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# Student loan calculations

(See attached file for full problem description)

1. John is planning to use student loans to pay for graduate school tuition starting next year. His tuition will be \$25,000 a year for three years. The loan program has a 12% annual rate of interest.
A. If John borrows to pay all of his tuition, how much will he owe at the end of three years, assuming annual compounding?
B. The student loan program will allow John to defer payment on the loan for up to five years after graduation. Interest, however, will continue to accumulate (compounded annually). If John exercises this option for the full five years, how much will he owe by the time he starts paying back the loan?

2. Kathleen has \$5,000 today and she would like to double her money in 6 years. What interest rate does she need to earn to accomplish her goal?

3. What is the required annual deposit if you want to retire in 40 years as a millionaire and the expected annual interest rate is 5.2%?

4. What is the present value of four consecutive annual payments of \$100 each at a rate of 3%?

5. You place \$25,000 in a savings account paying monthly compound interest of 6% for three years and then move the balance to another account that pays 9% compounded monthly. How much will you have after 3 more years have passed?

6. What rate of return will you earn if you pay \$900 now for three consecutive annual (annuity) payments of \$50 and an additional \$1,000 at the end of the three years?

7. Calculate the interest rate on each of the following annuities and choose one on the basis of the greatest rate of return.

Annuity Initial Payment Amount Received per Year # of Years
A -\$50,000 \$8,500 12
B -\$60,000 \$7,000 25
C -\$70,000 \$8,000 20

8. Which of the following would you prefer on a present value basis: (a) \$10,000 for each of the next three years; (b) \$25,000 in three years; or, (c) \$10,000 now plus \$30,000 in five years? The applicable interest rate is 10%.

9. Suppose that the Times and the Sun are competing newspapers in the same city, and that if one has large returns, the other has small returns. The pattern of their returns can be summarized as follows:

Sun has: Probability Sun's return Times' return
Good year 0.3 20% (5%)
Average year 0.4 10% 5%
Poor year 0.3 (10%) 20%
A. Find the expected return, standard deviation of returns, and coefficient of variation for each firm.
B. Find the expected return on a portfolio composed of 75% Times shares and 25% Sun shares.

10. Stock X has a beta of 0.5, stock Y a beta of 1.0, and stock Z a beta of 1.25. The risk-free T-bill rate is 5%, and the expected return on the S&P 500 Index (the "market" portfolio) is 12%. Find the beta and the required rate of return on a portfolio consisting of 40% X, 20% Y, and 40% Z. Graph the Securities Market Line (SML), making sure you identify the beta and the required rate of return for risk-free T-bills, the "market" portfolio, and the XYZ portfolio on the graph.

11. Describe the circumstances under which the AFN formula is appropriate for forecasting capital financing requirements. Describe three situations under which using the AFN is not appropriate. What adjustments can be made in these circumstances?

12. Fill in the blanks on the financial statements provided. Then, calculate return on assets (ROA), total asset turnover, and book value per share (assume 50 million shares outstanding). All dollar figures are in thousands.

Cash and securities \$ 100,000 Accounts payable \$ 150,000
Accounts receivable _________ Notes payable 50,000
Inventory _________ Long-term debt _________
Fixed assets _________ Common stock _________
Retained earnings 200,000
Total assets 1,000,000 Total liabilities & equity _________
Sales \$1,200,000 Ratios:
Costs of goods sold _________ Current 2.00
EBIT _________ Quick 1.00
Interest 100,000 Times Interest Earned 2.00
EBT _________ Debt 0.50
Taxes 40,000 Profit margin 0.05
Net Income _________ Return on equity 0.12

#### Solution Summary

The solution shows calculations for a student loan and how they can be used and financed in the context of an annuity.

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