Exam 4: The Time Value of Money

Sipho just signed a long-term lease on a townhouse in Johannesburg (near Sandton) that requires him to make equal monthly payments for the next five years.The payments Sipho has promised to make represent a(n) __________ for the landlord.

Which of the following statements is correct?

A recent advertisement in the financial section of a magazine carried the following claim: "Invest your money with us at 14 percent, compounded annually, and we guarantee to double your money sooner than you imagine." Ignoring taxes, how long would it take to double your money at a simple rate of 14 percent, compounded annually?

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.)

You want to borrow R1,000 from a friend for one year, and you propose to pay her R1,120 at the end of the year.She agrees to lend you the R1,000, but she wants you to pay her R10 of interest at the end of each of the first 11 months plus R1,010 at the end of the 12th month.How much higher is the effective annual rate under your friend's proposal than under your proposal?

The coupon rate is the rate of return you could earn on alternative investments of similar risk.

You plan to invest an amount of money in five-year certificate of deposit (CD) at your bank.The stated interest rate applied to the CD is 12 percent, compounded monthly.How much must you invest if you want the balance in the CD account to be R8,500 in five years?

Your company is planning to borrow R1,000,000 on a 5-year, 15 percent, annual payment, fully amortised term loan.What fraction of the payment made at the end of the second year will represent repayment of principal?

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.

Suppose you put R100 into a savings account today, the account pays a simple annual interest rate of 6 percent, but compounded semi-annually, and you withdraw R100 after 6 months.What would your ending balance be 20 years after the initial R100 deposit was made?

By definition, what type of annuity best describes payments such as rent and magazine subscriptions (assuming the costs do not change over time)?

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).

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 company must make payments of R100,000 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?

Your father, who is 60, plans to retire in 2 years, and he expects to live independently for 3 years.He wants a retirement income which has, in the first year, the same purchasing power as R40,000 has today.However, his retirement income will be of a fixed amount, so his real income will decline over time.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?

You are currently at time period 0, and you will receive the first payment on an annual payment annuity of R100 in perpetuity at the end of this year.Six full years from now you will receive the first payment on an additional R150 in perpetuity, and at the end of time period 10 you will receive the first payment on an additional R200 in perpetuity.If you require a 10 percent rate of return, what is the combined present value of these three perpetuities?

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?

At an inflation rate of 9 percent, the purchasing power of R1 would be cut in half in 8.04 years.How long to the nearest year would it take the purchasing power of R1 to be cut in half if the inflation rate were only 4%?

If you buy a factory for R250,000 and the terms are 20 percent down, the balance to be paid off over 30 years at a 12 percent rate of interest on the unpaid balance, what are the 30 equal annual payments?

Sarah is thinking about purchasing an investment from HiBond Investing.If she buys the investment, Sarah will receive R100 every three months for five years.The first R100 payment will be made as soon as she purchases the investment.If Sarah's required rate of return is 16 percent, to the nearest rand, how much should she be willing to pay for this investment?