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PART THREE Valuation of Future Cash Flows

Intermediate

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48. Calculating Present Value of Annuities Congratulations! You've just won the $15 million first prize in the Subscriptions R Us Sweepstakes. Unfortunately, the sweepstakes will actually give you the $15 million in $375,000 annual installments over the next 40 years, beginning next year. If your appropriate discount rate is 11 percent per year, how much money did you really win?

49. Present Value and Multiple Cash Flows What is the present value of $1,000 per year, at a discount rate of 12 percent, if the first payment is received 8 years from now and the last payment is received 20 years from now?

50. Variable Interest Rates A 10-year annuity pays $1,500 per month, and payments are made at the end of each month. If the interest rate is 15 percent compounded monthly for the first four years, and 12 percent compounded monthly thereafter, what is the present value of the annuity?

51. Comparing Cash Flow Streams You have your choice of two investment accounts. Investment A is a 10-year annuity that features end-of-month $1,000 payments and has an interest rate of 11.5 percent compounded monthly. Investment B is an 8 percent continuously compounded lump-sum investment, also good for 10 years. How much money would you need to invest in B today for it to be worth as much as Investment A10 years from now? Calculating Present Value of a Perpetuity Given an interest rate of 6.5 percent per year, what is the value at date t = 7 of a perpetual stream of $500 payments that begin at date t = 13?

Calculating EAR A local finance company quotes a 13 percent interest rate on one-year loans. So, if you borrow $20,000, the interest for the year will be $2,600. Because you must repay a total of $22,600 in one year, the finance company requires you to pay $22,600/12, or $1,883.33, per month over the next 12 months. Is this a 13 percent loan? What rate would legally have to be quoted? What is the effective annual rate?

54. Calculating Future Values If today is Year 0, what is the future value of the following cash flows five years from now? What is the future value 10 years from now? Assume a discount rate of 9 percent per year.

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