Personal Finance: a Gospel Perspective BM200 Assessment Exam #2: Review Problems

Preparing for the 2 nd Assessment Exam 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 and readings Think through the purpose for each problem

Problem 1: Insurance 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. 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?

Answer a. Earnings Multiple Approach Salary $50,000 Expense reduction % reduction (4 to 3) Amount needed 37,000 Life insurance needed $550,467 PMT = 37,000, I = 3%, N = 20 Company life insurance ($150,000) or 3 times salary Additional needed $400,467 Multiple needed: 8.0 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. [.5 point] Notice that the earnings multiple approach does not take into account your individual level of savings or your current financial condition.

Problem 2: Mutual Fund Fees Which of the funds in the following table (next slide) 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%

Answer Fund 1 Fund 2 Fund 3 Fund 4 Initial Purchase$5,000 $5,000 $5,000 $5,000 Load $400 $288 $0 $0 Net Invested = PV $4,600 $4,712 $5,000 $5,000 Annual 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.

Problem 3: Mutual Fund Returns 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, 2003 Dec. 31, 2004 Market value of portfolio $900 mn $950 mn Liabilities of the fund$50 mn 75 mn Shares outstanding 50 mn 55 mn The investment company just announced its year-end distributions for 2004 of (on a per share basis) of: Long-term capital gains distributions of $1.95. Bond dividend distributions of $1.45.

Answer Dec. 31, 2003 Dec. 31, 2004 Market value of portfolio $900 mn $950 mn Liabilities of the fund $50 mn 75 mn Shares outstanding 50 mn 55 mn Beginning NAV = ($900-50) / 50 million = $17.00 Ending NAV = ($950 - $75) / 55 million = $15.91 Before-Tax Return = ($ $ ($ $17.00)) / $17.00 = 13.6% After-Tax Return = ($1.95 * (1 - ( )) + $1.45 * (1 - ( )) + ($ $17.00)) / $17.00 = 7.3%

Problem 4: After-tax Returns You are choosing a 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 FundsFund A Fund B Beginning NAV $10.00 $10.00 YTD Nominal returns10% 10% Estimated Turnover10% 90% Short-term distributions Ending NAV

Answer Mutual FundsFund A Fund B Beginning NAV $10.00 $10.00 Short-term distributions Ending NAV Tax on ST distributions 35%+7% 35%+7% Taxes paid (w/o selling) 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

Problem 5: Stock Performance 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. What was your total rate of return on your investment in MAM stock?

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%

Problem 6: Stock Performance 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. 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

Problem 7: Bond Performance Nathan recently purchased a bond with a 10 year maturity for $1,000. The bond pays annual interest of $ 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 rates N=10, I=7%, PMT=100, FV=1,000, solve PV? At 7% Tim can sell his bond for $1, At 12% interest rates N=10, I=12%, PMT=100, FV=1,000, solve PV? Tim can sell his bond for $ This implies a negative relationship between bond prices and interest rates.

Problem 8: Retirement Planning 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 in today’s dollars, but they currently only have $25,000 annually with expected Social Security and savings. 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 diagram 1. Calculate the Shortfall 2. Inflation adjust the shortfall 3. Calculate the real return and the annuity 4. Calculate the period payment Time 30 years 25 years Return 8% Return 6% Inflation 3% Inflation 2% Now Retirement Death

Answer 1. The annual shortfall is: 80,000 – 25,000 = ? The shortfall is $55, 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 = ? The annuity needed is $2,103, to get the amount to save, it is I = 8%, N = 30, FV = $2,103,279, and PMT = ? To give what you need to save each year They need to save $18,567 each year to reach their goals