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Exhibit 4.21 Determine the annual payment schedule of a loan: Excel example 13.
Uneven Cash Flow Exercise
In Exhibit 4.11, we calculated the FV of an annuity with regular cash flows. In Exhibit 4.16, we
calculated the PV of the same annuity with regular cash flows. For this exercise, we are going to
modify the cash flow in both of these examples to help us understand what occurs to the future and
present values during uneven cash flows. We will keep the interest rate and time unchanged; however,
we will change the payments to reflect uneven cash flows.
Exhibit 4.23 represents regular cash flows of $500 into an ordinary annuity over 10 periods at 7%,
and the FV of the annuity.
Exhibit 4.24 has uneven cash flows in periods 4, 6, 7, and 8 compared to Exhibit 4.23. We see that
the FVs of the uneven cash flows in periods other than 4, 6, 7, and 8 are unchanged. In the periods
where the cash flow payments changed, we see that the FV has increased or decreased, depending on
the difference in the value of the payment versus the original values in Exhibit 4.23; the final value at
the end of the period has changed, too.
In calculating FV for an uneven cash flow, we are unable to use any Excel formulas and resort to
calculating the individual FV of each payment. Exhibit 4.25 represents regular cash flows of $500 into
an ordinary annuity over 10 periods at 7%, and the PV of the annuity.