FIN668 Exam#1, Spring 2024
1. (10 points) Susan has just signed a contract with your wealth management firm. She brings $18 million to your firm and agrees to the fee schedule below. Today is April 9, 2024. How much management fee should you charge Susan today?
AUM Annual fee rate
First $500,000 1.40%
Next $1.5 million 1.20%
Next $3 million 1.00%
Next $5 million 0.80%
Above $10 million 0.60%
1) Annual fee = 0.5x1.4% + 1.5x1.2% + 3x1.0% + 5x0.8% + 8x0.6% = $143,000.
2) This quarterly fee = 143,000 / 4 = $35,750
3) Susan needs to pay management fees for the remainder of the quarter. There are 22 days (from 4/9 to 4/30 in April) and 61 days in May and June left in the 91-day quarter [30+31+30]. Her fees are 35,750 x (83/91) = $32,607.14, deducted from her $18 million deposit on 4/9. The next management fee is due on 7/1, 10/1, then 1/1, 4/1, …
2. (10 points) The following information summarizes Rose’s account. Compute Rose’s money-weighted return since
inception and time-weighted return since inception. Keep your answer in 2 decimal places, e.g., 12.34%. Show your work and highlight your final answers.
1) Rose set up the account with an initial investment of $237,000 on 1/16/2023.
2) The account balance was $173,000 at the market open on 2/15/2023. Rose withdrew $26,000 from the account before the market close on the same day.
3) The account balance was $298,000 at the market open on 4/20/2023. Rose invested $86,000 in the account before the market close that day.
4) Rose paid a $4600 account service fee at the end of 2023.
5) The account balance was $481,000 at the market open on 6/23/2023. Rose withdrew $92,000 from the account during that trading day.
6) The account balance reached its record high of $512,000 on 2/16/2024.
7) The account has received $5,900 in total dividends and interests since account inception.
8) The current account balance today (4/9/2024) is $387,000.
3. (4 points) Based on our class discussion on the left panel on Slide #31, what is the estimated probability that the portfolio return is lower than - 14.6% in a given year?
Answer: 2.50%
4. (6 points) Based on Slide #51, compute two Sharpe ratios for the time between Jan 1990 and Dec 2020, one for the non- rebalanced portfolio and one for the rebalanced portfolio. Use the risk-free rate of 4.2% in both calculations. Which
Sharpe ratio is more desirable, the non-rebalanced or the rebalanced? Keep 4 decimal places in your final answers, e.g., 5.1234. Show your work and highlight your final answers.
A higher Sharpe ratio is more desirable. In this case, the rebalanced SR of 0.4157.
5. (8 points) Jacob just celebrated his 76th birthday last week. His 401(k) account balance on his 76th birthday was $422,000. His 401(k) account balance at the end of last year was $396,000. (a) Compute the amount of Jacob’s RMD for the year
2024. (b) If Jacob withdraws $12,700 from this 401(k) account in 2024, how much is the tax penalty from the IRS in 2024? Show your work and highlight your final answers.
RMD = 396,000 / 23.7 = $16,708.86
Tax penalty = (16,708.86 – 12,700) x 0.25 = $1,002.22
6. (8 points) The Addams family has an annual earned income of $200,000 and long-term capital gains of $100,000 in 2024, how much capital gains tax should they pay? Addams family uses the standard deduction. Show your work and highlight your final answer.
Taxable income = 200,000 – 29,200 = $170,800
Capital gains tax = tax(170,800 + 100,000) – tax(178,000) = 100,000 x 15% = $15,000
7. (8 points) Sharma is single and has an AGI in 2024 of $302,000. How much is his Federal income tax based on the AMT calculation? Show your work and highlight your final answers.
AMT taxable income = 302,000 – 85,700 = $216,300
Taxes based on AMT = $216,300 x 26% = $56,238.00
8. (8 points) Bob’s estate has a total income of $124,800 in 2024. Compute the estate’s federal income tax for the year.
