Exam 9: Time Value of Money

Because we usually assume positive interest rates in time value analyses, the present value of a three year annuity will always be less than the future value of a single lump sum, if the annuity payment equals the original lump sum investment.

Your parents start saving for your sister's college education.She will begin college when she turns age 18 and will need $4,000 at that time and at the end of each of the following 3 years.They will make a deposit at the end of this year in an account which pays 6 percent compounded annually, and an identical deposit at the end of each year with the last deposit occurring when she turns age 18.If an annual deposit of $1,484 will allow them to reach their goal, how old is your sister now?

Your lease calls for payments of $500 at the end of each month for the next 12 months.Now your landlord offers you a new 1-year lease which calls for zero rent for 3 months, then rental payments of $700 at the end of each month for the next 9 months.You keep your money in a bank time deposit that pays a simple annual rate of 5 percent.By what amount would your net worth change if you accept the new lease? (Hint: Your return per month is 5%/12 = 0.4166667%.)

Discounted payback's primary advantage over traditional payback is that

A project with a 3-year life has the following probability distributions for possible end of year cash flows in each of the next three years: Using an interest rate of 8 percent, find the expected present value of these uncertain cash flows.(Hint: Find the expected cash flow in each year, then evaluate those cash flows.)

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?

Gomez Electronics needs to arrange financing for its expansion program.Bank A offers to lend Gomez the required funds on a loan where interest must be paid monthly, and the quoted rate is 8 percent.Bank B will charge 9 percent, with interest due at the end of the year.What is the difference in the effective annual rates charged by the two banks?

Assume that, to help build your nest-egg, you made two deposits of $100, one on January 1, 2014, and one on July 1, 2014, in a savings account that paid 10 percent compounded semiannually.On January 1, 2015, the bank increased the interest rate paid on savings accounts to 12 percent, annual compounding.Then you made a third $100 deposit on April 1, 2015.How much should there be in your account on January 1, 2016?

Hillary is trying to determine the cost of health care to college students, and parents' ability to cover those costs.She assumes that the cost of one year of health care for a college student is $1,000 today, that the average student is 18 when he or she enters college, that inflation in health care cost is rising at the rate of 10 percent per year, and that parents can save $100 per year to help cover their children's costs.All payments occur at the end of the relevant period, and the $100/year savings will stop the day the child enters college (hence 18 payments will be made).Savings can be invested at a simple rate of 6 percent, annual compounding.Hillary wants a health care plan which covers the fully inflated cost of health care for a student for 4 years, during years 19 through 22 (with payments made at the end of years 19 through 22).How much would the government have to set aside now (when a child is born), to supplement the average parent's share of a child's college health care cost? The lump sum the government sets aside will also be invested at 6 percent, annual compounding.

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.

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?

Which of the following statements is most correct?

You are considering an investment in a 40-year security.The security will pay $25 a year at the end of each of the first three years.The security will then pay $30 a year at the end of each of the next 20 years.The simple interest rate is assumed to be 8 percent, and the current price (present value) of the security is $360.39.Given this information, what is the equal annual payment to be received from Year 24 through Year 40 (i.e., for 17 years)?

Your company must make payments of $100,000 each year for 10 years, with the first payment to be made 10 years from today.To prepare for these payments, your company must make 10 equal annual deposits into an account which pays a simple interest rate of 7 percent, daily compounding (360-day year).Funds will remain in the account during both the accumulation period (the first 10 years) and the distribution period (the last 10 years), and the same interest rate will be earned throughout the entire 20 years.The first deposit will be made immediately.How large must each deposit be?

Assume that you just had a child, and you are now planning for her college education.You would like to make 43 equal payments over the next 21 years (the first payment to be made immediately, all other payments to be made at 6-month intervals, with the final payment to be made at her 21st birthday) so that you will be able to cover her expected expenses while in school.You expect to pay expenses on her 18th, 19th, 20th, and 21st birthdays.Assume that the current (time period 0) annual cost of college is $6,000, that you expect annual inflation to be 8 percent for the next 5 years, and then 5 percent thereafter.If you expect to be able to earn a return of 4 percent every 6 months on your investments (a simple rate of 8 percent with semiannual compounding), what will be the amount of each of the 43 payments?

You have the opportunity to buy a perpetuity which pays $1,000 annually.Your required rate of return on this investment is 15 percent.You should be essentially indifferent to buying or not buying the investment if it were offered at a price of

You have just taken out an installment loan for $100,000.Assume that the loan will be repaid in 12 equal monthly installments of $9,456 and that the first payment will be due one month from today.How much of your third monthly payment will go toward the repayment of principal?

There exists an IRR solution for each time the direction of cash flows associated with a project is interrupted.

Assume that you inherited some money.A friend of yours is working as an unpaid intern at a local brokerage firm, and her boss is selling some securities which call for four payments, $50 at the end of each of the next 3 years, plus a payment of $1,050 at the end of Year 4.Your friend says she can get you some of these securities at a cost of $900 each.Your money is now invested in a bank that pays an 8 percent simple (quoted) interest rate, but with quarterly compounding.You regard the securities as being just as safe, and as liquid, as your bank deposit, so your required effective annual rate of return on the securities is the same as that on your bank deposit.You must calculate the value of the securities to decide whether they are a good investment.What is their present value to you?

You are given the following cash flow information.The appropriate discount rate is 12 percent for Years 1−5 and 10 percent for Years 6−10.Payments are received at the end of the year. What should you be willing to pay right now to receive the income stream above?