TVM Review Problems
You are now 35 years old and will retire at the age of 65. While you currently have no savings, you are going to start a personal Investment plan now and learn that you can expect the following average annual returns in various investments: Investment After-inflation return Emerging stock market stocks 11. 5% Small-company U. S. Stocks European and Asian stocks 8. 2% S&P 500 Index (large U. S. Stocks) 7. 2% Art Residential real estate 2. 8% U. S. Corporate bonds 0. 9% Long-term U.
S. Government bonds 0. 4% -0. 3% (a) If you invest $10,000 each year for the next 30 years in small-company stocks how much would you retire with (before taxes)? (b) Suppose you wanted to retire with enough to buy a 1,000 acre spread in the Hill Country with horses, a ranch house and a very large Winnebago ($6 million). If you were willing to put off retirement until 75 and set aside $10,000 a year, what investment categories could you have to be in to achieve this objective? (c) Suppose you were risk-averse and would only invest in long-term government bonds.
How many years would you have to save at $10,000 a year to get that ranch? 2. Fred Macadam of Publisher’s Outhouse announced you have Just won $30,000,000! —To be paid in $1,000,000 installments at the end of each of the next 30 years, of course! If the appropriate discount rate is 7. 5%, what is this really worth to you? 3. A benefactor proposes to set up an endowment for student scholarship at the Business School. The proposal is to provide scholarship of $1 5,000 (at the end of) each year. Suppose the interest rate earned by endowments is 4%. How much should the benefactor donate?
What if the proposal is to provide $15,000 plus a raise of 3% each year? 4. You are buying a home listed at $220,000 and would like to arrange for a 30-year mortgage to finance the cost. You find that the local bank requires a minimum down payment of 5% of the purchase price in order to grant you a loan. A. What is the amount you will need to finance? B. If the current annual interest rate on a 30-year mortgage is 7. 125%, then what would be your monthly payment? The bank tells you that you can get a lower interest rate if you are willing to pay “points” up front. Points” is a fee paid immediately to the bank and is expressed as percentage points of the loan amount. ) You are told that if you are willing to pay a fee equal to 2 percentage points of the loan amount to the bank immediately, you can finance your mortgage at the lower interest rate of only 6. 75%. C. How much would you have to pay the bank immediately to get the lower interest rate? D. If you agree to pay the points and finance your same loan amount at the annual interest rate of 6. 75%, then what would be your monthly payment? E. What is the amount you would save each month between the payment in part ‘b’ .
If you plan to live in the house for four years and then sell it, what is the present value of your monthly savings over these four years at an annual discount rate of 7. 125%? Are you better off paying the points or not? 5. Chuck’s Publishing, Inc. Borrows $20,000 from Citron to finance the purchase of a new office cooling system. The loan has an interest rate of 10% and Chucks will be required to make annual payments for the next 3 years. Fill in the following loan amortization schedule for this transaction. Year 2 3 Payment Interest Paid Principle paid Balance $20,000