IRREVERSIBLE INVESTMENTS AND REGULATORY RISK

Transcription

1 IRREVERSIBLE INVESTMENTS AND REGULATORY RISK PAOLO M. PANTEGHINI CARLO SCARPA CESIFO WORKING PAPER NO. 934 CATEGORY 1: PUBLIC FINANCE APRIL 2003 An electronic version of the paper may be downloaded from the SSRN website: from the CESifo website:

2 CESifo Working Paper No. 934 IRREVERSIBLE INVESTMENTS AND REGULATORY RISK Abstract This paper addresses the issue of how regulatory constraints affect firm s investment choices when the firm has an option to delay investment. The RPI-x rule is compared to a profit sharing rule, which increases the x factor in case profits go beyond a given level. It is shown that a pure price cap and profit sharing are identical in their impact on investment choices: the change in the option value that we have with a profit sharing regime exactly compensates the change in the direct profitability of investment. Regulatory risk breaching of the regulatory contract may or may not affect negatively investment decisions. Even if a distortion exists, we show that this distortion is the same, even if a pure price cap could be considered riskier than a profit sharing rule. JEL Code: L51, D92, G31. Keywords: regulation, investment, RPI-x, profit sharing. Paolo M. Panteghini University of Brescia Department of Economics Via San Faustino 74/B Brescia Italy panteghi@eco.unibs.it Carlo Scarpa University of Brescia Department of Economics Via San Faustino 74/B Brescia Italy cscarpa@eco.unibs.it We would like to thank Giacomo Calzolari, Vesa Kanniainen, Pia Koskenoja, Michele Moretto and participants to seminars at the Universities of Bologna, Helsinki and Padova, at CESifo in Munich and at the RES Conference in Warwick for comments on earlier drafts.

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23 C f o n b q E% c,c do BE%,c o n dq E%,c o j 2 dqg zkhuh q E%,cf duh wkh urrwv ri wkh fkdudfwhulvwlf htxdwlrq 5: j 2 qeq n Eo BE%,cfq Eo n b 'f Lw lv zruwk qrwlqj wkdw C f pxvw eh srvlwlyh lq rughu iru d vroxwlrq wr eh rewdlqhg1 Ohw wkh erxqgdu frqglwlrq T cf Ef ' f krog1 Wklv lpsolhv wkdw M 'f 2 Qrwlfh wkdw/ xqghu surw vkdulqj/ M 7 9' fc vlqfh wkh up*v ydoxh pxvw dffrxqw iru wkh vzlwfk lq wkh %0idfwru zklfk wdnhv sodfh zkhqhyhu : h Xqghu wkh sxuh sulfh fds vfkhph/ lqvwhdg/ zh kdyh M 'fc rq frqglwlrq wkdw qr exeeohv h{lvw1 Qrwlfh wkdw wkh frpsxwdwlrq ri M 7 fdq eh rewdlqhg e ohwwlqj wkh eudqfkhv ri wkh suh0fkdqjh ydoxh ixqfwlrq phhw dw srlqw ' h Krzhyhu/ wklv frpsxwdwlrq lv qrw uhohydqw iru rxu sxusrvhv1 Jlyhq wkh deryh frqglwlrqv/ wkh forvhg0irup vroxwlrq uhgxfhv wr T cf E ' M f nc f bu q Q E%,cQ n M q Q E%,cB +57, Iroorzlqj wkh vdph surfhgxuh/ zh fdq frpsxwh wkh rswlrq ixqfwlrq1 Vwduw zlwk wkh Ehoopdq htxdwlrq cf E ' E b_ e!o_. d cf En_o n b_ e!o_. d c En_o H{sdqglqj wkh uljkw0kdqg vlgh dqg xvlqj Lw *v ohppd lhogv Eo n b cf E ' Eo BE%,cf Y cfe Y Vxevwlwxwlqj +54, lqwr +58, lhogv Eo n b cf E ' b q Q E%,cQ n Eo BE%,c Y cfe Y n Y 2 cfee j2 n b 2 2 c E Y 2 +58, n Y 2 cfe j2 2 2 Y 2 #: Wkh srvlwlyh urrw lv " +{ 4 5 u +{ o>!, #. L u +{o>!, # 4 5 #. 5 +u., # = 55

