210 RATEOF RETURNANALYSIS
If, on the other hand, borrowed money was involved, the NPW plot would appear as
in Figure 7-4. This form of cash flowtypically results when one is a borrower of money. In
such a case, the usual pattern is a receipt of borrowed money early in the time period with
a later repayment of an equal sum, plus payment of interest on the borrowed money. In all
cases in which interest is charged, the NPW at 0% will be negative.FIGURE 7-4 TYPical NPW plot for borrowed money.How do we determine the interest rate paid by the borrower in this situation'l ~ically.
we would write an equation, such as PW of income=PW of disbursements,aild solve for
the unknown IRR. Is the resulting IRR positive or negative from the borrower's point of
view? If the lender said he was receiving, say, + 11% on the debt, it might seem reasonable
to state that the borrower is faced with -11 % interest. Yet this is not the way interest is
calculated. A banker says he pays 5% interest on savings accounts and charges 11% on
personal loans. Both rates are positive.
Thus, we implicitly recognize interest as a charge for the use of someone else's money
and a receipt for letting others use our money.In determining the interest rate in a particular
situation, we solve for a single unsigned value of it. We then view this value ofiin the
customary way, that is, as either a charge for borrowing money or a receipt for lending
money.A new corporate bond was initially sold by a stockbroker to an investor for $1000. The issuing
corporation promised to pay the bopdholder $40 interest on the $1000 face value of the bond
every 6 months, and to repay the $1000 at the end of 10 years. After one year the bond was sold
by the original buyer for $950.
(a) ~at.rate of.,J:etl1lJ1d,!dJ!1eor!ginaJ.buy~rreceiv~ on pisjnve§.tment?
(b) What rate of return can the new buyer (paying $950) expect to receive if he keeps the bond
for its remaining 9-year life?
a ii..E.__ - -- -- __ _ _ _ :1 a...~ .,.Year Cash Flow
(^0) +p +
(^1) - RepaymentA
2 -A
3 -A^0
(^4) -A