Personal Finance: Another Perspective

Preparing for the Final Exam –

Review #2

Preparing for the Final Exam – Review #2

How to do well on my exams (by order of what I think is most important):• 1. Review the PowerPoints for each class

• These are the things I consider important• Especially look for application problems

and know how to do them• 2. Review the previous quizzes and exams

• Check your answers from the net• 3. Review the homework problems, review

problems, and readings • Think through the purpose for each problem

Insurance

Data: Jonathan is a widower with two children and earns $50,000 per year.

His group life insurance policy from work will pay 3 times his salary. He has $70,000 saved in his company 401K, $10,000 in a Roth IRA, and $5,000 in his savings and checking account. He wants to purchase life insurance until is youngest graduates from college, which will likely be 20 years. He is not concerned about his outstanding mortgage, as his kids could go live with his brother and sister-in-law in the event of his death.

Calculations and Application • a. Assuming his brother can earn 3% after-tax, after-inflation

return, use the earning multiple approach to calculate his life insurance needs. b. What other information would you need to calculate the needs approach for Jonathan?

Widower, two children, $50,000 per year, s group life insurance policy will pay 3 times salary, $70,000 in 401K, $10,000 in IRA, and $5,000 in savings. Wants life insurance for 20 years. a. Assuming a 3% after-tax, after-inflation return, use the earning multiple approach to calculate

his life insurance needs. Other information necessary for needs approach?

Answer

a. Earnings Multiple ApproachSalary $50,000 Expense reduction 0.74 26% reduction (3 to 2)Amount needed 37,000 Life insurance needed $566,981 PMT = 37,000, I = 3%, N = 20Note that you want payments at the beginning of each year so

you will want your calculator in begin modeCompany life insurance ($150,000) or 3 times salaryAdditional needed $416,981 Multiple needed: 8.3 times salary

Answer

b. Other information for a needs approach would be funeral expenses, debt elimination, children’s educational expenses, mission expenses, social security benefits, etc. Notice that the earnings multiple approach does not take into account your individual level of savings or your current financial condition.

Mutual Fund Fees

Data and Calculations Which of the funds in the following table would be the

better investment for someone who initially invests $5,000 and knows the fund will be sold at the end of five years? (Assume that each fund’s total pre-expense return is 10 percent a year.) Fund 1 Fund 2 Fund 3 Fund 4

Front-end load 8.00% 5.75% 0.00% 0.00%Back-end load 0.00% 0.00% 2.00% 0.00%

(within 3 years)Management fee 0.55% 0.95% 1.50% 0.18%12b-1 fee 0.00% 0.25% 0.50% 0.00%

Fund 1 Fund 2 Fund 3 Fund 4Front-end load 8.00% 5.75% 0.00% 0.00%Back-end load 0.00% 0.00% 2.00% 0.00%

(within 3 years)Management fee 0.55% 0.95% 1.50% 0.18%12b-1 fee 0.00% 0.25% 0.50% 0.00%

Answer

Fund 1 Fund 2 Fund 3 Fund 4Initial Purchase $5,000 $5,000 $5,000 $5,000Load $400 $288 $0 $0Net Invested = PV $4,600 $4,712 $5,000 $5,000Annual Fees 0.55% 1.20% 2.00% .18%Net Return after fees=I 9.45% 8.80% 8.00% 9.82%Future Value $7,225 $7,184 $7,347 $7,987 Fund 4 would be the better investment for someone who knows that

the fund will be sold at the end of five years. The negative impact of front-end loads outweighs the negative impact of a higher annual fee.

Mutual Fund Returns

Data and Calculations:• You just started investing, and decided to include a balanced fund,

Mega Bucks Mutual Fund, as your first asset. Assume ordinary income tax rates of 35%, state tax of 8%, long-term capital gains rates of 15%, dividend rates for equities of 15%, and dividend rates (bonds) at ordinary income rates. What is your before tax and after-tax return for this period for your mutual fund?

Dec. 31, 2005 Dec. 31, 2006

Market value of portfolio $900 mn $950 mnLiabilities of the fund $50 mn 75 mnShares outstanding 50 mn 55 mn

• The investment company just announced its year-end distributions for 2006 (on a per share basis) of: • Long-term capital gains distributions of $1.95.• Bond dividend distributions of $1.45.

Ordinary tax rates 35%, state tax 8%, long-term capital gains 15%, dividend rates for equities of 15%, and dividend rates (bonds) at ordinary income rates, what is your before tax and after-tax return for this period for this mutual fund?

