9. You buy a 30 year zero coupon bond which will pay you $1000 in 30 years at an
ID: 2819407 • Letter: 9
Question
9. You buy a 30 year zero coupon bond which will pay you $1000 in 30 years at an annual yield of i 14% compounded once per year, 25 years later it will be a 5 year zero coupon bond. Suppose the interest rate on this bond will be 1496, what will the price of this bond be in 25 years? 10. You are offered an annuity that will pay you $200,000 once per year, at the end of the year, for 25 years. The first payment will arrive one year from now. The last payment will arrive twenty five years from now. Suppose your annual discount rate is 5.25%, how much are you willing to pay for this annuity? (hint: this is the same as the present value of an annuity) 11. You would like to develop an office building. Your analysts forecast that it will cost you $1,000,000 immediately (time 0), and it will cost you $500,000 in one year (time 1). They forecast you can sell the building for $2,400,000 in two years (time 2), If your discount rate is i 25%, what is the net present value of this investment?Explanation / Answer
(9) The price of the zero-coupon bond will be equal to the present value of its expected future cash flow (in the form of its face value redemption of $ 1000) discounted at its rate of interest. The period of discounting will be equal to the time period at which its value needs to be determined. For example, if bond price is needed 10 years before its maturity (at the end of Year 30), the discounting period would be t=10 years.
In this context, the discounting period is 5 years as the bond price is needed after 25 years from now, when the time left to maturity is 5 years.
Therefore, Bond Price after 25 years = P(25) = 1000 / (1.14)^(5) = $ 519.37 approximately.
NOTE: Please raise separate queries for solutions to the remaining unrelated questions.
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