1. Loeng 5. Maksete seeria - nüüdis- ja tulevane väärtus Natalja Viilmann, PhD

2. Intertemporaalne valik Annuiteedid Maksete seeria nüüdis- ja tulevane väärtus Praktilisest elust võib tuua palju näiteid: Laenumaksed Üüri või rendimaksed Loengu kava

3. The Intertemporal Choice Problem u Let m 1 and m 2 be incomes received in periods 1 and 2. u Let c 1 and c 2 be consumptions in periods 1 and 2. u Let p 1 and p 2 be the prices of consumption in periods 1 and 2.

4. The Intertemporal Choice Problem u The intertemporal choice problem is: Given incomes m 1 and m 2, and given consumption prices p 1 and p 2, what is the most preferred intertemporal consumption bundle (c 1, c 2 )? u For an answer we need to know: – the intertemporal budget constraint – intertemporal consumption preferences.

5. The Intertemporal Budget Constraint u Suppose that the consumer chooses not to save or to borrow. u Q: What will be consumed in period 1? u A: c 1 = m 1. u Q: What will be consumed in period 2? u A: c 2 = m 2.

6. The Intertemporal Budget Constraint c1c1 c2c2 So (c 1, c 2 ) = (m 1, m 2 ) is the consumption bundle if the consumer chooses neither to save nor to borrow. m2m2 m1m1 0 0

7. The Intertemporal Budget Constraint u Now suppose that the consumer spends nothing on consumption in period 1; that is, c 1 = 0 and the consumer saves s 1 = m 1. u The interest rate is r. u What now will be period 2’s consumption level?

8. The Intertemporal Budget Constraint u Period 2 income is m 2. u Savings plus interest from period 1 sum to (1 + r )m 1. u So total income available in period 2 is m 2 + (1 + r )m 1. u So period 2 consumption expenditure is

9. The Intertemporal Budget Constraint c1c1 c2c2 m2m2 m1m1 0 0 is the consumption bundle when all period 1 income is saved.

10. The Intertemporal Budget Constraint u Now suppose that the consumer spends everything possible on consumption in period 1, so c 2 = 0. u What is the most that the consumer can borrow in period 1 against her period 2 income of $m 2 ? u Let b 1 denote the amount borrowed in period 1.

11. The Intertemporal Budget Constraint u Only $m 2 will be available in period 2 to pay back $b 1 borrowed in period 1. u So b 1 (1 + r ) = m 2. u That is, b 1 = m 2 / (1 + r ). u So the largest possible period 1 consumption level is

12. The Intertemporal Budget Constraint c1c1 c2c2 m2m2 m1m1 0 0 is the consumption bundle when all period 1 income is saved. the present-value of the income endowment

13. The Intertemporal Budget Constraint c1c1 c2c2 m2m2 m1m1 0 0 Saving Borrowing slope = -(1+r)

14. Annuiteedid Tavaline annuiteet (ordinary annuity) Annuiteet, mille rahavood toimuvad teatud aja jooksul iga perioodi lõpul, esimene rahavoog toimub esimese perioodi lõpul. Avansiline annuiteet (annuity due): Annuiteet, mille rahavood on nihkunud iga perioodi algusesse, seega esimene rahavoog Viitannuiteet (deferred annuity): Annuiteet, mille esimene rahavoog on rohkem kui ühe perioodi pärast (nt 10 aasta pärast hakkame saama viie aasta jooksul 10 000 krooni aastas).

15. Kasutame järgmisi lühendeid

16. Present and Future Value Translating cash flows forward and backward through time

22. Näide annuiteedi nüüdisväärtuse kohta

24. Näide:

25. Lahendus: