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Why PV Savings Exceed Cash Flow Savings
By Felipe Ferrand
Jul 25, 2002, 13:46

Normally, the present value ( 'pv' ) of a cash flow is less than the undiscounted sum over time. The essential idea underlying pv analysis is that a dollar today is worth more than a dollar tomorrow. Since most of the cash flows of a bond issue occur in the future, the pv of the principal and interest payments are always less than the gross undiscounted total debt service. How can a cash flow comparison yield a result where the pv savings exceed the cash flow savings?


Overview
Note that when comparing alternate financing plans, the analysis is based on the differential cash flows, i.e. on the difference in debt service payments between alternate issue structures. Typically, the differential cash flow consists of both negative and positive amounts. If the pv of the positive cash flows exceeds the pv of the negative cash flows, then the sum of the pv positive benefits will exceed the sum of the negative losses.

This occurs under following conditions :
1. The debt service comparison generates a consistent pattern of savings followed by losses.

2. The total undiscounted cash flow savings are minimal.

For example, consider a refunding transaction that results in exactly one dollar of savings followed by exactly one dollar of losses so that the total gross undiscounted difference in debt service is exactly zero. Since every dollar of savings occurs one period earlier than the loss that offsets it, the pv of every dollar of savings will be greater than the pv of the dollar of loss that follows it.
The total pv savings will therefore exceed the cash flow savings.

This pattern of alternating savings followed by losses can occur when the refunding issue's bond year ends on a later month than the refunded issue. For example, if the old refunded bonds are due each March 1st, but the new refunding issue bonds are due each September 1st then the issuer will have effectively deferred principal repayments for six months each year. Assuming that interest rates have not changed substantially, the total debt service payments of the refunding will be somewhat higher than the original issue because the refunding is extending the average life. If the costs of the refunding are low enough,
however, the transaction will show a net pv benefit. This benefit is essentially the value of the six month float created by the transaction.







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