电子科技大学：《金融学基础》（英文版）Chapter 5: Life-Cycle Financial Planning

Finance School of management Chapter 5: Life-Cycle Financial Planning Objective Human capital, permanent income decisions over uesTc

1 Finance School of Management Chapter 5: Life-Cycle Financial Planning Objective Human capital, permanent income decisions over life cycle

Finance School of management Consumption over the Life cycle You are currently 35 years old, expect to retire in 30 years at age 65, and then to live for 15 more years until age 80 u You current income is $30,000 per year, and you real labor income adjusted for inflation remains at $30,000 per year until age 65 u The real rate of interest is 3% per year u Assume you plan to consume a constant stream of the same amount in each of the next 45 years denoted by C uesTc

2 Finance School of Management Consumption over the Life Cycle u You are currently 35 years old, expect to retire in 30 years at age 65, and then to live for 15 more years until age 80 u You current income is $30,000 per year, and you real labor income adjusted for inflation remains at $30,000 per year until age 65 u The real rate of interest is 3% per year u Assume you plan to consume a constant stream of the same amount in each of the next 45 years, denoted by C

Finance School of management Target Replacement Rate of Preretirement Income You should aim for a replacement rate equal to 75% of your preretirement income. That is 0.75*$30000=$22,500 ni pv fv PMT Rsult 15 22,500$268,604 PV FV PMT Rsult 30308268,604985,646 uesTc

3 Finance School of Management Target Replacement Rate of Preretirement Income u You should aim for a replacement rate equal to 75% of your preretirement income. That is 0.75*$30000=$22,500. n i P V F V PMT Rsult 1 5 3 ？ 0 -22,500 $268,604 n i P V F V PMT Rsult 3 0 3 0 $268,604 ? $5,646

Finance School of management Consumption over the Life Cycle PV FV PMT Result 303% 0 1$4758 PV FV PMt Result 153% 1194 uesTc

4 Finance School of Management n i PV FV PMT Result 30 3% 0 ? 1 $47.58 n i PV FV PMT Result 15 3% ? 0 1 $11.94 Consumption over the Life Cycle

Finance School of management Consumption over the Life Cycle 47.58(30,000-C)=11.94C C=$23,982-Permanent income 45 30 Human capital (1+)=1(1+i) uesTc

5 Finance School of Management 47.58(30,000 −C) =11.94C Consumption over the Life Cycle C = $23,982 — Permanent income   — Human capital = = + = + 45 1 30 t (1 ) t 1 (1 ) t t t i Y i C

Finance School of management Labor Income and consumption 35000 300001 25000 20000 lab inc s15000 consump 10000 5000 0 45 55 60 70 75 80 -5000 esTc Age

6 Finance School of Management Labor Income and Consumption -5000 0 5000 10000 15000 20000 25000 30000 35000 35 40 45 50 55 60 65 70 75 80 Age Real $ lab_inc consump

Finance School of management Human Capital and wealth 700000 600000 fund 500000 HumanCap Capital 400000 300000 200000 100000 0 65 100000 ge uesTc See exce

7 Finance School of Management Human Capital and Wealth -100000 0 100000 200000 300000 400000 500000 600000 700000 35 45 55 65 75 Age Real $ fund HumanCap Capital See Excel

Finance School of management The Inter-temporal Budget Constraint B R W。+ t=1 7=1(1+ i= real interest rate R= number of years to retirement T=number of years of remaining life Wo=initial wealth B- bequest uesTc

8 Finance School of Management The Inter-temporal Budget Constraint ( ) ( ) ( )   = = + = + + + + R t t t T T t t t i Y W i B i C 1 0 1 1 1 1 i = real interest rate R = number of years to retirement T = number of years of remaining life W0 = initial wealth B = bequest

Finance School of management The Optimal Choice Optimization model The economists usually research the optimal choice of agents under intertemporal budget constraint a feasible plan uesTc

9 Finance School of Management The Optimal Choice: Optimization Model u The economists usually research the optimal choice of agents under intertemporal budget constraint. – a feasible plan

Finance School of management Omar's Problem Dr. Omar has just graduated from medical school at age 30 and has started training to be a surgeon His real salary for the next five years will be $25,000 per year. After completing his residency Omar expects to earn $300,000 per year in real terms until he retires at age 65. assume that the real interest rate is 3 If he wants to maintain the same level of consumption until his life expectancy 85 years old, should omar allocate his wealth? uesTc 10

10 Finance School of Management Omar’s Problem u Dr. Omar has just graduated from medical school at age 30 and has started training to be a surgeon. u His real salary for the next five years will be $25,000 per year. After completing his residency, Omar expects to earn $300,000 per year in real terms until he retires at age 65. Assume that the real interest rate is 3%. u If he wants to maintain the same level of consumption until his life expectancy 85 years old, should Omar allocate his wealth?