Dec. 31, 2005 Dec. 31, 2006 DistributionsMarket value of portfolio $900 mn $950 mn Long-term capital gains distributions of $1.95.Liabilities of the fund $50 mn 75 mn Bond dividend distributions of $1.45.Shares outstanding 50 mn 55 mn

Answer

Dec. 31, 2005 Dec. 31, 2006Market value of portfolio $900 mn $950 mnLiabilities of the fund $50 mn 75 mnShares outstanding 50 mn 55 mn

• Beginning NAV = ($900-50) / 50 million = $17.00• Ending NAV = ($950 - $75) / 55 million = $15.91• Before-Tax Return = ($1.95 + $1.45 + ($15.91 -

$17.00)) / $17.00 = 13.6%• After-Tax Return = ($1.95 * (1 - (.15 + .08)) +

$1.45 * (1 - (.35 + .08)) + ($15.91 - $17.00)) / $17.00 = 7.3%

After-tax Returns

Data and Calculations: You are choosing a bond fund that you will put in your

investment (non-retirement) account. Assuming distribution and operating activities which occurred in the past will likely continue, which of the following funds should you include in your taxable (non-retirement) account. Assume federal taxes on short term distributions are 35% and state taxes are 7%. How would this change if these were both stock funds?Mutual Funds Fund A Fund B

Beginning NAV $10.00 $10.00YTD Nominal returns 10% 10%Estimated Turnover 10% 90%Short-term distributions .10 .90Ending NAV 10.90 10.10

Answer

Mutual Funds Fund A Fund BBeginning NAV $10.00 $10.00Short-term distributions .10 .90Ending NAV 10.90 10.10Tax on ST distributions 35%+7% 35%+7%Taxes paid (w/o selling) .042 .378

After-tax return 9.58% 6.22%Loss from return due to taxes .42% 3.78%Although both have the same before-tax return, fund B had

a 35% lower return due to taxes. Fund A is the better choice for a taxable account, while either fund could be used for a retirement account. If these were stock mutual funds, the federal tax rate would be 15%.

Stock Performance

Data:Last year you purchased 100 shares of MAM

Corporation for $40 per share. Over the past 12 months MAM’s share price has gone up to $45 per share, and you received a dividend of $1 per share.

CalculationsWhat was your total rate of return on your

investment in MAM stock last year?

Answer

You can do this problem two ways.• First, total payout.

• (($4,500-$4,000) + 100) / $4,000 = ?• 15%

• Or, share amount• ($45 – 40) + 1 / 40 = ?

• 15%

Stock Performance

Data:Your investment in MAM stock was so

successful that you decided to hold it for 5 more years. Remember, you purchased 100 shares for $40 per share. Unfortunately, the price of MAM stock has not risen; it is back to where you purchased it. The good news is that you earned $1 per share for five years.

Calculations and Application:Calculate your annualized total rate of return.

Compared to a bank account earning 2% APY, how did your stock do?

Answer

The easy way:• $1/$40 = 2.50%• Or• [1+(($4,000-$4,000) + 500) / $4,000)](1/5) =

2.38%

• The stock performed better than the bank account

Bond Performance

Nathan recently purchased a bond with a 10 year maturity for $1,000. The bond pays annual interest of $100.• 1. What interest rate or current yield is Nathan

receiving on his investment? Today Nathan learned that market interest rates for ten

year bonds are 7%. • 2. How much can Nathan sell his bond for today? • 3. How much could he sell the bond for tomorrow if

interest rates move up to 12%? Based on your calculations, what is the relationship

between interest rates and the value between bonds?

Answer

1. The current yield = coupon payment / cost• Current yield = $100/$1000 = 10%

2. Nathan can sell his bond for = value of payments and repayment of principle at current interest rates

• At 7% interest ratesN=10, I=7%, PMT=100, FV=1,000, solve PV?• At 7% Tim can sell his bond for $1,210.71

3. At 12% interest rates N=10, I=12%, PMT=100, FV=1,000, solve PV?• Tim can sell his bond for $887.00

This implies a negative relationship between bond prices and interest rates.

Retirement Planning

Data:• Andrew and Suzy recently reviewed their future

retirement income and expense projection. They hope to retire in 30 years. They determined that they would need an annual retirement income of $80,000 before taxes in today’s dollars, but they currently only have $25,000 before taxes annually with expected Social Security and savings.

Calculations:• Calculate the total amount that Andrew and Suzy

must save for retirement if they wish to meet their income projection, assuming a 3% inflation rate before retirement and 2% after, and an 8% return before retirement and 6% after retirement. They believe they will be in retirement for 25 years.

Answer

First, draw the diagram1. Calculate the Shortfall 2. Inflation adjust the shortfall

3. Calculate the real return and the annuity 4. Calculate the period payment to save Time 30 years 25 years

Return 8% Return 6% Inflation 3% Inflation 2%

Now Retirement Death

Answer

1. The annual shortfall is: 80,000 before taxes – 25,000 before taxes = ?• The shortfall is $55,000.

2. To get the inflation adjusted amount, we use: PV = -55,000, I/Y = 3, N = 30, and solve for FV which gives the amount that they need annually in retirement.• FV of $133,499

Answer

3. To get the real return and the annuity for 25 years, calculate the real return with 6% nominal and 2% inflation, which gives a real return of ?• Real return of 3.92% = [(1.06)/(1.02)] – 1.

