Exam 4: The Time Value of Money

Find the present value of an income stream which has a negative flow of $100 per year for 3 years,a positive flow of $200 in the 4th year,and a positive flow of $300 per year in Years 5 through 8.The appropriate discount rate is 4 percent for each of the first 3 years and 5 percent for each of the later years.Thus,a cash flow accruing in Year 8 should be discounted at 5 percent for some years and 4 percent in other years.All payments occur at year-end.

A bank pays a quoted annual (simple)interest rate of 8 percent.However,it pays interest (compounds)daily using a 365-day year.What is the effective annual rate of return?

Your company is planning to borrow $1,000,000 on a 5-year,15 percent,annual payment,fully amortized term loan.What fraction of the payment made at the end of the second year will represent repayment of principal?

You are currently at time period 0,and you will receive the first payment on an annual payment annuity of $100 in perpetuity at the end of this year.Six full years from now you will receive the first payment on an additional $150 in perpetuity,and at the end of time period 10 you will receive the first payment on an additional $200 in perpetuity.If you require a 10 percent rate of return,what is the combined present value of these three perpetuities?

Which of the following statements is correct?

You can deposit your savings at the Darlington National Bank,which offers to pay 12.6 percent interest compounded monthly,or at the Bartlett Bank,which will pay interest of 11.5 percent compounded daily.(Assume 365 days in a year.)Which bank offers the higher effective annual rate?

Assume that your required rate of return is 12 percent and you are given the following stream of cash flows: If payments are made at the end of each period,what is the present value of the cash flow stream?

You just graduated,and you plan to work for 10 years and then to leave for the Australian "Outback" bush country.You figure you can save $1,000 a year for the first 5 years and $2,000 a year for the next 5 years.These savings cash flows will start one year from now.In addition,your family has just given you a $5,000 graduation gift.If you put the gift now,and your future savings when they start,into an account which pays 8 percent compounded annually,what will your financial "stake" be when you leave for Australia 10 years from now?

You plan to invest $2,500 in a money market account which will pay an annual stated (simple)interest rate of 8.75 percent,but which compounds interest on a weekly basis.If you leave this money on deposit for one year (52 weeks),what will be your ending balance when you close the account?

What is the effective annual return (EAR)for an investment that pays 10 percent compounded annually?

Assume that you will receive $2,000 a year in Years 1 through 5,$3,000 a year in Years 6 through 8,and $4,000 in Year 9,with all cash flows to be received at the end of the year.If you require a 14 percent rate of return,what is the present value of these cash flows?

The difference between an ordinary annuity and an annuity due is that each of the payments of the annuity due earns interest for one additional year (period).

Your client just turned 75 years old and plans on retiring in 10 years on her 85th birthday.She is saving money today for her retirement and is establishing a retirement account with your office.She would like to withdraw money from her retirement account on her birthday each year until she dies.She would ideally like to withdraw $50,000 on her 85th birthday,and increase her withdrawals 10 percent a year through her 89th birthday (i.e.,she would like to withdraw $73,205 on her 89th birthday).She plans to die on her 90th birthday,at which time she would like to leave $200,000 to her descendants.Your client currently has $100,000.You estimate that the money in the retirement account will earn 8 percent a year over the next 15 years.Your client plans to contribute an equal amount of money each year until her retirement.Her first contribution will come in one year; her tenth and final contribution will come in ten years (on her 85th birthday).How much should she contribute each year in order to meet her objectives?

A $10,000 loan is to be amortized over 5 years,with annual end-of-year payments.Given the following facts,which of these statements is correct?

You want to borrow $1,000 from a friend for one year,and you propose to pay her $1,120 at the end of the year.She agrees to lend you the $1,000,but she wants you to pay her $10 of interest at the end of each of the first 11 months plus $1,010 at the end of the 12th month.How much higher is the effective annual rate under your friend's proposal than under your proposal?

When a loan is amortized,the largest portion of the periodic payment goes to reduce principal in the early years of the loan such that the accumulated interest can be spread out over the life of the loan.

Of all the techniques used in finance,the least important is the concept of the time value of money.

Steaks Galore needs to arrange financing for its expansion program.One bank offers to lend the required $1,000,000 on a loan which requires interest to be paid at the end of each quarter.The quoted rate is 10 percent,and the principal must be repaid at the end of the year.A second lender offers 9 percent,daily compounding (365-day year),with interest and principal due at the end of the year.What is the difference in the effective annual rates (EFF%)charged by the two banks?

Which of the following statements is most correct?

Suppose an investor can earn a steady 5% annually with investment A,while investment B will yield a constant 12% annually.Within 11 years time,the compounded value of investment B will be more than twice the compounded value of investment A (ignore risk).