CASE STUDY CONTINUATION

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73. Present Value of a Growing Perpetuity What is the equation for the present value of a growing perpetuity with a payment of C one period from today if the payments grow by C each period?

74. Rule of 72 A useful rule of thumb for the time it takes an investment to double with discrete compounding is the “Rule of 72.” To use the Rule of 72, you simply divide 72 by the interest rate to determine the number of periods it takes for a value today to double. For example, if the interest rate is 6 percent, the Rule of 72 says it will take 72/6 = 12 years to double. This is approximately equal to the actual answer of 11.90 years. The Rule of 72 can also be applied to determine what interest rate is needed to double money in a specified period. This is a useful approximation for many interest rates and periods. At what rate is the Rule of 72 exact?

75. Rule of 69.3 A corollary to the Rule of 72 is the Rule of 69.3. The Rule of 69.3 is exactly correct except for rounding when interest rates are compounded continuously. Prove the Rule of 69.3 for continuously compounded interest.

Excel Master It! Problem

Excel is a great tool for solving problems, but with many time value of money problems, you may still need to draw a time line. For example, consider a classic retirement problem. A friend is celebrating her birthday and wants to start saving for her anticipated retirement. She has the following years to retirement and retirement spending goals:

Years until retirement 30 Amount to withdraw each year $90,000 Years to withdraw in retirement 20 Interest rate 8%

Because your friend is planning ahead, the first withdrawal will not take place until one year after she retires. She wants to make equal annual deposits into her account for her retirement fund.

1. If she starts making these deposits in one year and makes her last deposit on the day she retires, what amount must she deposit annually to be able to make the desired withdrawals in retirement?

2. Suppose your friend has just inherited a large sum of money. Rather than making equal annual payments, she has decided to make one lump sum deposit today to cover her retirement needs. What amount does she have to deposit today?

3. Suppose your friend’s employer will contribute to the account each year as part of the company’s profit sharing plan. In addition, your friend expects a distribution from a family trust several years from now. What amount must she deposit annually now to be able to make the desired withdrawals in retirement? The details are:

Employer’s annual contribution $ 1,500 Years until trust fund distribution 20 Amount of trust fund distribution$25,000

Page 134 Mini Case THE MBA DECISION

Ben Bates graduated from college six years ago with a finance undergraduate degree. Although he is satisfied with his current job, his goal is to become an investment banker. He feels that an MBA degree would allow him to achieve this goal. After examining schools, he has narrowed his choice to either Wilton University or Mount Perry College. Although internships are encouraged by both schools, to get class credit for the internship, no salary can be paid. Other than internships, neither school will allow its students to work while enrolled in its MBA program.

Ben currently works at the money management firm of Dewey and Louis. His annual salary at the firm is $65,000 per year, and his salary is expected to increase at 3 percent per year until retirement. He is currently

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28 years old and expects to work for 40 more years. His current job includes a fully paid health insurance plan, and his current average tax rate is 26 percent. Ben has a savings account with enough money to cover the entire cost of his MBA program.

The Ritter College of Business at Wilton University is one of the top MBA programs in the country. The MBA degree requires two years of full-time enrollment at the university. The annual tuition is $70,000, payable at the beginning of each school year. Books and other supplies are estimated to cost $3,000 per year. Ben expects that after graduation from Wilton, he will receive a job offer for about $110,000 per year, with a $20,000 signing bonus. The salary at this job will increase at 4 percent per year. Because of the higher salary, his average income tax rate will increase to 31 percent.

The Bradley School of Business at Mount Perry College began its MBA program 16 years ago. The Bradley School is smaller and less well known than the Ritter College. Bradley offers an accelerated, one-year program, with a tuition cost of $85,000 to be paid upon matriculation. Books and other supplies for the program are expected to cost $4,500. Ben thinks that he will receive an offer of $92,000 per year upon graduation, with an $18,000 signing bonus. The salary at this job will increase at 3.5 percent per year. His average tax rate at this level of income will be 29 percent.

Both schools offer a health insurance plan that will cost $3,000 per year, payable at the beginning of the year. Ben also estimates that room and board expenses will cost $2,000 more per year at both schools than his current expenses, payable at the beginning of each year. The appropriate discount rate is 6.3 percent.

1. How does Ben’s age affect his decision to get an MBA?

2. What other, perhaps nonquantifiable factors affect Ben’s decision to get an MBA?

3. Assuming all salaries are paid at the end of each year, what is the best option for Ben—from a strictly financial standpoint?

4. Ben believes that the appropriate analysis is to calculate the future value of each option. How would you evaluate this statement?

5. What initial salary would Ben need to receive to make him indifferent between attending Wilton University and staying in his current position?

6. Suppose, instead of being able to pay cash for his MBA, Ben must borrow the money. The current borrowing rate is 5.4 percent. How would this affect his decision?

Appendix 4A Net Present Value: First Principles of Finance

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Appendix 4B Using Financial Calculators

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