As the manager of the pension fund, considering different investment options wil

Question

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.

Submit your Time Value of Money Report and Calculations. Be sure to show your calculations in Excel and provide a narrative analysis. Your narrative analysis should summarize the results of your analysis and make recommendations for the benefit of the company.

Explanation / Answer

1) Present value = $ 95,000,000($ 95 million)

t = 10 years

rate of return = r = 3.5 % = 0.035

Future value at the end of 10 years = ?

future value = present value (1 + r)^t

= 95,000,000(1+0.035)^10

= $ 134,006,882.3

2) Here the future value to be accumulated = $ 14,000,000 (14 million)

future value = $ 14,000,000

here rate = r = 4% = 0.04

time = t = 13 years

Present value = ?

Present value = future value / (1 +r)^t

= 14,000,000/(1+0.04)^13

Hence present value = $ 8408037.20

(units digit of the result may change during calculations)

3) Using the same formula

Present value = future value / (1 +r)^t

Present value = $ 197,000,000

future value = $ 554,000,000

rate per year = 5%

Here it is monthly compounding hence rate per month = r = 5/12 = 0.14667% = 0.001467

time = t = ?

substitute in the formula

197,000,000 = 554,000,000/(1+0.001467)^t

calculate for t

we get t as 248.667252

which is the number of periods( here number of months)

convert this into years;

= 248.667252/12 = 21.191 years

4) Future value = 20,000,000

present value = 12,000,000

time = 10 years

Simplieifed IRR for a defined period

IRR = [(Future value / present value) ^ (1/t)] - 1

= [(20,000,000/12,000,000) ^ (1/10)] - 1

= 0.0524 = 5.24 %

Here IRR less than that of the required rate of return ( selection rules by using IRR)

hence the building should not be bought..

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