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a.What amount would Ms. Martin have at the end of the third year, leaving allinterest paid on deposit, in each bank?b.What effective annual rate(EAR) would she earn in each of the banks?c.On the basis of your findings in parts aand b,which bank should Ms.Martin deal with? Why?d.If a fourth bank (bank D), also with a 4% stated interest rate, compoundsinterest continuously, how much would Ms. Martin have at the end of thethird year? Does this alternative change your recommendation in part cExplain why or why not.ST 4–2Future values of annuitiesRamesh Abdul wishes to choose the better of twoequally costly cash flow streams: annuity X and annuity Y. X provides a cashinflow of $9,000 at the end of each of the next 6 years. Y provides a cash inflowof $10,000 at the end of each of the next 6 years. Assume that Ramesh can earn15% on annuity X and 11% on annuity Y.a.On a purely subjective basis, which annuity do you think is more attractive?Why?b.Find the future value at the end of year 6, FVA6, for both annuity X andannuity Y.c.Use your finding in part bto indicate which annuity is more attractive. Com-pare your finding to your subjective response in part aST 4–3Present values of single amounts and streamsYou have a choice of acceptingeither of two 5-year cash flow streams or single amounts. One cash flow streamis an ordinary annuity, and the other is a mixed stream. You may accept alterna-tive A or B—either as a cash flow stream or as a single amount. Given the cashflow stream and single amounts associated with each (see the accompanyingtable), and assuming a 9% opportunity cost, which alternative (A or B) and inwhich form (cash flow stream or single amount) would you prefer?ST 4–4Deposits needed to accumulate a future sumJudi Janson wishes to accumulate$8,000 by the end of 5 years by making equal annual end-of-year deposits overthe next 5 years. If Judi can earn 7% on her investments, how much must shedeposit at the end of each yearto meet this goal?Cash flow streamEnd of yearAlternative AAlternative B1$700$1,1002700900370070047005005700300Single amountAt time zero$2,825$2,800LG3LG2LG3LG4LG6?.CHAPTER 4Time Value of Money171
PROBLEMS4–1Using a time lineThe financial manager at Starbuck Industries is consideringan investment that requires an initial outlay of $25,000 and is expected to resultin cash inflows of $3,000 at the end of year 1, $6,000 at the end of years 2 and3, $10,000 at the end of year 4, $8,000 at the end of year 5, and $7,000 at theend of year 6.a.Draw and label a time line depicting the cash flows associated with StarbuckIndustries’ proposed investment.b.Use arrows to demonstrate, on the time line in part a,how compounding tofind future value can be used to measure all cash flows at the end of year 6.c.Use arrows to demonstrate, on the time line in part b,how discounting tofind present value can be used to measure all cash flows at time zero.d.Which of the approaches—future value or present value—do financial man-agers rely on most often for decision making? Why?4–2Future value calculation