186 PART 2 Important Financial Concepts
- Because the calculations required for finding interest rates and growth rates, given the series of cash flows, are
the same, this section refers to the calculations as those required to find interest orgrowth rates.
TABLE 4.8 Loan Amortization Schedule ($6,000
Principal, 10% Interest, 4-Year Repayment
Period)Payments
Beginning- End-of-year
End of-year Loan Interest Principal principal
of principal payment [0.10(2)] [(1) (3)] [(2) (4)]
year (1) (2) (3) (4) (5)1 $6,000.00 $1,892.74 $600.00 $1,292.74 $4,707.26
2 4,707.26 1,892.74 470.73 1,422.01 3,285.25
3 3,285.25 1,892.74 328.53 1,564.21 1,721.04
4 1,721.04 1,892.74 172.10 1,720.64 —a
aBecause of rounding, a slight difference ($0.40) exists between the beginning-of-year-4 principal
(in column 1) and the year-4 principal payment (in column 4).Interest or Growth Rates
It is often necessary to calculate the compound annual interest or growth rate
(that is, the annual rate of change in values) of a series of cash flows. Examples
include finding the interest rate on a loan, the rate of growth in sales, and the rate
of growth in earnings. In doing this, we can use either future value or present
value interest factors. The use of present value interest factors is described in this
section. The simplest situation is one in which a person wishes to find the rate of
interest or growth in a series of cash flows.^12EXAMPLE Ray Noble wishes to find the rate of interest or growth reflected in the stream of
cash flows he received from a real estate investment over the period 1999 through- The following table lists those cash flows:
By using the first year (1999) as a base year, we see that interest has been earned
(or growth experienced) for 4 years.Table Use The first step in finding the interest or growth rate is to divide the
amount received in the earliest year (PV) by the amount received in the latest year
(FVn). Looking back at Equation 4.12, we see that this results in the present valueYear Cash flow2003 $1,520
}^4
2002 1,440
}^3
2001 1,370
}^2
2000 1,300
}^1
1999 1,250