24 Lw lv hdv wr dvfhuwdlq wkdw wkh jhqhudo vroxwlrq ri cbe lv cbe ' C B b q Q E%,cQ n 2[ C q E%,cB Xvlqj wkh erxqgdu frqglwlrq cf Ef ' fc zh kdyh C 2 'f1wkxv/zhrewdlq ' cf E ' C f b q Q E%,cQ n C q Q E%,cB +59, Ohw xv qrz frpsxwh wkh wuljjhu srlqw deryh zklfk lqyhvwphqw lv surwdeoh xqghu srolf ulvn1 Vxevwlwxwlqj +57, dqg +59, lqwr wkh YPF dqg VSF/ zh rewdlq d wzr0htxdwlrq v vwhp M f nc f b u q Q E%,cQ n M C q Q E%,cB U 'f M f q E%,c C f b u q Q E%,cQ! n q E%,cf M C q Q E%,cB! 'f zlwk wzr xqnqrzqv/ l1h1 wkh glhuhqfh M C dqg wkh wuljjhu srlqw 9 E% fc Vlpsoli lqj lhogv q E%,cf M f n q E%,c C f b u q Q E%,cQ ' Uc +5:, q E%,cf q E%,cf zkhuh lv wkh wuljjhu srlqw xqghu srolf xqfhuwdlqw 1 Ohwxvqh{wuhzulwh+5:,dv 5 BE%,cfnb 9 E%,cf ' BE%,c 7 U q Q E%,cQ C f b 6 u q Q E%,cB q Q E%,cQ 8 BE%,c nbbe%,cf U zkhuh 9 E%,cf q Q E%,cB BE%,cfU lv wkh wuljjhu srlqw lq wkh devhqfh ri srolf q Q E%,cB! xqfhuwdlqw zkhq % ' %,cf Li %,cf :%,c zh kdyh BE%,cBnb BE%,cQ Pruhryhu/ wkh whup BE%,cQnb BE%,cB q Q E%,cQ q Q E%,cB lv srvlwlyh= wklv hqwdlov wkdw wkh vhfrqg whup lq vtxduhg eudfnhwv rq wkh UKV lv ohvv wkdq 4/ dv zhoo1 Wkhuhiruh wkh lqhtxdolw 9 E%,cf krogv1 Wklv suryhv srlqw d,1 Ohw xv qdoo dvvxph %,cf %,c Lq wklv fdvh/ zh kdyh BE%,cBnb BE%,cQ BE%,cQnb BE% :,cb Krzhyhu/ wkh vljq ri q Q E%,cQ lv dpeljxrxv1 Wkxv zh kdyh q Q E% : 9 E%,cf,cB Wklv suryhv srlqw e,1 Ilqdoo / dv fdq eh vhhq/ +5:, lv xqdhfwhg e wkh uhjxodwru uhjlph dssolhg1 Wkxv lv wkh wuljjhu srlqw luuhvshfwlyh ri wkh uhjlph lpsohphqwhg1 Wklv suryhv srlqw f,1 Sursrvlwlrq 5 lv wkxv suryhq1 56

