(Related to Checkpoint 6.5) (Present value of a growing perpetuity) What is the present value of a perpetual stream of cash flows that pays $5,500 at the end of year one and the annual cash flows grow at a rate of 3% per year indefinitely, it the appropriate discount rate is 11%? What if the appropriate discount rate is 9%? a. If the appropriate discount rate is 11%, the present value of the growing perpetuity is $ (Round to the nearest cent.) b. If the appropriate discount rate is 9%, the present value of the growing perpetuity is $ (Round to the nearest cent.)
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A perpetuity is a series of equal and regular payments that go on forever. These payments continue indefinitely. The present value of the payments is the discounted value of cash flows that occur in future.
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- (1) What is the value at the end of Year 3 of the following cash flow stream if the quoted interest rate is 10%, compounded semiannually? (2) What is the PV of the same stream? (3) Is the stream an annuity? (4) An important rule is that you should never show a nominal rate on a time line or use it in calculations unless what condition holds? (Hint: Think of annual compounding, when INOM = EFF% = IPER.) What would be wrong with your answers to parts (1) and (2) if you used the nominal rate of 10% rather than the periodic rate, INOM/2 = 10%/2 = 5%?Suppose you are going to receive $11,000 per year for 8 years. The appropriate interest rate is 11 percent per year. Requirement 1: What is the present value of the payments if they are in the form of an ordinary (a)annuity (cash flow starts at the end of the first compounding period)? (Click to select) (b) What is the present value if the payments are an annuity due (cash flow starts at the beginning of the first compounding period)? (Click to select) Requirement 2: (a)Suppose you plan to invest the payments for 8 years, what is the future value if the payments are an ordinary annuity? (Click to select) (b)Suppose you plan to invest the payments for 8 years, what is the future value if the payments are an annuity due? (Click to select)(Present value of a growing perpetuity) What is the present value of a perpetual stream of cash flows that pays $3,500 at the end of year one and the annual cash flows grow at a rate of 4% per year indefinitely, if the appropriate discount rate is 15%? What if the appropriate discount rate is 13%?
- This problem demonstrates the dependence of an annuity's future value on the size of the periodic payment. Suppose a fixed amount will be invested at the end of each year and that the invested funds will earn 5.3% compounded annually. What will be the future value of the investments after 15 years if the periodic investment is: (Do not round intermediate calculations and round your final answers to 2 decimal places.) Investment Future Value a. $2,300 per year $ b. S3, 300 per year $ c. S4, 300 per year $The present value of an annuity stream of $100 per year is $920 when valued at a 10% rate. By approximately how much would the value change if these were annuities due? A. An increase of $10 B. An increase of $92 C. An increase of $100 D. Unknown without knowing number of paymentsWhat is the present value of a perpetuity stream of cash flows that pays P1,000 at the end of year one, and the annual cash flows grow at a rate of 4% per year indefinitely, if the appropriate discount rate is 8%?
- 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. An annuity that pays $500 at the end of every six months An annuity that pays $1,000 at the end of each year An annuity that pays $1,000 at the beginning of each year*** This is the correct option**** An annuity that pays $500 at the beginning of every six months A. An ordinary annuity selling at $2,514.15 today promises to make equal payments at the end of each year for the next eight years (N). If the annuity’s appropriate interest rate (I) remains at 8.00% during this time, the annual annuity payment (PMT) will be . B. You just won the lottery. Congratulations! The jackpot is $10,000,000, paid in eight equal annual payments. The…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 beginning of every six months 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 $1,000 at the end of each year An ordinary annuity selling at $4,947.11 today promises to make equal payments at the end of each year for the next eight years (N). If the annuity's appropriate interest rate (1) remains at 6.50% during this time, the annual annuity payment (PMT) will be You just won the lottery. Congratulations! The jackpot is $35,000,000, paid in eight equal annual payı The first payment on the lottery jackpot will be made today. In present value terms, you really won -assuming…Q. No. 02: Find the future value of the following annuities. The first payment in these annuities is made at the end of Year 1, so they are ordinary annuities. a) $300 per year for 10 years at 10% b) $100 per year for 5 years at 5% c) $300 per year for 5 years at 0% d) Now rework parts a, b, and c assuming that payments are made at the beginning of each year; that is, they are annuities due. Q.No. 03: Solve following time line, draw a clear diagram in your answer sheet. Assume opportunity cost of 12% 6 7 3 500 500 500 300 300 300 300 300 Q. No. 04: Discuss following terms with examples; a) Perpetuity b) Par Value c) Coupon Rate d) Zero-Coupon Bond
- Please answer this question: What is the value at the end of Year 3 of the following cash flow stream if interest is 4% compounded semiannually? (Hint: you can use the EAR and treat the cash flows as an ordinary annuity or use the periodic rate and compound the cash flows individually.) What is the PV? What would be wrong with your answer to parts I(1) and I(2) if you used the nominal rate, 4%, rather than the EAR or the periodic rate, I sow /2=4%/2=2%, to solve the problems?What is the present value of a perpetual stream of cash flows that pays $80,000 at the end of year one and then grows at a rate of 6% per year indefinitely? The rate of interest used to discount the cash flows is 10%. The present value of the growing perpetuity is $enter your response here. (Round to the nearest cent.)A perpetuity will make its first payment in 20 years. The first payment will be $5,000, and future payments will increase at a 10 percent annual rate. What is the present value of this investment, assuming a 10% discount rate? Place Answer in Blank Above. What is the difference between a perpetuity and a growing perpetuity? What are real-world examples of each?