Required Return CFA 2014 Exam

"The current value of the Crusoes’ investment portfolio is USD 1,330,000. Scolari has determined that when the couple retires four years from today, a portfolio valued at USD 2,200,000 could sustain them through their retirement years. Scolari expects the Crusoes to earn an after-tax return of 4.5% per year on their current portfolio and any additions to the portfolio prior to retirement. The Crusoes believe they can continue to save an after-tax total of USD 35,000 per year during the next four years.

C. Demonstrate, given the current assumptions, that the Crusoes will not be able to retire in four years in accordance with their existing plan. Show your calculations.

So obviously it is N=4, PV=1330000, i=4.5%, PMT=-35000, CPT FV. I know you always input PV as a negative number, but I always screw up the PMT input on the calculator. How do you know if payment is -35000 or 35000?

if he is contributing to the fund, use negative payments, if he is withdrawing, use positive.

Assuming you have a negative sign in front of PV, If they are putting money into the portfolio (cash outflow), it’s a negative, if they are receiving money from the portfolio (cash inflow), it’s a positive.

Think of how you calculate the return on a bond in your calculator.

You pay 1,000 for a bond, hence, PV = -1000. You receive coupon pmt of 25 (cash inflow). PMT = +25

Think of it intuitively, too… You know they have 1,330,000 in the bank and need 2,200,000 in 4 years. If they are receiving money from the portfolio, they are going to have to earn a heck of a lot higher return on the portfolio (shrinking asset base) to get to 2,200,000 than if they are contributing money to the portfolio (growing asset base). change the sign on your payment value and see the difference.

^ +1 better answer than mine

Also one last thing: My first instinct was not to use the calculator at all but to do:

1300000*(1.045^4)+35000*(1.045)+35000*(1045^2)+35000*(1.045^3)+35000*(1.045^3) and show that this does not come close to 2200000. However, I get a different answer adding up these terms than from the calculator inputs. Why is that?

Because it should be

1,330,000 (1.045^4) + 35000(1.045^3) + 35000(1.045^2) + 35000(1.045^1) + 35000 = 1,735,786

Remember, end of year payments.

At the end of this year, you will make your first 35,000 payment to the account, therefore, it will only compound for 4-1 = 3 periods. the last payment will not compound since you essentially make that payment the day that you need the 2,200,000