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Time Value of Money and Rate of Interest

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1. How much would you accept in lump sum today, in place of a lottery payment of $50,000 at the end of each of 20 years. ($1.000,000 in total), assuming you could invest it at an 8% rate?

2. What will be the value in 20 years of $5,000 contributed at the end of each year into an IRA (individual retirement account) which pays 8%?

3. What should you be willing to pay today for a contract to receive $50,000 in 10 years assuming an 8% interest rate?

4. What rate of interest am I paying if my monthly payment is $400.00 on a $15,000 loan to be paid off in 4 years?

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Solution Summary

This solution shows step-by-step calculations in an Excel file to determine the lump sum payments, value of individual retirement accounts, contracts with interest rate, and loan interest rates.

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Apply the concept of TVM

The Acme Company 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 dollar figures are in whole dollars (not dollars 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 dollars (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 1 = SUN digits 1-3; year 3 = SUN digits 4-6; year 5 = 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 23 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 23th 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 $1,000,000 to the construction of a new physical fitness facility for its employees. It is estimated that in E years (E = 10 + the fifth digit of SUN) the total cost of the new gym will be $1,850,000. What annual percentage interest rate must the initial contribution earn to attain the required amount in E years? (Note: your answer should be accurate to two decimal places - e.g., 5.79%.)

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.)

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