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Today is your 21st birthday, you just started a new job and you are planning to save for | |

retirement. You plan to save a percent of your salary each year through age 64, quit your | |

job on your 65th birthday, then begin withdrawing that day and each year thereafter. Your | |

salary is expected to increase each year by the rates in column D on the Starter sheet | |

so the amount saved each year will be growing. Inflation will impact the rate you earn as | |

well as purchasing power so you will need to express some of the future amounts in real | |

(or today's) dollars. Once you retire the amount you withdraw each year needs to be able | |

to purchase the same amount as $90,000 would today. Assume all cash flows are at | |

year end. Ignore taxes. To simplify assume that your salary is paid annually in a lump | |

sum after working for one year. | |

Of course if you knew the rate you would earn each year on your account and the age at | |

which you would die you could easily calculate how much to save for any size | |

withdrawal. But in reality you do not know these annually compounded rates and must | |

estimate them. You may assume each year's rate is normally distributed with the | |

parameters listed on the Starter sheet and independent of (not dependent on) any other | |

year's rate. Also assume that the rates given are annually compounded rates. | |

Modify the Starter sheet to simulate 10,000 times the age to which you will be able to | |

continue the withdrawals, understanding that you may eventually run out of money! The | |

Starter sheet shows ages XXXXXXXXXXby which time you will likely be long gone from this | |

world. Cells with "XXXXX" must be replaced with formulas. Use empty cells on the | |

starter sheet in column L to help impute the approximate age (years and fraction of year) | |

you run out of money (ex XXXXXXXXXXAssume that this age cannot be larger than 121. | |

L111 should be replaced with a formula to show what year (and fraction) your money ran | |

out. Note that L111 should be less than or equal to 121. You will need to create a way to | |

determine to what age your money will last. Assume that your balance earns a rate of | |

return only if it is invested for the entire year. If there is only enough money for a partial | |

withdrawal in the last year that your money runs out then adjust age proportionately, i.e. | |

half a payment lasts half a year. Hint: Use cells in L53:L110 for intermediate calculations | |

using an IF function. | |

Read the section below describing the Fisher equation to help with inflation calculations. If | |

you use the Fisher equation be sure to use the exact formula and not the approximation. | |

Double check all of your calculations. One way to do this would be to use different formulas | |

in another workbook along with some common sense about what is reasonable. | |

Build the simulation table at the bottom of the Starter sheet. After completing the | |

simulation, show (in the purple fill range at the top right of the Starter sheet) a formula to | |

calculate the average, minimum and maximum age at which your money ran out based | |

on the 10,000 results. Show in O2:O5 the 5, 10, 50 and 75 percentile ages using the | |

| |

to show statistics for the 10,000 values simulated. | |

Now, rerun the simulation six times by changing C6 and show in the yellow-fill region in | |

L7:Q7 the 10%ile age for the six different percentages saved (L6:Q6). Replace each | |

"???" with VALUES (NOT formulas) with as many decimals as the simulation produces. | |

When finished with this step replace C6 with the original value of 15.0%. | |

Assume that your 10,000 simulated ages arerepresentative of what might happen in the | |

future. In M12:R29 below Part 1 on the Starter sheet carefully explain the meaning of the | |

10 percentile age shown in O3 when 15% of salary is saved. Target your explanation to | |

an English major with no understanding of Finance asking you how long their money | |

might last in retirement. | |

| |

For this part you will need to use the model you built in Part 1, changing only the | |

formulas in column G (to reference new mean and standard deviations) and A115. You | |

will need to add a few formulas in the gray workspace (V43:AD76). Carefully label any | |

new entries in this workspace. | |

Assume now that you divide your portfolio into two pieces, the risky part (stocks, equity | |

funds, hedge funds, options, futures, etc.) and the riskless part (T-bills, guaranteed rate | |

investments, etc. having no risk). This strategy is consistent with the two-fund separation | |

result of the Markowitz model we discussed in class. If you have difficulty completing the | |

tasks below review the Ch 8 Edited workbook and associated lectures. | |

The weights on the risky portfolio part will be between 1% and 100%. Use the assumptions | |

in R36:R40 for the following. Run 24 simulations to determine the value of your | |

retirement portfolio in today's dollars (i.e., deflated) at age 65 immediately before the first | |

withdrawal. For each simulation change the balance of your portfolio using the weights in | |

the green fill table along with the different percentiles shown. Be sure to adjust the | |

portfolio expected return (simulated in column G) and standard deviation for each | |

simulation run. As you fill in the table "XXXXX"s with values (NOT formulas) from the | |

simulations the chart below the graph will automatically adjust to display the results. | |

Below the graph in the blue fill region explain how you would use it to determine the best | |

balance of the risky and riskless parts of your portfolio. What weights would | |

form your portfolio and | |

adverbs and adjectives, and economical in the use of words. | |

Lastly, if you had the option to invest in any Vanguard fund as the risky part of your | |

retirement portfolio which fund or funds would you pick? Why? Answer in the region | |

provided on the Starter sheet. Vanguard funds can be seen at | |

https://investor.vanguard.com/home |

May 09, 2021

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