Exam 4: The Time Value of Money

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, R50 at the end of each of the next 3 years, plus a payment of R1,050 at the end of Year 4.Your friend says she can get you some of these securities at a cost of R900 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?

All else equal, the future value of a lump-sum amount invested today will increase if the

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?

In its first year of operations, 1999, the Gourmet Cheese Shoppe had earnings per share (EPS) of R0.26.Four years later, in 2003, EPS was up to R0.38, and 7 years after that, in 2010, EPS was up to R0.535.It appears that the first 4 years represented a supernormal growth situation and since then a more normal growth rate has been sustained.What are the rates of growth for the earlier period and for the later period?

As the discount rate increases without limit, the present value of the future cash inflows

You have a 30-year mortgage with a simple annual interest rate of 8.5 percent.The monthly payment is R1,000.What percentage of your total payments over the first three years goes toward the repayment of principal?

You will receive a R100 annual perpetuity, the first payment to be received now, at Year 0, a R300 annual perpetuity payable starting at the end of Year 5, and a R200 semi-annual (2 payments per year) perpetuity payable starting midway through Year 10.If you require an effective annual interest rate of 14.49 percent, what is the present value of all three perpetuities together at Year 0? (Hint: The semi-annual annuity can be thought of as two annual annuities.)

At an effective annual interest rate of 20 percent, how many years will it take a given amount to triple in value? (Round to the closest year.)

In 1958 the average tuition for one year at a private school was R1,800.Thirty years later, in 1988, the average cost was R13,700.What was the growth rate in tuition over the 30-year period?

Vegit Corporation needs to borrow funds to support operations during the summer.Vegit's CFO is trying to decide whether to borrow from Fruit Bank or Vegetable Bank.The loan offered by Fruit Bank has a 12.5 percent simple interest rate with annual interest payments, whereas the loan offered by Vegetable National Bank has a 12 percent simple interest rate with monthly payments.Which bank should Vegit use for the loan?

Your father, who is 60, plans to retire in 2 years, and he expects to live independently for 3 years.Suppose your father wants to have a real income of R40,000 in today's Rands in each year after he retires.His retirement income will start the day he retires, 2 years from today, and he will receive a total of 3 retirement payments.Inflation is expected to be constant at 5 percent.Your father has R100,000 in savings now, and he can earn 8 percent on savings now and in the future.How much must he save each year, starting today, to meet his retirement goals?

An annuity is a series of equal payments made at fixed equal-length intervals for a specified number of periods.

Bank A offers a 2-year certificate of deposit (CD) that pays 10 percent compounded annually.Bank B offers a 2-year CD that is compounded semi-annually.The CDs have identical risk.What is the stated, or simple, rate that Bank B would have to offer to make you indifferent between the two investments?

Steaks Galore needs to arrange financing for its expansion program.One bank offers to lend the required R1,000,000 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?

You have just borrowed R20,000 to buy a new car.The loan agreement calls for 60 monthly payments of R444.89 each to begin one month from today.If the interest is compounded monthly, then what is the effective annual rate on this loan?

All else equal, if you expect to receive a certain amount in the future, say, R500 in ten (10) years, the present value of that future amount will be lowest if the interest earned on such investments is compounded

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

The effective annual rate is always greater than the simple rate as a result of compounding effects.

You are given the following cash flows.What is the present value (t = 0) if the discount rate is 12 percent? R0 R1 R2,000 R2,000 R2,000 R0 -R2,000

You expect to receive R1,000 at the end of each of the next 3 years.You will deposit these payments into an account which pays 10 percent compounded semi-annually.What is the future value of these payments, that is, the value at the end of the third year?