A pension fund projects its cash flow obligations to be constant at $5Mln for the next 10 years and then grow by 5% in perpetuity starting year 11. Assume that interest rates are constant at 4% for the next ten years and will then increase to 6% from year 11 onwards. Determine the present value of the pension fund obligations. (Hint: You may want to divide the cash flows into the annuity and the growing perpetuity component.)
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- A pension fund is expected to produce a cash flow of $1,000 at the end of the upcoming year. This cash flow will grow at a rate of 10% for five years and then at the rate of 7% indefinitely. Assume the annual interest rate for pension-related investments is 12%. 1) What is the value of the pension fund?A pension fund must pay out $1 million next year, $2 million the following year, and then $3 million the year after that. If the discount rate is 8%, what is the duration of this set of payments?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)
- 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…Consider a pension plan that will pay $10,000 once a year for a 5-year period (5 annual payments). The first payment will come in exactly 5 years (at the end of year 5) and the last payment in 9 years (at the end of year 9). a. What is the duration of the pension obligation? The current interest rate is 9% per year for all maturities. b. To generate the scheduled pension payments, the pension fund wants to invest the present value of the future payouts in bonds and match the duration of its obligation in part a). If the fund uses 5-year and 10-year zero-coupon bonds to construct its investment position, how much money (dollar amount) ought to be placed in each bond now? What should be the total face value (not current market value) of each zero coupon bond held? c. Right after the fund made its investment outlined in part b), market interest rates for all maturities dropped from 9% p.a.to 8% p.a. Show that the investment position constructed in part b) can still approximately fund 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…
- What is the equivalent average annual effective rate of interest over 5-year period if the fund earns d^{(4)} = 4% for the initial 1 year, d^{(12)} = 6% for the next 2 years, and i^{(6)} = 9% in the last 2 years?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?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 An annuity that pays $500 at the beginning 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 An ordinary annuity selling at $14,130.15 today promises to make equal payments at the end of each year for the next twelve years (N). If the annuity's appropriate interest rate (I) remains at 8.00% during this time, the annual annuity payment (PMT) will be You just won the lottery. Congratulations! The jackpot is $85,000,000, paid in twelve equal annual payments. The first payment on the lottery jackpot will be made today. In present value terms, you really won…
- 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 $1,000 at the end of each year An annuity that pays $500 at the end of every six months An annuity that pays $1,000 at the beginning of each year An annuity that pays $500 at the beginning of every six monthsFind the present value PV of the annuity account necessary to fund the withdrawal given. HINT [See Quick Example 3.] (Assume end-of-period withdrawals and compounding at the same intervals as withdrawals. Round your answer to the nearest cent.) $2,500 per quarter for 10 years, if the account earns 6% per yearFind the present value PV of the annuity account necessary to fund the withdrawal given. (Assume end-of-period withdrawals and compounding at the same intervals as withdrawals. Round your answer to the nearest cent.) PV = $ $300 per month for 10 years, if the account earns 2% per year and if there is to be $10,000 left in the annuity at the end of the 10 years X Need Help? Read It Watch It