Question

Matt has just completed his MBA and landed a new job that will pay him $50,000 this year. He expects his salary to grow at the historical inflation rate 3.5% APR, plus 1% annually until he retires in 25 years. He is estimating that he will live for 30 years after retirement. Matt will use his forecasted salary on the day he retires as a target for the annual withdraws he will make at the beginning of each year during retirement. However, he wants to increase his retirement salary by the estimated inflation rate 3.5 % APR, each year during his retirement as well. (This is called a growing annuity). Matt currently has $25,000 in a bond mutual fund retirement account and will use that money for his retirement. He is also planning to start another retirement account and contribute $250 in a high-risk stock mutual fund each month until he retires. Matt expects his bond account to earn 4% APR Semi-Annual Bond Return and his stock account to earn 16% EAR, Stock Return until he retires. After his retirement, he will take a more conservative approach to managing his retirement funds and will place all his retirement funds in a mutual fund that will earn 7% APR Annual, Return after retirement.

PART 1: Calculate if Matt will have enough for retirement given the above information, showing all work and illustrating with a timeline. If he does not, estimate how much more he should put in his stock account each month to sustain his retirement. If he does, calculate by how much he can reduce his stock account contribution.

PART 2: Discuss your concerns about any risk that might be associated with his current strategy. Recommend and explain, illustrate with your own calculations and historical data, at least one alternative investment strategy that you might recommend prior to retirement.

Answer 1

we have the following timelines

inflstion during working period =3.5+1=4.5%

inflation during retirement period =3.5%

target salary during retirement =50000(1.045)^24=143800.69

PV of this salary at the retirement@ 7%(as this salary would come from a fund which earns 7% annual)

PV of a growing annuity =C1*(1-((1+g)/(1+r))^n)/(r-g)

where

g=3.5%

r=7%

n=29(as the cashflows are at begenning)

C1=cashflow next year=C0*1.035=143800.69*1.035=153491.21

PV=153491.21*(1-(1.035/1.07)^29)/(.07-.035)+143800.69( cash flow at the beggenning of year 1 i.e. at time 0)

PV=2857572.63

now let us calulate the FV of investments at retirement (i.e. at time =25)

FV of bond investment=25000(1+.04/2)^(25*2)=67289.7

FV of equity investment= FV of first 24 inestments+ last investment=250*(1.16^24 -1)/(1.16^(1/12)-1) + 250=687996.84

total FV =687996.84+67289.7=755286.54

Shortage =2857572.63-755286.54=2102286.09

let the additional amount of stock investment be = x

hence FV of x @16% Should be =2102286.09

x*(1.16^24 -1)/(1.16^(1/12) -1)+x=2102286.09

x*2751.99=2102286.09

x=763.92

he needs to put 763.93 each month extra in stocks.

Part2:

since all the investments have been made in mutual funds , overall risk is minimised the only risk that remains is systematic risk which impact every one simultaneously and he can't do anything with this however bond portfolio doesn't have even that kind of risk that is it offers a lower interest rate now as we can see stock fund provides better returns then he should transfer this dollar from bond fund to stock fund it will have the following implications

EXtra FV = 25000*1.16^25 - 25000*1.02^50
= 1021856.09-67289.7=954566.39

because of this extra money contribution in stock would only b( 2102286.09-954566.39)/2751.99 =417.05