Amount needed to deposit in mutual fund

Problem 1:

A) Saving for child’s college. 

You estimate that your child will start school 18 years from today. You want to follow an aggressive investment strategy and plan to invest a lump sum amount at the end of the month every month for the next 17 years into a mutual fund that earns 16.2%.  At the end of the seventeenth year, you will withdraw the money from the mutual fund and place it in a savings account that earns 4 percent compounded quarterly.   You will make tuition payments from this account.  You estimate that tuition will cost $22,000 per year for the four years.  Given your investment strategy, how much will you need to deposit in this mutual fund each month?  Assume the following:

The expected return on the mutual fund will be the same each year, 16.2%, for the next seventeen years.
The expected return on the mutual is an annual percentage rate (A.P.R.)
The first deposit to the mutual fund will be made one month from today.
The first tuition payment is made one-year after the savings account is opened (at the end of year 18).

B) You realize that all the above calculations for your child’s college savings plan are missing one essential element, INFLATION!  You estimate that the inflation rate over the next 22 years is going to 3.5%.  In real dollars, college will cost $22,000 per year while the return on the two investments, 16.2% and 4%, are nominal returns.  Except for the inflation effects, all of your other assumptions from the previous night are correct.  In real dollars, what will you need to deposit in the mutual fund each month?

Problem 2. You need to value a stock that you estimate will have the following quarterly dividends.  Over the next year (4 quarters), the firm will not pay any dividends.  The firm will then start paying dividends.  The first dividend will be $1 and will experience super growth of 5% per quarter for 2 years.  After that period of super growth you estimate the dividend growth rate will drop to 1% per quarter for the next 4 years.  Finally dividends will level off and remain constant forever.  If the appropriate rate of return for this stock is 18%, what is the value of the stock today?

Problem 3: Your CEO is very concerned with maximizing shareholder wealth and wants you to estimate the value of the firm under several different investment choices.  The current assets in place of the firm generate 5 million dollars a year in earnings, the expected return on equity is 12% and there are a million shares outstanding.  The CEO is debating two different investment plans for the company. 

The first plan involves putting in place an acquisition strategy where the firm will use 10% of its earnings to purchase other companies each year.  The finance department estimates that these mergers will have a return on investment of 15% and opportunities will be available starting at the end of this year and continue indefinitely.

The second plan involves making a one-time acquisition two years from now for 5 million dollars and it will have a yearly return on investment of 15%.

What is the value of the assets in place?
What is the value of the firm if it adopts the first investment plan?
What is the value of the firm if it adopts the second investment plan?
What course of action would you recommend to the CEO? Why?

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Finance Basics: Amount needed to deposit in mutual fund
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