Investment Under Certainty

2. Investment Under Certainty

Intertemporal consumption ( Ho) does an investor investor decide decide *et)ee *et)een n consumi consumin+ n+ today and de,errin+ consumption until next period( %upp %uppos osee &is &is inc incom omee is Y  today and Y 1 next period ( I, inve invest sto or can can lend or borrow at /same0 rate R" t&en &e can position &imsel, any)&ere on t&e budget line t&at passes t&rou+& /Y "Y 10 )it& slope /1R0

IB253 Principles of Finance 1 Lecture 3

Consumption next period

lend lend Y  at rate R  consume Y /1R0  Y 1 next period

Y  ⋅ (1+ R) + Y  0 1 Y 1

Key readings Hillier et al. al. Appendix 4A Bodie et al. al. 1.11.! Copeland" Copeland" #eston #eston $ %&astri 1A1'" 2A2B 2A2B 1

Y 0

Y  Y  + 1 0 1+ R

Consumption this period

2 borr borrow ow Y 1/1R0 at rate R  consume Y   Y 1/1R0 now

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Consumption vs. Investment

Capital Investment ( %upp %uppos osee inve invest stor or can can inve invest st I now in a capital pro6ect t&at )ill pay C 1 for sure next period Consumption next period

( I, R89R" capital pro6ect adds value (Y 

0

) (1+ R)

− I  ⋅

+

 ALL investo investors rs )ill )ill underta:e underta:e pro6ec pro6ect" t" re+ardles re+ardlesss o, t&eir individual pre,erences a*out )&en to consume t&eir )ealt&

(Y  + C  ) 1

1

Y 1+C 1

Y 1

( 7ate o, o, re return RP on capital pro6ect is +iven *y slope –(1+ RP) o, line t&at 6oins / Y "Y 10 to /Y I "Y 1C 10

Y  − I  0

+

NPV

Y  + C  1 1 1+ R

Consumption

Consumption next period invest I no) in capital pro6ect lend Y   I at rate R consume /Y I 0/1 0/1R0 Y 1C 1 next period

Y 1+C 1

invest I no) in capital pro6ect consume Y   I no) consume Y  C  next period

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>i,,erent lendin+ and *orro)in+ rates

;is&er %eparation ( 8rovid 8rovided ed lendin lendin+ + and *orr *orro)i o)in+ n+ rates rates are are equal" t&en all investors a+ree on )&et&er capital pro6ect adds value or not ( Criterion Criterion ,or capital capital in investm vestment ent is t&at t&at ecision to invest in capital pro6ect is separate ,rom consumption decision

Consumption next period slope RL

Y 1+C 1

Y 1+C 1

slope RB @ R8 Y 

slope RB9R8

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ultiperiod case