Find the present values at the end of time period zero for each of these three investments if the

QUESTION

Find the present values at the end of time period zero for each of these three investments if the discount rate is 15 percent. Also find the present values for each investment using 10 percent and 20 percent discount rates.
Find the future values of these three investments at the end of year five if the compound interest rate is 12.5 percent. Also find the future values for each investment using 2.5 percent and 22.5 percent compound rates.
Find the present values of the three investments using a 15 percent annual discount rate but with quarterly discounting. Also find the present values for both semiannual and monthly discounting for a 15 percent stated annual rate.
Find the future values of the three investments using a 12.5 percent annual compound rate but with quarterly compounding. Also find the future values for both semiannual and monthly compounding for a 12.5 percent stated annual rate.
Assume that the present value for each of the three investments is $75,000. What is the annual interest rate (%i) for each investment?
Show how your answers would change in (e) if quarterly discounting takes place.
Assume that the future value for each of the three investments is $150,000. What is the annual interest rate (%i) for each investment? [Note: (e) and (g) are independent of each other.]
Show how your answers would change in (g) if quarterly compounding takes place.
Note: For question 5 what are the cash flows each year. Unless you know the cash flow you will not be able to find the interest rate. Similar is the case for question 7. Hence aonly Qns 1, 2, 3, 4 are answered here whose data sets are complete to be answered. ===================== Solution: Assume cash flow is $100 1. Present Value @15% = 100/(1+15%) =$86.96 Present Value @10%= 100/(1+10% ) = $90.91 Present Value at 20%= 100/(1+20%) =$83.33 2. Future value after 5 years @ 12.5%=100*(1.125^5)=$180.20 Future value after 5 years @ 2.5%= 100*(1.025^5)=$113.14 Future value after 5 years @ 22.5%= 100*(1.225^5)=$275.85 3. With quarterly discounting the discount rate=15%/4=3.75% With semi annual discounting the discount rate=15%/2=7.5% with monthly discounting the discount rate=15%/12=1.25% The rate is 3.75% and the value of the bond is: For each of these the cash flows are divided by the periods with quarterly discounting the present value is (discount rate=3.75%) Years 1 2 3 4 Cash flow 25 25 25 25 Present Value 24.10 23.23 22.39 21.58 Sum of Present Value (Value of the bond) 91.28 with semi-annual discounting the present value is (discount rate=7.5%) Years 1 2 Cash flow 50 50 Present Value 46.51 43.27 Sum of Present Value 89.78 with

y discounting the present value is (discount rate=1.25%) Years 1 2 3 4 5 6 7 8 9 10 11 12 Cash flow 8.33 8.33 8.33 8.33 8.33 8.33 8.33 8.33 8.33 8.33 8.33 8.33 Present value 8.23 8.13 8.03 7.93 7.83 7.73 7.64 7.54 7.45 7.36 7.27 7.18 Sum of Present Value 92.33 4. Future values using 12.5% discount rate (quarterly, semi annually and monthly) Using quarterly discounting @ 3.75% rate Years 1 2 3 4 Cash flow 25 25 25 25 Future value 27.92 26.91 25.94 25.00 Sum of Future Value 105.77 Using semiannual discounting @ 7.5% Years 1 2 Cash flow 50 50 Future Value 53.75 50.00 Sum of Future Value 103.75 Using monthly discounting at 1.0125% Years 1 2 3 4 5 6 7 8 9 10 11 12 Cash flow 8.33 8.33 8.33 8.33 8.33 8.33 8.33 8.33 8.33 8.33 8.33 8.33 Future value 9.55 9.44 9.32 9.20 9.09 8.98 8.87 8.76 8.65 8.54 8.44 8.33 Sum of Future Value 107.17

ANSWER:

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