Return Swaps
A very popular arrangement encouraged by financial engineers can be termed a return swap.
Consider the following case. Investor A promises to pay investor B the return on a notional value of $1 of Asset 1, while B promises to pay A the return on a notional value of $1 of Asset 2. Is this fair?
Recall that the value relative for an investment is the ratio of its value at the end of a stated period to its value at the beginning. Thus, for example, the three-year value relative for an asset is the value at the end of year 3, assuming no intermediate withdrawals or contributions, divided by the value at the outset (year 0). The return on an asset is the difference between its value relative and 1.0. For a holding period of t years:
r(t) = vr(t) -1
We know that the present value of $1 of an asset is worth (obviously) $1. This will, in turn, equal the sum of the present values of all the state-contingent ending value relatives. On the other hand, the present value of $1 certain at the end of a given period will equal the corresponding discount factor. Thus for our t-period case:
pv(r(t)) = pv(vr(t)-1) = 1 - df(t)
From this it follows that the present value of an offer to pay the cumulative return on $1 of notional value of any trades asset at the end of time period t will equal $1 minus the present value of $1 certain at time t, as long as the party promising to make the payments is sufficiently credit-worthy that default is out of the question.
Given this observation, the swap of a promise to pay the return on one asset for a promise to pay the return on another is fair as long as both parties have AAA credit ratings. Why? Becuase both sides have the same present value at the time of the agreement. Later, of course, these values may diverge, causing one party to undergo a loss and the other a gain. But such are the vagaries of markets.
Risky Debt
Risky Debt A bond represents debt in which a borrower promises to pay a lender specified amounts in the future. More precisely, the borrower promises to pay if he or she can. If the borrower is a corporation with limited liability, the payment will be made in full and on time only if the borrower's cash inflows and cash outflows associated with claims with greater priority permit. Otherwise, some or all of the promised payment will be in default (i.e. not paid).
Consider an owner of an apple tree who issues a bond that promises to pay $80 in period 1 (if possible). If the weather turns out to be good, the payment will be made in full. If it turns out to be bad, only $70 will in fact be paid.
The value of such a bond is shown below.
Note that the bond will not sell for as much as a similar bond that is riskless. The latter would sell for $80x0.90, or $72. The (promised) yield-to-maturity on this bond is:
or 19.40% (again, to two decimal places). A bond's yield-to-maturity can be considered its promised rate of interest. If everything works out (i.e. the weather is good), the purchaser of such a bond will in fact earn 19.40%. But there is at least a chance that things will not work out (i.e. the weather will be bad). In this event, the purchaser will earn only:
or 4.48%.
It is easy to calculate a bond's yield-to-maturity. One needs only the set of promised payments and the current price. To determine what other possibilities the purchaser might experience requires estimates of the characteristics of future states of the world -- a considerably more difficult task.
Of course, the issuance of risky debt does nothing to affect the principle of value additivity. In this case the residual claimants (stockholders) will face the prospects shown below. The sum of the values of all the claims is 67+8=75, as before.
******* BELOW NEEDS WORK **************
Re-allocating Value Among Claimants
One of the problems associated with financing via two or more classes of claims is that of avoiding decisions that may increase a firm's value but actually decrease the value of one or more set of claims. A simple example can illustrate the point.
Consider the apple tree firm that has bonds outstanding with promised payments of $80. As shown earlier, the value of the firm is $75, divided between the value of the bonds ($67) and that of the stocks ($8). Now, assume that management has an opportunity to trade its present apple tree for one that will produce 90 apples if the weather is good and 80 apples if the weather is bad. The value of this new tree is shown below. Clearly the proposed trade is desirable, since it will increase value by $1 (from $75 to $76).
Consider, however, the cash flows to the bondholders and stockholders associated with the new investment, shown in the first table below. The resulting values are shown in the next two tables. The change has added $5 (72-67) to the value of the outstanding bonds and decreased the value of the outstanding stock by $4 (8-4). While those holding bonds (or even proportional amounts of bonds and stocks) would endorse the change, those holding only stock would be violently opposed.
In principle, stockholders and bondholders in such a situation could work out a re-arrangement of terms to their mutual advantage so that such an opportunity could be exploited. However, this may require time, bargaining, legal costs, etc., making the cost greater than the benefit.
In this case a change in the firm's business to one of lower risk advantaged holders of (formerly) risky debt and disadvantaged holders of junior claims (here, stock). In the converse situation, an increase in the risk of a firm's operations may lower the value of bonds and increase the value of stock. Such a change may not enhance the firm's total value, but may still prove desirable for stockholders. To minimize temptations on the part of management to engage in such tactics, bondholders typically require covenants placing at least some restrictions on management prerogatives. The danger, of course, is that profitable (value-enhancing) undertakings that may increase risk will be foregone as a result.