Show your work and highlight your final answers.
Federal income tax = 3,659.50 + 0.37 x (124,800 – 15,200) = $44,211.50
9. (2x4+6 points) You make a one-time investment of pre-income-tax funds of $7,000 in each of the following accounts for 42 years, earning 10.1% per year. Assume that all your tax rates stay at 20% over time. How much do you have after
liquidating the accounts and paying all taxes at the end of Year 42? How much capital gains tax do you pay in case (d)? Show your work and highlight your final answers. Avoid rounding errors. Clearly label your answers.
a) A traditional IRA account.
b) A Roth IRA account.
c) A non-qualified account and you realize all gains by the end of each year.
d) A non-qualified account and you don’t realize any gains until account liquidation.
a) $7,000x(1.101)42x(1-0.20) = $318,607.08
b) $7,000x(1-0.20)x(1.101)42 = $318,607.08
c) $7,000x(1-0.20)x(1+0.101(1-0.20))42 = $ 146,383.50
d) $7,000x(1-0.20)x[(1+0.101)42 – [(1+0.101)42 – 1](0.20)] = $256,005.66
e) The amount of capital gains tax paid in (d) is $7,000x(1-0.20)x[(1+0.101)42 – 1](0.20) = $62,601.42. Note that the amount is exactly the difference between (b) and (d), which makes sense.
10. (10 points) Use the 2024 tax table in Slide #81 and compute the federal marriage tax penalty for a couple where the wife and the husband each individually have an adjusted gross taxable income (AGI) of $560,000 in 2024. Show your work and highlight your final answer.
11. (4 points) Which choice carries a higher after-tax dollar amount of investment?
a) An annual contribution of $12,000 to a traditional 401k.
b) An annual contribution of $12,000 to a Roth 401K.
c) The first two options provide the same amount.
Answer: (b).
12. (10 points) Based on Slides #66-67, compute the final answer “annual savings amount to achieve retirement goals” using the following set of input data. Show your formula and input to get the answers for Steps #2 through #6. Show your work and highlight your final answers. You will not get credit unless you show your formulas and inputs. Just showing the final outcome is NOT enough.
Comments:
1) To access your exam: BlackboardàFIN668àMy gradesàExam 1 àclick on your score to view your exam.
2) All exam questions are highly correlated with our PPT lecture notes and in-class discussions. You need to study and fully understand the class material to do well. The remaining exams will be of the same nature.
3) When you study, do not just read the PPT files. Use Excel and a calculator to repeat all answers in all PPT slides in the course. Exams need you to demonstrate your ability to deliver correct numerical results. Do not just read.
Calculate.
4) Prepare for the exam. You do not have time to study a topic during the exam. You may not have time to construct a fresh Excel file during the exam. Have your Excel files ready before the exam.
5) Always show your work. If you use Excel, you need to show me all your formulas. If you don’t use Excel, you need to show me formulas/inputs. No work = no credit. Highlight your final answers or make a clear statement about your final answers. Don’t let me guess your final answers. Don’t describe how you solve the question. Solve the question with numbers and equations. This course is a finance course. I understand mathematics.
6) Avoid rounding errors. 7%/12 is not the same as 0.58%! For dollar amounts, keep 2 decimal places, e.g., $12.34. For rates, keep 4 decimal places as a percentage, e.g., 5.1234%.
7) Read my solutions to see the style of answering questions. Do not provide any thoughts or comments that the questions do not ask. Just answer the questions and move on. Don’t elaborate. Save your time.
8) Understand the solutions to this exam. The final exam is comprehensive. Your final course letter grade is based on a curve on the course total: Total = 0. 15(attendance) + 0.45(exam 1 + exam 2).
9) The next two days are for you to self-study. If you have any questions related to grading, ask me starting Thursday, but before the final exam. I am available during my office hours and after every class.