The annuity required is PMT = $133,499, I = 3.92, N = 25, PV = ? (use begin mode)• The annuity needed is $2,185,397

4. to get the amount to save, it is I = 8%, N = 30, FV = $ 2,185,397, and PMT = ? To give what you need to save each year• They need to save $19,291 each year to reach their

retirement goal

The Auto Decision

Data: Bill and Brenda’s oldest daughter Kimberly really needs a car, as she is

going away to school next semester. She likes the idea of leasing a car because she only pays for the amount she uses. She has approached you for some advice on the automobile decision. She is looking at the new 4 wheel drive Kia Sportage LX for the snow as she is planning to go to school in Utah. They have found one that she really likes, but she isn’t sure about whether she should lease or buy. Bill and Brenda told her to come to you for advice.

Calculations: Using the information below, calculate the total cost of leasing and

buying for the 3-year term (assume you can sell the purchased car at the residual value),

• MSRP $17,500 Fees:Negotiated Price 15,500 Acquisition 300Down Payment 15% Registration 200Lease & Loan term 3 years License 35Residual Value 50% Documentation 200Rent charge and loan rate 8.25% Termination 250Sales Tax 6.25%

Answer

LeasingDown payment $2,325.00

Tax on Down Payment 145.31Payments

Depreciation: (remember to take out the down payment) Usage Charge (Net Cap Cost-Down Payment-Residual Value)

4,425.00 (15,500-2,325-8,750)Interest Charge (15,500 -2,325+ 8,750) * .0825/24 * 36 (Net Cap Cost – Down Payment + Residual) * Money Factor

(Money Factor is APR/24) 2,713.22Taxes (4,425+2,713.22) * .0625 446.14

FeesAcquisition 300 Termination 250Documentation 200 Registration 200License 35 Total Lease Payments $11,039.67

Answer

BuyingDown payment $2,325.00

Tax on Down Pmt 145.31Payments

PV = 13175. 14,917.60 I = 8.25 / 12 n = 36Taxes (13,175 * .0625) 823.44FeesAcquisition 0 Termination 0Documentation 200 Registration 200License 35 Less Residual Value -8,750.00Total Payments $9,896.35

Note: For a better understanding of this problem, see Teaching Tool 22: Lease versus Buy.

Portfolio Returns

Data and Calculations:• You invested in the following mutual funds last year. You and your spouse are in the

30% federal and 9% state marginal tax brackets. Remember that stock dividends and long-term capital gains are federal taxes and are taxed at 15%.

• a. Calculate the before tax and after-tax return on each of your funds in the portfolio

• b. Calculate your overall portfolio before-tax and after-tax return. Note that the first three funds are all taxable, the municipal bond fund is federal tax-free, and the Treasury bond fund is state tax-free.

• Funds End Begin Short-T. LTCG Stock . % of Total• NAV NAV Distrib. Distrib. Distrib. Portfolio• Vanguard ST Bond 10.25 10.00 .20 .05 0.00 20%• Fidelity 500 Index 110.00 100.00 0.00 0.00 2.00 50%• Schwab Small Cap 115.00 110.00 5.00 5.00 2.00 10%• American Muni Bond 5.25 5.00 .05 .20 0.00 10%• Scudder T- Bond 52.00 50.00 .25 .25 0.00 10%

Notes

• Notes: ST = short-term distributions, LTCG Distr. = Long-term capital gains distributions, Stock Distr. = stock dividend distributions, and % Portfolio is the beginning weight of the assets in your portfolio. Remember your overall portfolio return is your return of each asset times your beginning period weight.

• To calculate the after-tax return from each asset, determine the amount of taxes you will pay on each type of earning. Since you have not sold the assets, the only taxes you will pay will be those on the distributions you have received. Subtract out the taxes on distributions to give you the distributions you get to keep, and calculate your return.

Answer

• Funds End Begin ST LTCG Stock % Fund • NAV NAV Distr. Distr. Distr. Portfolio

Return• Vanguard ST Bond 10.25 10.000 .20 0.05 - 20% 5.00%• Tax Rate (all taxable) 0.39 0.24 • AT Return 10.25 10.000 .13 0.04 - 4.10%• Fidelity 500 Index 110.00 100.00 - - 2.00 50% 12.00%• Tax Rate 0.39 0.24 0.24 • AT Return 110.00 100.00 - - 1.52 11.52%• Schwab Small Cap 115.00 110.00 5.00 5.00 2.00 10% 15.45%• Tax Rate 0.39 0.24 0.24 • AT Return 115.00 110.00 3.02 3.90 1.52 12.15%• Am. Muni Bond 5.25 5.00 0.05 0.20 - 10% 10.0% • Tax Rate (Fed tax free) 0.09 0.09 0.09 • AT Return 5.25 5.00 0.05 0.19 - 9.55• Scudder T- Bond 52.00 50.00 0.25 0.25 - 10% 5.00%• Tax Rate (state tax free) 0.30 0.15 0.15 • AT Return 52.00 50.00 0.18 0.21 - 4.78• Portfolio Return before Tax 10.05% Portfolio Return After Tax 9.23%