6-50. (Present value of an uneven stream of payments) You are given three investment alternatives to analyze. The cash flows from these three investments are as follows: End of Year S 5,000 5,000 $2,000 2.000 2,000 2000(5,000 5,000 (5,000) (5,000) 5,000 What is the present value of each of these three investments if the appropriate discount rate is 10 percent? 6-51. (Present value of complex cash flows) You have an opportunity to make an invest- ment that will pay $100 at the end of the first year, $400 at the end of the second year, $400 at the end of the the end of the fifth year a. Find the present value if the interest rate is 8 percent. (Hint: You can simply bring third year, $400 at the end of the fourth year, and 5300 at each cash flow back to the present this problem is to either use the- NPV function in Excel or to use the CF key on your fore you use this key. Keep in mind that with the -NPV function in Excel, there is no initial outlay. That is, all this function does is bring all of the future cash flows back to the present. With a financial calculator, you should keep in mind that CFo is the initial outlay or cash flow at time 0, and, because there is no cash flow at time 0, CF,.-0.) and then add them up. Another way to work financial calculator-but you"ll want to check your calculator's manual be- b. What would happen to the present value of this stream of cash flows if the interest rate were 0 percent? 6-52. (Present value of complex cash nows) How much do you have to deposit today so that beginning 11 years from now you can withdraw S10,000 a year for the next five years (Periods 1 through 15) plus an additional amount of $20,000 in the last year (Period 13)? Assume an interest rate of 6 percent. 6-53. (Comprehensive problem) You would like to have $50,000 in 15 years To accumulate this amount, you plan to deposit an equal sum in the bank each year that will earn 7 percent interest compounded annually. Your first payment will be made at the end of the year CHAPTER 6 The Time Value of Money 187 a. How much must you deposit annually to accumulate this amount? b. If you decide to make a large lump-sum deposit today instead of the annual de- posits, how large should this lump-sum deposit be? (Assume you can earn 7 per- cent on this deposit.) c. At the end of five years, you will receive $10,000 and deposit this in the bank to- ward your goal of S50,000 at the end of 15 years. In addition to this deposit, how much must you deposit in equal annual deposits to reach your goal? (Again, as- sume you can earn 7 percent on this deposit.)