QUESTION

1. Consider the $50,000 excess cash. Assume that Gary invests the funds in a one-year CD.

a.What is the CDs value at maturity (future value) if it pays 10.0 percent (annual) interest?

b. What would be its future value if the CD pays 5.0 percent interest? It pays 15.0 percent interest?

c. Bank South offers CDs with 10.0 percent nominal (stated) interest, but compounded semiannually. What is the effective annual rate on this CD? What would the future value be after one year if $50,000 were invested?

d. The Pensacola Branch of Bank of America offers a 10.0 percent CD with daily compounding. What is the CDs effective annual rate and its value at maturity one year from now if $50,000 is invested? (Assume a 365 day year)

2. Rework Parts (a) through (d) of Question 1 assuming that each CD has a five-year maturity.

a. FV = PV x (1 + i)n

b. FV = PV x (1 + i)n

c. FV = PV x (1 +i/m)n x m

d.FV = PV x (1 +i/m)n x m

3. Now consider the Surgery Centers goal of having $200,000 available in five years to buy a new patient billing system.

a. What lump sum amount must be invested today in a CD paying 10.0 percent annual interest to accumulate the needed $200,000?

b. What annual interest rate is needed to produce $200,000 after five Years if only $100,000 is invested?

4. Now consider a second alternative for accumulating funds to buy the new billing system. In lieu of a lump sum investment, assume that five annual payments of $32,000 are made at the end of each year.

a. What type of annuity is this?

b. What is the present value of this annuity if the opportunity cost rate is 10.0 percent annually? 10.0 percent compounded semiannually?

c. What is the future value of this annuity if the payments are invested in an account paying 10.0 percent annually? 10.0 percent compounded semiannually?

d. What annual interest rate is required to accumulate the $200,000 needed to make the purchase assuming a $32,000 annual payment?

e. What size annual payment would be needed to accumulate $200,000 under annual compounding at a 10.0 percent rate?

f. Suppose the payments are only $16,000 each, but they are made Every six months, starting six months from now. What would be the future value if the ten payments were invested at 10.0 percent interest? If they were invested at BankSouth at 10.0 percent compounded semiannually?

5. Assume now that the payments are made at the beginning of each period. Repeat the analysis in Question 4.

a. An annuity due is a series of cash flows that occur at the beginning of an accounting period.

6. Now consider the uneven cash flow stream stemming from the lease agreement given in the case.

a. what is the present (year 0) value of the annual lease cash flows if the opportunity cost rate is 10.0 percent annually?

What is the value of this cash flow stream at the end of year 5 if the cash flows are invested at 10.0 percent annually? What is the present value of this future value when discounted at 10.0 percent? What does this result indicate about the consistency inherent in the time value analysis?

c. Does the office renovations and subsequent lease arrangement appear to be a good investment for the company? (Hint: Compare the cost of renovation with the present value of the lease payments)

7. Now assume that it is five years later and the company was unable to accumulate the $200,000 needed to make the software purchase. Instead, the company is forced to borrow the $200,000. The loan calls for repayment in equal annual installments over a four-year period, with the first payment due at the end of one year. Assuming that the firm can borrow the funds at a 10.0 percent rate, what amount of interest and principal will be repaid at the end of each year of the loan?

Throughout this case, you have been either discounting or compounding cash flows. Many financial analyses, such as bond refunding decisions, capital investment decisions, and lease decisions, involve discounting projected future cash flows. What is the appropriate rate in such situations? What factors influence the value of this rate?

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