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# Growing Annuity Payments: Amount of Your First Deposit

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You want to accumulate \$1 million by your retirement date, which is 25 years from now. You will make 25 deposits in your bank, with the first occurring today. The bank pays 8% interest, compounded annually. You expect to receive annual raises of 3%, which will offset inflation, and you will let the amount you deposit each year also grow by 3% (i.e your second deposit will be 3% greater than your first, the third will be 3% greater than the second, etc) How much must your first deposit be if you are to meet your goal?

\$2.19

## Acme Company Global issues: TVM concepts, FV, PV, periodic deposit, discounted value

Global Finance

Details: The Acme Company has its European subsidiary based in the Euro zone. The subsidiary must solve a series of five problems that require you to apply the concept of "time value of money," or TVM.

The five problems are listed below. Solving them will require the use of Microsoft Excel.

Before you begin your work, each student is to select a unique nine-digit random number that contains no zeros, no "patterns," and should use most of the digits between one and nine. This value will be referred to as the student unique number (SUN). Further, digits within the SUN are read from left to right. For example, if the SUN = 123456789, the first digit = 1, the second digit = 2, etc. Please note that the interest rate used in all questions represents an annual rate and all Euro figures are in whole Euros (not Euros and cents).

1) Acme plans to construct a new manufacturing facility in 14 years. If Acme estimates that today's cost of the new plant is SUN Euros (use all 9 digits) and annual inflation is A% (A = the first digit of SUN), how much will the manufacturing plant cost in 14 years?

2) Acme has decided to establish a sinking fund for its outstanding preferred stock issue. SUN (use all 9 digits) represents the amount of the issue that will be retired in 26 years. At the beginning of each of these 26 years, Acme will deposit an equal amount into an account that earns B% (B = the second digit of SUN). What is the value of this periodic deposit?

3) One of Acme's new projects will generate the following cash flows at the end of each of the stated years: year 2 = SUN digits 1-3; year 4 = SUN digits 4-6; year 7 = SUN digits 7-9. If these cash flows are discounted at 12%, what is the sum of their present values?

4) Acme is assessing its employee pension fund. At the end of each of the next 25 years Acme will have to pay its retirees (use the first 4 digits of your SUN). If the fund is estimated to earn D% (D = the fourth digit of SUN), how much does Acme need to have set aside today to ensure that it can meet its future obligations? (At the end of the 25th year, the balance should be drawn down to zero.)

5) As part of a new labor contract, Acme has agreed to make a one-time contribution of Euros 1,000,000 to the construction of a new physical fitness facility for its employees. This amount will be placed in an account earning E% (E = the fifth digit of SUN). When the account grows to Euros 1,850,000, construction will commence. How long must employees wait until construction of their new gym begins? (Your answer should be accurate to two decimal places, e.g., 1.57 years).

IMPORTATANT TO DO:
Prepare for Acme's CFO an analysis that contains solutions for all five problems. Be sure to clearly present and label all values and variables, provide Excel TVM formulas, and conclude each question with a brief interpretation of your results. Your entire submission must be contained within an Excel document. (Note: You must use Excel TVM functions to complete this assignment; using a hand calculator or website and plugging values into a template is not acceptable.) Note: The books of the subsidiary being held in Euros, the exchange rate Euro/US dollars has no influence on the result of the exercise.

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