16.3. HOW TO WEIGH YOUR BORROWING ALTERNATIVES 623
Evaluation under Idealized Circumstances
We could look at the sum of discounted risk spreads and other costs, using the swap
rate as the discount rate. This is similar to what we did in Chapters 5 (on forward
contracts) and 7 (on swaps), except, trivially, that now we add an upfront cost. But
there we took the swap dealer’s point of view, whose risk is not the same as those
born by a lender. So let’s first bring a story that tells us why a procedure like this
also makes sense, subject to a caveat, for lenders and borrowers without right of
offset.
We regard a bond issue or a bank loan as annpvproblem. To the borrower,
the proceeds are immediate, and the costs are the subsequent service flows—just
the reverse of what one sees in capital budgeting, but that is not important. Let us
denote the swap rate, a risk-free yield-at-par, bys; the spread as asked by banker
bover and abovesbyρb; and the required discount rate byR. Finally, letVnom
denote the gross size of the loan, andUbthe upfront cost proposed by bankerb.
Thenpvof acceptingb’s proposal equals the net proceeds,Vnom−Ub, over and
above thepvof the future service streams. We write this in line one, below. In line
two, we just simplify and regroup, as follows:
NPVb = V︸nom︷︷−U︸b
net IN−︸Vnom×(1 + (s+ρb︷︷−R)×a(R,#years)︸
PV of subsequent outflows,= Vnom×(s−R)×a(R,#years)−[Ub+Vnom×ρb×a(R,#years)]
︸ ︷︷ ︸
the bank-specific part.(16.5)Offers may have been asked from various bankers, all for the same amountVnom;
andsandRare market-wide numbers. Thus, the first part in thenpvexpression,
Equation [16.5], is common to all offers, and for that reason the competing offers
from various banks can be ranked by looking just at the second part, the upfront cost
plus thepv’ed spreads, labeled “bank-specific part” in the equation. The spread
asked consists of the “objective” risk premium one would see in perfect markets,
plus, in realistic bond markets, a compensation for the investors’ unfamiliarity with
the borrower: unknown parties look more risky. The investment bank, in the case
of a bond issue, tries to reduce the unfamiliarity premium by road shows etc, but
this increasesUb, the upfront cost. In addition, part of the bank’s upfront expenses
may be paid for not via the upfront feeUbbut by an extra interest spread instead;
alternatively, as we have seen, the parties may agree to lower the very visible spread,
and increase the less visible upfront feeUbinstead. That’s why we should look at
the whole package. Thus, we propose thepvcriterion,
pv’ed total bank-specific component =Ub+Vnom×ρb×a(R,#years). (16.6)This is what we did when we compared risk spreads in the Swaps chapter, except
that we add the upfront cost and we useRnots. Usingswas justified for a swap
dealer, who benefits from the right of offset and the credit trigger. For a bank (or