Introduction to Finance

TA B L E 9 . 2
Present Value Interest Factor (PVIF) of $1
Year
5%
6%
7%
8%
9%
10%
1
.952
.943
.935
.926
.917
.909
2
.907
.890
.873
.857
.842
.826
3
.864
.840
.816
.794
.772
.751
4
.823
.792
.763
.735
.708
.683
5
.784
.747
.713
.681
.650
.621
6
.746
.705
.666
.630
.596
.564
7
.711
.665
.623
.583
.547
.513
8
.677
.627
.582
.540
.502
.467
9
.645
.592
.544
.500
.460
.424
10
.614
.558
.508
.463
.422
.386

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9.3 Discounting to Determine Present Values
229
$1,116.40 at the end of two years if the interest rate is 8 percent. Note that to reduce the impact 
of rounding errors, we are carrying our calculations here to four decimal places:
FV
2
= $1,000(1 + 0.08)
2
= 
$1,000(1.1664)
= 
$1,166.40
Now, what is the present value of a $1,166.40 future value if we must wait two years to 
receive the future value amount and if the interest rate is 8 percent? The solution would be,
PV = $1,166.40[1 ÷ (1 + 0.08)
2
]
= $1,166.40(1 ÷ 1.1664)
= 
$1,166.40(0.8573)
= 
$1,000
Thus, an investor should be indiff erent about receiving a $1,000 present value now or a 
$1,166 future value two years from now if the compound interest rate is 8 percent.
0
1
2
3
4
5
6
7
8
9
10
Years
Compound Annual
Interest Rate
Present Value (of $1)
$1.00
0.90
0.80
0.70
0.60
0.50
0.40
0.30
10%
5%
0%
($1.00)
($0.61)
($0.39)
FIGURE 9.2
 Present Value, 
Interest Rate, and Time Period 
Relationships
Calculating Rates of Return for Venture Capitalists 
and Other Investors
Venture capitalists represent an important source of fi nancing for 
small businesses. Venture capitalists, of course, are in the busi-
ness of providing fi nancial capital to small businesses with the 
expectation of earning a return on their investments commensur-
ate with the risks associated with those investments. A typical 
“exit strategy” of venture capitalists is to maintain an investment 
in a fi rm for approximately fi ve years and, if the investment is 
successful, then sell the fi rm to another company or take the fi rm 
public in an initial public off ering (IPO).
A venture capitalist usually will invest in a small business by 
either taking a direct ownership position in the form of common 
stock or by accepting the fi rm’s bond plus an “equity kicker,” or 
the right to purchase a certain portion of the fi rm (e.g., 50 per-
cent). For example, let’s assume that a venture capitalist invests 
$5 million in a fi rm. In return, the venture capitalist receives 
shares of stock representing 50 percent ownership in the fi rm. 
Let’s assume that the fi rm can be sold for $40 million at the end of 
fi ve years. What will be the rate of return that the venture capitalist 
will earn on the $10 million investment? The present value is $5 
million and the future value is $20 million (i.e., $40 million times 
.5, or 50 percent). Since we know the time period is fi ve years, we 
solve for the interest rate, 
r
. Using a fi nancial calculator results in 
a compound interest rate (%i) of 32.0 percent.
What would have been the venture capitalist’s rate of return 
if the fi rm had been sold for $40 million at the end of six years 
instead of at the end of fi ve years? Again, the present value is $5 
million, the future value is $20 million, and the time period is six 
years. Solving for the interest rate yields 26.0 percent. Thus, if the 
sale of the fi rm is delayed by one year, the compound rate of return 
on the venture capitalist’s investment drops six percentage points, 
from 32 percent down to 26 percent.