# Step 1 – time value of money calculations

As the manager of the pension fund, considering different investment options will help you make better decisions for your company and your clients.  Please respond to the following questions, providing supporting data and showing your calculations.

Question 1: If the pension plan invests \$95 million today in 10-year US Treasury bonds (riskless investment with guaranteed return) at an interest rate of 3.5 percent a year, how much will it have by the end of year 10?

Question 2: If the pension plan needs to accumulate \$14 million in 13 years, how much must it invest today in an asset that pays an annual interest rate of 4 percent?

Question 3: How many years will it take for \$197 million to grow to be \$554 million if it is invested in an account with a quoted annual interest rate of 5 percent with monthly compounding of interest?

Question 4: The pension plan also invests in physical assets. It is considering the purchase of an office building today with the expectation that the price will rise to \$20 million at the end of 10 years. Given the risk of this investment, there should be a yield of 10 percent annually on this investment. The asking price for the lot is \$12 million. What is the annual yield (internal rate of return) of the investment if the purchase price is \$12 million today and the sale price 10 years later is \$20 million? Should the pension plan buy the office building given its required rate of return?

Question 5a: The pension plan is also considering investing \$70 million of its cash today at a 3.5 percent annual interest for five years with a commercial bank. How much will the \$70 million grow to at the end of 5 years?

Question 5b: Now take the amount of your answer in Ques 5a, and assume this money is invested in an annuity due with the first payment made at the beginning of the 6th year. The annuity due makes a total of 15 yearly (equal) payments. How much will the annual payments be from years 6 to 20, if the rate at which these payments are discounted is also 3.5 percent?

Question 6: The pension plan is about to take out a 10-year fixed-rate loan for the purchase of an information management system for its operations. The terms of the loan specify an initial principal balance (the amount borrowed) of \$4 million and an APR of 3.75 percent. Payments will be made monthly. What will be the monthly payment? How much of the first payment will be interest, and how much will be principal? Use the Excel PMT function to provide the answers to these questions.

Be sure to show all your calculations in Excel and provide a narrative analysis in Excel. Your narrative analysis should summarize the results of your analysis and make recommendations for the benefit of the company.

Before you submit your assignment, review the competencies below, which your instructor will use to evaluate your work. A good practice would be to use each competency as a self-check to confirm you have incorporated all of them in your work.

• 3.1      Identify numerical or mathematical information that is relevant in a      problem or situation.
• 3.2      Employ mathematical or statistical operations and data analysis techniques      to arrive at a correct or optimal solution.
• 3.3      Analyze mathematical or statistical information, or the results of      quantitative inquiry and manipulation of data.
• 3.4      Employ software applications and analytic tools to analyze, visualize, and      present data to inform decision-making.
• 10.3      Determine optimal financial decisions in pursuit of an organization’s      goals.
• 10.4      Make strategic managerial decisions for obtaining capital required for      achieving organizational goals.

For Ques 1 to 6, note that these are time value problems.  Use the framework I shared with you to help you derive the answers.

Here’s the framework:

NPER = years * compounding period

INT(RATE) = interest rate / compounding period

PMT  = payment (use as annuity payments – regular periodic payments (daily, monthly, etc)

PV = present value

FV = future value

Typically, the question will provide you with 4 out of the 5 factors, and you solve for the missing item.  Use the Excel functions to help you solve these problems.  For example, for a present value problem, in Excel, enter =PV(rate, nper, pmt, (fv), type), Excel will then display the requirements needed to derive present value.   Also, remember that if the problem asks for a value today — this implies present value, whereas a value in the future, implies future value.  How much should one pay each month for the next 5 years to pay off a car loan … equal monthly payment over time implies annuity payments or PMT, etc.

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