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- Assume that you are given the following historical returns for the Market and Security J. Also assume that the expected risk-free rate for the coming year is 4.0 percent, while the expected market risk premium is 15.0 percent. Given this information, determine the required rate of return for Security J for the coming year, using CAPM. Year 1 2 O21.20% 3 4 5 6 O22.34% O 23.49% O24.63% O24.10% Market 10.00% 12.00% 16.00% 14.00% 12.00% 10.00% Security J 12.00% 14.00% 18.00% 22.00% 18.00% 14.00%If Po is the initial price of the security, P₁ is the price after you hold it for a year, and X represents a direct payment, an asset's rate of return is equal to: rate of return = (P₁ - Po) rate of return = (P₁ - Po) + X rate of return = (P₁-Po) / Po + XPo rate of return = (P₁ - Po)/Po + XDetermine the present value P that must be invested to have the future value A at simple interest rate rather time A = $4000.00, r= 11.0%, t = 6 months
- 1) What is the future value at time t=3 for a present value of PV=$100 (e.g., t=0) if the interest rate is r=0.10 (e.g., r=10%)? 2) What is the future value at time t=18 for a present value of PV=$1525 (e.g., t=0) if the interest rate is r=0.085 (e.g., r=8.5%)? 3) What is the present value of a future value of FV=$500 at time t=5 if the interest rate is r=0.10 (e.g., r=10%)? 4) What is the present value for a future value of FV=$500,000 at time t=36 if the interest rate is r=0.05 (e.g., r=5%)? 5) What is the interest rate “r” if PV=$100 and the FV=$350 in year t=12? 6) What is the interest rate “r” if PV=$1250 and the FV=$2150 in year t=10? 7) How long will it take to double your investment if the interest rate is r=0.06 (r=6%)?8) How long will it take to increase your investment by 2.5 times if the interest rate is r=0.14 (r=14%)?9) Which is the better option if the interest rate is r=0.10 (r=10%)? Show all work used to arrive at your answer. a. Option I: Receive $1000 today at time…Suppose the term structure of risk-free interest rates is as shown below: 5 yr 7 yr 10 yr 20 yr Term 1 yr 2 yr 3 yr 2.42 2.77 3.31 3.75 4.15 4.93 1.98 Rate (EAR %) What is the present value of an investment that pays $103 at the end of each of years 1, 2, and 3? If you wanted to value this investment correctly using the annuity formula, what discount rate should you use? What is the present value of an investment that pays $103 at the end of each of years 1, 2, and 3? The present value of the investment is $294.08. (Round to the nearest cent.) If you wanted to value this investment correctly using the annuity formula, what discount rate should you use? The discount rate you should use if you want to use the annuity formula is 2.94%. (Round to two decimal places.)Suppose the term structure of risk-free interest rates is as shown below: 5 yr 7 yr 10 yr 20 yr Term 1 уг 2 yr 3 yr 3.24 3.79 4.09 5.05 2.07 2.46 2.71 Rate (EAR %) a. Calculate the present value of an investment that pays $1,000 in two years and $3,000 in five years for certain. b. Calculate the present value of receiving $100 per year, with certainty, at the end of the next five years. To find the rates for the missing years in the table, linearly interpolate between the years for which you do know the rates. (For example, the rate in year 4 would be the average rate in year 3 and year 5.) c. Calculate the present value of receiving $1,800 per year, with certainty, for the next 20 years. Infer rates for the missing years using linear interpolation. (Hint: Use a spreadsheet.)
- What is the present value for a future value of FV=$500,000 at time t=36 if the interest rate is r=0.05 (e.g., r=5%)? What is the interest rate “r” if PV=$100 and the FV=$350 in year t=12? What is the interest rate “r” if PV=$1250 and the FV=$2150 in year t=10? How long will it take to double your investment if the interest rate is r=0.06 (r=6%)? How long will it take to increase your investment by 2.5 times if the interest rate is r=0.14 (r=14%)? Which is the better option if the interest rate is r=0.10 (r=10%)? Show all work used to arrive at your answer. a. Option I: Receive $1000 today at time t=0. b. Option II: Receive $1615 at time t=5.10) Which is the better option if the interest rate is r=0.07 (r=7%)? Show all work used to arrive at your answer. a. Option I: Receive $510 today at time t=0. b. Option II: Receive $1000 at time t=10.Q) Compare the alternatives shown below on the basis of a future worth analysis, using an interest rate of 8% per year. Choose option A.A=-78983.65 B= -25193.45 B.A= 38987.65 B= 39125.45 C.A= 87983.65 B= 52193.45Q) Compare the alternatives shown below on the basis of a future worth analysis, using an interest rate of 8% per year. Choose correct option A.A=-78983.65 B= -25193.45 B.A= 38987.65 B= 39125.45 C.A= 87983.65 B= 52193.45
- Suppose the risk - free interest rate is 4.2%.a. Having $200 today is equivalent to having what amount in one year?b. Having $200 in one year is equivalent to having what amount today?c. Which would you prefer, $200 today or $200 in one year? Does your answer depend on when you need the money? Why or why not?a. Having $200 today is equivalent to having what amount in one year?Having $200 today is equivalent to having Sin one year. (Round to the nearest cent.)If the risk-free rate is 3.80 percent and the risk premium is 2.8 percent, what is the required return? (Round your answer to 1 decimal place.) Required returnDetermine the present value, P, you must invest to have the future value, A, at simple interest rate r after time t. Round answer to the nearest dollar. A = $2140 r = 7% t = 1 year $2000 $2070 $2007 $2035