Transcript L11

L11
Intertermporal Choice II
Intertemporal Choice
periods: C1 C2
 Consumption smoothing
 Two
 Today:
Many periods
3 Periods
 Cash
flows
Many Periods
 Cash
flow
0 1 2 ...
tim e
PV0 
 E:
T=3, r=100%. Choose:
$1 in each of the three period or $8 in the third
Translation
 Cashflow
0 12
PV 0 
tim e
Important cashflow: Perpetuity
 Gives
constant payment x forever
 Cashflow
0 12
PV 0 
tim e
Perpetuity (Example)
 You
can rent an apartment for $1000 each
month (r=0.5%=0.005)
PV 0 
 You
can buy it P=300.000
 Renting
vs buying?
Quiz
 Consider
consol that pays $10,000 per year.
(r=5%=0.05)
 Q:
In terms of todays dollars consol is worth
A) $ 10,000
B) $100,000
C) $ 200,000
D) $1000,000
P V0 
Important cashflow: Annuity
 “Tree”
that gives constant payment in T
following periods
 Cashflow
0 12
PV 0 
T T 1
tim e
Quiz: Leasing or Buying A Car
Lease T=3, x=$800, r=100% or buy P=750
You should
A) Buy a car
B) Lease a car
C) Both options are equally attractive
Loan Payment
 Take
a loan (how much do you pay monthly)
Loan=1000, T=3, r=100% and x=?
Asset Valuation: Bonds
 Treasury
bill: Face, Coupon, Maturity
0 12
 PV
of T-bills (F, c, T) and r
PV 0 
T
Asset Valuation: Example
 T-bond
(F=100, c=10, T=6) and r=5%
Life cycle problems
 Consumption
– savings problem
 Pension:
– How much to put aside?
– How much am I going to get?
20 21
60
80 tim e
Consumption Smoothing
 Income:
100 in the first 40 years
 Consumption C during 60 years,
 Constant consumption! Find C if r=5%
20 21
60
80
tim e
Pension Plan
 You
want C=100 when retired (61-80)
 How much do you have to save if r=5%,
20 21
60
80
tim e
Pension Plan
 You
save S=100 (21-60)
 How much will you get (per year) if r=5%,
20 21
60
80 tim e