000 in 
year three. The operating cash fl ows are unknown, but they will increase by $40,000 in year 
three due to the recovery of net working capital.
To make this information easier to work with, let’s simplify the information presented 
in the table. Let’s add the 
present value
of the year three cash infl ow of $52,000 to the initial 
cash outfl ow of $170,000. This gives a present value of the known cash fl ows of the following:
–$170,000 + $52,000(1∕1.20)
3
= –$139,907.41
This removes the eff ects of the salvage value and the recovery of net working capital from the 
project’s annual cash fl ows. The cash fl ows in years one through three are now a three-year 
annuity, with a net year zero investment of $139,907.41 in present value terms:
Year
Cash flow
0
–$139,907.41
1
X
2
X
3
X
The NPV of this series of cash fl ows is the PV of the three-year $X annuity, less $139,907.41. 
To determine the minimum operating cash fl ow that will leave shareholder wealth unharmed, 
we set NPV to zero and solve for X:
NPV = 0 = ($X)(PVIFA for 3 years, 20%) – $139,907.41
Using interest factor table or a fi nancial calculator, the present value interest factor of an 
annuity (PVIFA) for three years and 20 percent is 2.1065. Solving for $X, we fi nd the operat-
ing cash fl ow annuity is $66,417.58.
Using this minimum operating cash fl ow, we can work backward to determine the min-
imum sales revenue consistent with a zero-NPV bid. Recall the project’s annual costs are 
TA B L E L E 1 7 . 7
Cash Flow Summary
Year
Initial 
Outlay