25 81315 SurririSursrvlwlrq 6 Ghqh T 7c E dv wkh ydoxh ixqfwlrq xqghu wkh rog + 'f,dqgwkhqhz + ', uhjlph/ uhvshfwlyho 1 Zh uvw frpsxwh wkh forvhg0irup vroxwlrqv ri wkh ydoxh ixqfwlrq dqg ri wkh rswlrq ixqfwlrq diwhu wkh fkdqjh1 Wkhq zh wxuq wr wkh suh0fkdqjh fdvh1 Ilqdoo / d frpsdulvrq ehwzhhq wkh wzr wuljjhu srlqwv rewdlqhg lv pdgh1 Dv zloo eh vkrzq/ wkh duh htxdo1 Vwduw zlwk wkh qhz uhjlph1 Wkh vroxwlrq rewdlqhg lv htxdo wr wkdw frp0 sxwhg lq wkh devhqfh ri srolf ulvn1 Xvlqj g qdplf surjudpplqj/ wkh up*v ydoxh T 7cQ E fdqehzulwwhqdv T 7cQ E ' _ n e!o_. dt 7cQ En_o H{sdqglqj wkh uljkw0kdqg vlgh dqg xvlqj Lw *v ohppd rqh rewdlqv ot 7cQ E ' n Eo BE% YT 7cQE Y zkhuh % ' %, c% c Ht1 +5;, fdq eh vroyhg dv ; A? T 7c E ' A= n T BE%, q Q E%, li h c n T BE% cq 2 q E% cq li : h n j2 2 2 Y2 T 7c E Y 2 c +5;, Vlploduo / wkh Ehoopdq htxdwlrq ri wkh rswlrq ixqfwlrq lv rewdlqhg 7c E ' e!o_. d 7c En_o H{sdqglqj wkh uljkw0kdqg vlgh dqg xvlqj Lw *v ohppd rqh rewdlqv o 7c E ' Eo BE% Y 7c E Y +5<, n j2 2 2 Y2 7c E Y 2 c +63, zkhuh % ' %, c% c Wkh htxdwlrq +63, kdv wkh iroorzlqj vroxwlrq ;? q Q E%, li h c 7c Ec%' +64, = q Q E% cq n 2 q E% cq li : h Ohw xv irfxv rq wkh 5 fc h uhjlrq1 Xvlqj wkh YPF dqg VSF/ zh rewdlq wkh wuljjhu srlqw 5; #; 8hh Sursrvlwlrq 41 9 q E%, q E%, BE%,U ' 9 E%, c +65, 57

26 dqg U T Q Q ' q Q E%, d9 o!q QE%, +66, Lw lv hdv wr dvfhuwdlq wkdw YET Q!Q 'f Y D Ohw xv qrz wxuq wr wkh suh0fkdqjh fdvh1 Wr qg wkh wuljjhu srlqw deryh zklfk lqyhvwphqw lv surwdeoh/ zh irfxv rq wkh 5 fc 4?E h f c h uh0 jlrq1 Wklv hqwdlov wkdw erwk wkh vzlwfk ohyhov h f dqg h duh vx!flhqwo kljk wr hqvxuh wkdw d wljkwhu uhjxodwlrq lv dssolhg rqo xqghu jrrg vwdwhv1 Li/ rwkhuzlvh/ dw ohdvw rqh ri wkh wzr vzlwfk srlqwv zhuh orz wkh surw0vkdulqj uhjxodwlrq zrxog eh lpsohphqwhg lq wkh edg0qhzv uhjlrq1 Wklv zrxog ohdg wr d glvwruwlrq1 Ohw xv vwduw zlwk wkh up*v ydoxh1 Wkh Ehoopdq htxdwlrq lv T 7cf E ' _ n E b_ e!o_. dt 7cf En_o n b_ e!o_. dt 7c En_o H{sdqglqj wkh uljkw0kdqg vlgh dqg xvlqj Lw *v ohppd rqh rewdlqv Eo n bt 7cf E ' n Eo BE%, YT 7cfE Y n j2 Y2 T 7cfE 2 2 n bt Y 2 7c E +67, Ghqh fe T 7cf E T 7c E Vxewudfwlqj +5;, e +67, lhogv Eo n bfe ' Eo BE%, YfE Y Wkh ixqfwlrq fe kdv d vwdqgdug vroxwlrq n j2 Y2 fe 2 2 Y 2 fe ' 2[ f q E%,cb ' q E%, cb duh wkh urrwv ri wkh fkdudfwhulvwlf htxdwlrq j 2 2 qeq n Eo BE%,q Eo n b 'f Jlyhq wkh frqglwlrq fef ' fc f 2 lv qlo1 Xvlqj wkh vroxwlrq ri fe dqg htxdwlrq +5<, zh rewdlq T 7cf E ' BE%, n T q Q E%, n f q Q E%,cb c +68, 58