Page 269 - Analysis, Synthesis and Design of Chemical Processes, Third Edition

When cash flows occur at different times, each cash flow must be brought forward (or
backward) to the same point in time and then compared.

The point in time that is chosen is arbitrary. This is illustrated in Example 9.13.

Example 9.13

The CFD obtained from Example 9.10 (for the borrower) is repeated in Figure E9.13. The annual interest
rate paid on the loan is 8% p.a.

Figure E9.13 CFD for Example 9.13

In year 7, the remaining money owed on the loan is paid off.
a. Determine the amount, X, of the final payment.
b. Compare the value of X with the value that would be owed if there were no interest paid on the
loan.

With the final payment at the end of year 7, no money is owed on the loan. If we sum all the positive and
negative cash flows adjusted for the time of the transactions, this adjusted sum must equal zero.

We select as the base time the date of the final payment.
a. From Equation (9.5) for i = 0.08 we obtain the following.
For withdrawals:
6
$1000 end of year 1: F = ($1000)(1 + 0.08) = $1586.87
6
5
$1200 end of year 2: F = ($1200)(1 + 0.08) = $1763.19
5
4
$1500 end of year 3: F = ($1500)(1 + 0.08) = $2040.73
4
Total withdrawals = $5390.79
For repayments:
2
$2000 end of year 5: F = –($2000)(1 + 0.08) = – $2332.80
2
0
$X end of year 7: F = –($X)(1 + 0.08) = – $X
0
Total repayments = – $(2332.80 + X)
Summing the cash flows and solving for X yields
0 = $5390.79 – $(2332.80 + X)