1. You are a financial advisor helping a young family create a college fund to provide for their daughter Mary's education. Mary just turned 5. Her parents want to make sure that they can afford to send her wherever her potential allows her to go, starting school on her 18th birthday. She will only take four years to complete her degree. Currently, tuition and housing costs at top private schools total $35,000 per year, which are paid at the beginning of each school year. These expenses are expected to increase at the rate of inflation which will run at 4% annually for the next 25 years. In each year through her 18th birthday, Mary's parents will make a deposit into the college fund so that her college fund will exactly provide for all of the costs of her education when she begins college (the first deposit will be made one year from today). Since her parents expect their income to grow at the rate of 2% annually, they would like the amount that they put each year into the fund to increase in nominal terms at the rate of 2% annually. Mary's parents can earn a nominal rate of 10% annually on their investments and they face a 30% tax rate.
a. What do you expect tuition and housing at top private schools to cost during Mary's first year at college?
b. In nominal dollars, how much must be in the savings account on Mary's 18th birthday after the last deposit has been made but before the first tuition and housing payment?
c. What should be the amount of the first deposit to the savings account?
d. Alternatively, Mary's parents could open a 529 account that allows college savings to grow tax-free. If they saved in this account rather than in a normal investment fund, and still earned the same pre-tax return, how much should be their first deposit?
2. You are a bank officer designing a mortgage for a young couple. The current mortgage rate for 30 year fixed-rate mortgages is 6.5%, compounded monthly. The couple is buying a $300,000 house and has a down payment of $60,000. They wish to take out a fixed-rate mortgage on the remainder.
a. What would be their monthly payment?
b. Suppose the couple takes the mortgage. After 5 years, what would be the remaining principal amount owed on the mortgage?
c. Suppose that after 5 years, fixed-rate mortgage rates drop to 5.5%. If the couple refinanced the loan (at no cost for now), how much could they reduce their monthly payment such that they still pay off the loan at the same time (25 years from when they refinance, for a total of 30 years)?
d. Alternatively, the couple could decide to refinance at 5.5%, continue to make the same mortgage payment, and reduce how long it takes to repay their mortgage. If they kept their same payment, how much earlier would they pay off the mortgage?
e. Suppose that there were title and escrow fees associated with refinancing the mortgage, paid at the time of the refinancing. What is the most these fees could be in order for it to be worthwhile for the couple to refinance?
3. You are starting to plan for your retirement and want to determine the optimal type of retirement account to establish in light of different tax treatments on the accounts. Suppose that you are 30 years from retirement and that your investments will be in government and corporate bonds. You expect that you will be able to afford pre-tax contributions of $5,000 per year for the next ten years. After that, you expect to have gotten promoted at work, allowing for pre-tax contributions of $10,000 per year for the remaining 20 years. During the first 10 years, you expect your income tax on wages and interest to be only 25% but that commensurate with your higher income, the tax rate in the final 20 years will be 36%. At retirement, you expect your tax rate to fall back to 28%.
Under a standard IRA, the contributions reduce your taxable income in the year the contributions are made but the total balance in the account is taxable at the normal income tax rate upon withdrawal. Under a Roth IRA, the contributions do not reduce your taxable income (meaning that you will only be able to afford to contribute $3,750 ( = $5,000 * (1-25%)) per year in the first ten years and $6,400 per year in the final 20 years) but the principal and interest are tax-free.
a. If you expect to earn 8% on the account and must put all of your money into only one of the investment vehicles for the entire 30 years, which do you prefer? Hint: Calculate the after tax values in each of the accounts at the end of the 30 years.
b. Assume that you expect to live another 25 years after you retire. If you expect to earn a pre-tax return of 8% on the investment account and would like to withdraw the same amount every year for the next 25 years (the first payment occurring one year after retirement), how much would you receive every year, on an after-tax basis?
c. If you could have both a Roth IRA and a traditional IRA, what would be the optimal investment strategy?
4. A motor manufacturer (ticker RPM) currently pays out 40% of their annual net income, retaining the rest for further investments in new opportunities. The estimated return on equity (ROE) of these new projects is 12%.
a. Estimate the dividend growth rate, assuming that the payout ratio and expected returns on investment stay constant.
b. Next year's expected dividend is $0.66 per share. If the market requires a 15% expected return on the firm's equity, what is your estimate of the current stock price of RPM?
c. If the firm decided to cut its investment and instead pay out 100% our annual earnings in dividends, what do you expect would be the new price of RPM stock?
d. Why would the market respond positively to this announcement, i.e. why did the stock price increase? Hint: If you did not find that the stock price in part c is higher than the price found in part b, you may want to re-check your numbers.
5. MFLF Technologies is a privately held developer of advanced security system based in Chicago. As part of your business development strategy in late 2012 you initiate discussions with MFLF founders about the possibility of acquiring the business. Estimate the value of MFLF's share using a discounted free cash flow approach. Here is some relevant information:
- Debt: $30 million
- Excess cash: $100 million
- Shares outstanding: 50 million
- Expected free cash flow in 2013: $45 million
- Expected free cash flow in 2014: $50 million
- Future free cash flow growth beyond 2014: 5%
- WACC: 9.4%