7. Present value of annuities and annuity payments The present value of an annuity is the sum of the discounted value of all future cash flows. You have the opportunity to invest in several annuities. Which of the following 10-year annuities has the greatest present value (PV)? Assume that all annuities earn the same positive interest rate. O An annuity that pays $500 at the end of every six months O An annuity that pays $1,000 at the beginning of each year O An annuity that pays $500 at the beginning of every six months O An annuity that pays $1,000 at the end of each year An ordinary annuity selling at $11,417.87 today promises to make equal payments at the end of each year for the next six years (N). If the annuity's appropriate interest rate (I) remains at 9.50% during this time, the annual annuity payment (PMT) will be You just won the lottery. Congratulations! The jackpot is $35,000,000, paid in six equal annual payments. The first payment on the lottery jackpot will be made today. In present value terms, you really won_ -assuming annual interest rate of 9.50%. 8. Perpetuities Perpetuities are also called annuities with an extended or unlimited life. Based on your understanding of perpetuities, answer the following questions. Which of the following are characteristics of a perpetuity? Check all that apply. A perpetuity is a stream of regularly timed, equal cash flows that continues forever. The current value of a perpetuity is based more on the discounted value of its nearer (in time) cash flows and less by the discounted value of its more distant in the future) cash flows. The value of a perpetuity is equal to the sum of the present value of its expected future cash flows. The value of a perpetuity cannot be determined. A local bank's advertising reads: "Give us $15,000 today, and we'll pay you $600 every year forever." If you plan to live forever, what annual interest rate will you earn on your deposit? O 5.60% 4.00% O 6.40% O 3.20% Oops! When you went in to make your deposit, the bank representative said the amount of required deposit reported in the advertisement was incorrect and should have read $22,500. This revision, which will the interest rate earned on your deposited funds, will adjust your earned interest rate to 9. Uneven cash flows A series of cash flows may not always necessarily be an annuity. Cash flows can also be uneven and variable in amount, but the concept of the time value of money will continue to apply. Consider the following case: The Purple Lion Beverage Company expects the following cash flows from its manufacturing plant in Palau over the next five years: Year 1 $250,000 Annual Cash Flows Year 2 Year 3 Year 4 $37,500 $480,000 $300,000 Year 5 $550,000 The CFO of the company believes that an appropriate annual interest rate on this investment is 4%. What is the present value of this uneven cash flow stream, rounded to the nearest whole dollar? $1,410,275 $2,167,500 $767,500 $1,650,000 Identify whether the situations described in the following table are examples of uneven cash flows or annuity payments: Description Uneven Cash Flows Annuity Payments Debbie has been donating 10% of her salary at the end of every year to charity for the last three years. Her salary increased by 15% every year in the last three years. You deposit a certain equal amount of money every year into your pension fund. Amit receives quarterly dividends from his investment in a high-dividend yield, index exchange-traded fund. Aakash borrowed some money from his friend to start a new business. He promises to pay his friend $2,650 every year for the next five years to pay off his loan along with interest