NORTHWESTERN UNIVERSITY
J.L. KELLOGG GRADUATE SCHOOL OF MANAGEMENT

Tim Thompson
Finance D42
Revised, June 1995

Contingent Claims Analysis - PERCS

0. Introduction
The PERCS security is a Preference Equity Redemption Cumulative Stock, invented by Morgan
Stanley in the mid-1980's. The PERCS is a cumulative preferred stock with an initial maturity of three to five years, with mandatory conversion at maturity and subject to early conversion at a premium at the option of the issuing corporation. The upside potential of the PERCS is limited relative to the common: if the common stock price at expiration, S T , is less than the "PERCS Capped price," X, the PERCS holder receives one common share per PERCS share; if S T $ X, the PERCS holder receives X/S T common shares per PERCS.1 If the PERCS is called (forced conversion) prior to maturity the redemption prices are larger than X by an amount that decreases with time to maturity.
The structure of the security is similar to a "buy-write" option strategy, where the holder buys the underlying common stock and sells a call option against his/her share. The security is designed to be issued at a price very close to the current stock price (in fact, the PERCS security is sometimes used in an exchange offer for common on a one-to-one basis). In order for the PERCS security to be worth as much

1 X/S

T is clearly less than one when ST>X. The payoff per PERCS is thus capped at X per PERC: X/S T shares each worth ST equals a payoff of X.

as a common share, the PERCS holder must be compensated for giving away some of the upside potential of the common stock. What the PERCS holder receives in exchange is a higher dividend stream than the common stock holder receives. This is, in essence, the price the PERCS holder receives for "selling the call option."
Before discussing the valuation of the PERCS security, it is useful to contrast the terms on PERCS to the common stock underlying the instrument:
Dividends. The PERCS dividend is set higher than the current common dividend. The PERCS dividend is a preferred dividend, fixed at its dollar level at the time of issue: should the management raise, cut or eliminate the common dividend, the preferred dividend would remain the same.2
Preferred status. The PERCS dividend would have higher priority than the common dividend and the
PERCS dividend is cumulative, so any arrearages or passed preferred dividends would have to be paid in full before any common dividends could be resumed.
Voting. PERCS, in some cases, have voting rights, but not generally.
Liquidation. In liquidation, PERCS would have a priority claim to common, but this issue is probably moot because shareholders can force early conversion if it is in their interest.
The rest of the paper is organized as follows: Section 1 derives the valuation model for PERCS under the simplifying assumptions that the company does not redeem the PERCS prior to maturity, that all dividends on the PERCS and the common are expected to be remain unchanged from current levels.
Section 2 applies the model to an example company, discusses estimation of the call value and uses the model to evaluate the fairness of an exchange offer to trade in common shares for PERCS on a one-for-one basis; Section 3 gives some concluding comments.

2 The

PERCS contract usually specifies a limit on the dividends paid to common shares during the life of the PERCS

security.

PERCS Analysis - Page 2

1. PERCS Valuation model
We start by defining some notation:
T = maturity date of the PERCS t = some date prior to T
S t = common stock price (date t) of the firm with both PERCS and common outstanding
PERCSt = PERCS price (date t)
X = PERCS cap price
S* t = price of pseudo-common stock on date t (the common stock of a firm identical to the
PERCS issuing firm but with only regular common stock outstanding)
PDIV = dividend on PERCS
SDIV = dividend on common
S*DIV =