Investment. Net Present Value. Stream of payments A 0, A 1, Consol: same payment forever Common interest rate r

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1 Bfo going o Euo on buin, a man dov hi Roll-Royc o a downown NY Ciy bank and wn in o ak fo an immdia loan of $5,. Th loan offic, akn aback, qud collaal. "Wll, hn, h a h ky o my Roll-Royc", h man aid. Th loan offic omly had h ca divn ino h bank' undgound aking fo af king, and gav him $5,. Two wk la, h man walkd hough h bank' doo, and akd o l u hi loan and g hi ca back. "Tha will b $5, in incial, and $5.4 in in", h loan offic aid. Th man wo ou a chck and ad o walk away. "Wai i", h loan offic aid, "whil you w gon, I found ou you a a millionai. Why in h wold would you nd o boow $5,?" Th man mild. "Wh l could I ak my Roll-Royc in Manhaan fo wo wk and ay only $5.4?" Invmn N Pn Valu Sam of aymn A, A, A A2 A NPV A Conol: am aymn fov Common in a v

2 Mogag Pay $ iod, n iod NPV n n Ca Loan ½% monh $/ monh fo 6 monh NPV To boow $2, qui $2, $ / mo Valu of h Loy $M/y, 2 ya PV PV 3% $5,324 4% $4,34 5% $3,85 6% $2,58 7% $,336 % $9,365 2

3 Bond Pic Bond ay $ in ya Pic NPV $ In a inca cau bond ic o fall MBA Invmn Sagy Comu NPV Undak ojc if NPV > Pfabl o calculaing innal a of un olv quaion NPV fo bcau IRR no wll dfind Invmn Und Uncainy MBA Sagy: U ik-adjud in a Rik adjumn fo ojc, no an! Ibboon Co of Caial Yabook Comu xcd NPV Undak if E NPV > 3

4 Ra of Run If you had invd $ in h following fom nd of 925 o nd of 999 i would hav incad o A Cla Annual Run Ending Walh S&P 5.3% $2, Small comany ock indx 2.6% $6,64.79 Long-m cooa bond indx 5.6% $56.38 Long-m govnmn bond indx 5.% $4.22 Inmdia-m govnmn bond indx 5.2% $43.93 U.S. Tauy Bill 3.8% $5.64 Inflaion 3.% $9.39 Rik and Run A Cla Small comany ock Lag comany ock Long-m cooa bond Long-m govnmn bond Inmdia-m gov bond U.S. Tauy Bill Inflaion Gomic Man 2.6%.3% 5.6% 5.% 5.2% 3.8% 3.% Sandad Dviaion 33.6% 2.% 8.7% 9.3% 5.8% 3.2% 4.5% Aihmic Man 7.6% 3.3% 5.9% 5.5% 5.4% 3.8% 3.2% Man Run Gomic man Aihmic man / n n a i i n a i n i / n n n n Log ai Log[ ai ] Log ai n n i i i 4

5 Man Run, Coninud Gomic mak n whn uing a of un ov val ya Aihmic would b ud fo xcd un in a givn ya Oion Valu NPV i aoia fo now o nv dciion Now o la qui an addiional conidaion Sll a aining Dill an oil wll Build a facoy Invmn doy oion o inv Examl Snd C < o oduc a valu V V U[,], in a U cuoff valu V : inv if V V Poduc NPV JV V J V V C V J V. 2 5

6 Invmn Valu V V C 2 J V. V Maximizd whn 2 V 2 C. V fo C,.25, Rouc Exacion Fixd uly of a ouc R Conan dmand laiciy L Q n h quaniy conumd a im. Abiag: ic i a in a aq Q Q aq 6

7 Rouc U R Q Q Q2... Q 2 Q... Abiag ad u ou Nv un ou Pic i a in a Mak don viw naual ouc hi way flcing alnaiv, chnological chang.5, 2, - 9.3% annual Half lif 7 ya T-Cuing Tim o hav hn lan T, lob, fih, cow Valu af gowh of b Coninuou im in a δ NPV δt 2δT 3δT b T b T b T K δt b T b T δt δt FOC b T δ b T δt 7

8 Soluion 3 25 δδ δ T δt 2 5 Gowh Ra 5 Oimum T T-Cuing Ramy Rul: cu down h whn hy a gowing a h in a b T δ b T δt Aoximaly coc US olicy of maximum uainabl yild nd δ, yild b T b T T Collcibl im a o Quaniy ulid δ q q laiciy of dmand g gowh a of oulaion dicoun a - 8

9 Poch Sd Dmand and Suly Dmand xd, a Dmand and uly qua o giv h maginal u valu of an own a im δ g q q xd v, a v o δ g a v q g Dminaion of Pic Maginal hold mu b ju indiffn o holding Maginal hold who buy a and ll a g u δ v du 9

10 P Piod Valu of Holding δ lim du v u lim δ v v δ Maginal Own i Indiffn Maginal own Yild g q a v δ g q a v δ δ δ Soluion δ δ δ δ δ δ δ g q a g

11 Ncay Condiion Pn valu of maginal u valu i fini: δ g δ > No vyon wan o own h good: lim <. Eih o Saing Pic a q δ g δ δ a q δ g δ δ and q q Imlicaion May doy om quaniy iniially Pic i xonnially Soag co n linaly δ g a q δ g δ δ