16.3. HOW TO WEIGH YOUR BORROWING ALTERNATIVES 627
Table 16.5:Percentage total spreads of borrowing alternativesusdloan eurloan difference
Using swap rates
(a)pv’ed cost inusd 10.002 10.151
(b) Eq. annuity:pv/6.002 054 67 1.666 1.691
(c) id/200,000,000 0.833% 0.846% 0.012%
Usingirrs
(a)pv’ed cost inusd 9.823 9.951
(b) Eq. annuity:pv/5.819 229 22 1.688 1.710
(c) id/200,000,000 0.844% 0.855% 0.011%
difference of % cost estimates 0.011% 0.009%pvspvs instead? First, basic financial logic tells us to generally trustpvs, i.e.
numbers in dollars or euros or pounds, not percentages: we pay for our shopping
with money not percentages, and 1% extra on 1,000,000 means more money than 2%
extra on 100. True, in this particular instance this is no issue since the alternatives,
by design, all have the same scale,usd200m, implying that there is no harm in
looking at the percentages here. But there is a second reason whypvs, in units of
money, are better than spreads: amounts of money are easily understood and easily
compared across currencies. In contrast, to many business people it would be hard
to see whether a spread of 0.75% on top of a swap rate of 8% is better or worse than
a spread of 0.30% on top of a swap rate of 2%.
Despite all this, some traditional financebabus insist on percentage spreads. If
your boss really presses you, here is how you could respond without giving up rigor.
The simple way to come to ap.a.-spread type number is to divide thehc pv
numbers by thehcannuity factor, which means that we compute the equivalent
annuity of all costs, upfront or not. Then we express the equivalent annuity as a
percentage. Table 16.5 shows the results. Note how, by always using the same
number —hcannuity factor times hcface value—to rescale thepv’ed costs we
cannot possibly change the ranking of the alternatives. It is, in fact, easily shown
that thefccosts are those of swappedfcloans, not of the originalfcloans. Just
hope that your boss does not raise the question; and if (s)he does, say that the
numbers are adjusted for currency risk.
The calculations show, first, that the estimated total spreads are not very much
affected by whether you use swap rates orirrs: these intra-column differences,
shown in the bottom line, amount to one basis point only. The second conclusion
is that both methods agree that theeur andusdoffers are very close, with a
disadvantage of slightly over one basis point for theeurloan. These differentials
across columns are shown in the rightmost column of the table.