Chapter 5: Life Cycle Financial Planning Objective Financial decisions in an uncertain world; Human capital, permanent income decisions over life cycle Objectives – How much to save for retirement – Whether to defer taxes or pay them now – Whether to get a professional Degree – Whether to buy or rent an apartment Labor Income and Consumption 35000 30000 25000 Real $ 20000 lab_inc consump 15000 10000 5000 35 40 45 50 55 60 65 -5000 Age 70 75 80 Human Capital and Wealth 700000 600000 fund HumanCap Capital 500000 Real $ 400000 300000 200000 100000 35 45 55 65 -100000 Age 75 The Inter-temporal Budget Constraint T R Ct Yt B + = W0 + ∑ ∑ t T t (1 + i ) t =1 (1 + i ) t =1 (1 + i ) i = real interest rate R = number of years to retirement T = number of years of remaining life W0 = initial wealth B = bequest Solution by Real Conversion We are almost done All that remains is to assemble the parts, and solve the resulting equation PV = 391816.3459 − 8.208829897 * X − 19876.29308 − 391816.3459 + 19876.29308 X= = $45,309.75 − 8.208829897 Solution by Growing Annuity • Equation  1+ g  Xa 1 −  PV =  a −1  ( r − g )(1 + r )   + r  b − a +1     Solution by Growing Annuity j a j bj gj Xaj PVj 1 10 10% 35,000 ? 13 3% ? 11 13 3% X1 15,000*1.03 10 ? Algebra   1.15 10    1.03 13  35000 x 1 −  1 −  PV = = +   −   1−1  1−1  ( 0.1 − 0.15)(1.1)   1.1   ( 0.1 − 0.03)(1.1)   1.1   10   1.03 13−11+1  15000(1.03) 1 −   −  11−1   ( 0.1 − 0.03)(1.1)   1.1   ⇒ = 391816.3459 − 8.208829897 x − 19876.29308 ⇒ x = 45309.75 Year NetSalary Fees 10 11 12 13 StartExp 35000 40250 46288 53231 61215 70398 80957 93101 107066 123126 -20159 -20764 -21386 Expend -45310 -46669 -48069 -49511 -50997 -52526 -54102 -55725 -57397 -59119 -60893 -62719 -64601 45309.75 10 Sum -10310 -6419 -1782 3719 10219 17871 26855 37375 49669 64007 -81051 -83483 -85987 Account -10310 -17760 -21317 -19730 -11484 5239 32618 73255 130249 207281 146957 78170 How Much Must I Save? The Nominal Approach n n   X (1 + g )   + g   1+ g  PV = 1−  = P ⇒   ( r − g )   + r    + r  P( r − g ) 20000( 0.12 − 0.03) X0 = = n  1+ r     1.12 8   (1 + g ) 1.03   −   −   1.03     + g       X = $1,830.79 11