L11

Intertermporal Choice II

Intertemporal Choice

Two periods: Consumption smoothing

Today: Many periods

1C 2C

3 Periods Cashflows

Many Periods Cashflow

E: T=3, r=100%. Choose:$1 in each of the three period or $8 in the third

0 1 2 . . . time

0PV

Translation Cashflow

0 1 2 . . . time

0PV

Gives constant payment x forever Cashflow

Important cashflow: Perpetuity

0PV

0 1 2 . . . time

You can rent an apartment for $1000 each month (r=0.5%=0.005)

You can buy it P=300.000 Renting vs buying?

Perpetuity (Example)

0PV

Valuate a consol that pays $10,000 per year. (r=5%=0.05)

You inherit $1000,000. How much monthly interest are you going to get ? (r=5%=0.05)

Perpetuity (Example)

0PV

“Tree” that gives constant payment in T following periods

Cashflow

Important cashflow: Annuity

0PV

0 1 2 . . . timeT 1T

Leasing or buying a car?

Lease T=3, x=$800, r=100% or buy P=750

Take a loan (how much do you pay monthly)

Loan=1000, T=3, r=100% and x=?

Leasing or Buying A Car

Treasury bill: Face, Coupon, Maturity

PV of T-bills (F, c, T) and r

Asset Valuation: Bonds

0PV

0 1 2 . . . T

T-bond (F=100, c=10, T=6) and r=5%

Asset Valuation: Example

Consumption – savings problem Pension:

–How much to put aside?

–How much am I going to get?

Life cycle problems

20 21 . . . time60 80

Income: 100 in the first 40 years Consumption C during 60 years, Constant consumption! Find C if r=5%

Consumption Smoothing

20 21 . . . time60 80

You want C=100 when retired (61-80) How much do you have to save if r=5%,

Pension Plan

20 21 . . . time60 80

You save S=100 (21-60) How much will you get (per year) if r=5%,

Pension Plan

20 21 . . . time60 80