Title Exercises_for_Midterm.docx ✅

REVIEW EXERCISES RMIT Classification: Trusted Exercise 1. Justin wants to have 6000 USD at the end of year 3. How much does he need to invest now to receive that amount in the future if? a) The annual interest rate is 4.5% and compounded daily. b) The annual interest rate is 5.5% and compounded monthly. Exercise 2. Daniel predicts that he will live for 20 years after retirement, and he plans to spend 8000 USD per year in 20 years. How much does he need to save at the time of his retirement to follow that plan if r = 12%? Exercise 3. The initial investment of a project is 300000 USD. The project has the following cashflows: Year 1 2 3 120000 260000 100000 If r = 11%, what is the NPV of the project? Should one invest in such a project? Exercise 4. If the dividend in year 1 () is $4, and its growth rate is 5% per year forever, what is the rate of return if the current price of the stock is $25. Exercise 5. Calculate the Macaulay duration of a 4-year bond with face value = $120, coupon rate = 7%, yield to maturity = 7.5% Exercise 6. What is the present value of a stream of cashflows that pays 400 in year 1, 700 in year 2 and 1600 in year 3 if the interest rate is 12%? Exercise 7. A lottery price is $30 million paid in equal instalments over 5 years. What is the present value of the lottery if the first payment is received immediately and r = 8%? Exercise 8. Stanley plans to travel for 5 years after his retirement and spend $200000 per year. He must work for the next 35 years to prepare this plan. What is the equal monthly payment needed to put in Stanley’s account so that he will have enough money to travel at the time of his retirement? Assume that r = 9% Exercise 9. HP has just paid $1 as dividend. Its dividend is expected to grow 18% in year 1, 14% in year 2 and 6% after that. So calculate the price of its share at r = 18%. Exercise 10. A 3-year bond has 7% coupon rate, $1000 face value and 12% yield to maturity. What is the price of this bond if the coupon payments are made semi-annually? Exercise 11. Consider a cash flow that pays $3000 in the next year, $2000 four years from now and $3000 six years from now. Calculate the present value using r = 8%. Exercise 12. Calculate the NPV of the following project with 12% interest rate: Year 0 1 2 -120 400 -50 Exercise 13. A $300 million lottery pays an equal installment for 30 years each year. What is the present value of this lottery if each payment is made at the end of each year? Assume r = 8% Exercise 14. If the monthly interest rate is 1.25%, calculate the EAR and APR. Exercise 15. You lease a car for 4 years for $400/month. You receive no payment upfront or at the end of the leasing period. If r = .8%/month, what is the cost of the lease?
REVIEW EXERCISES RMIT Classification: Trusted Exercise 16. In June 2020 you bought 300 Yen of bond (face value) with 9% coupon rate. The bond matures in 2025 and its yield to maturity is 5%. Calculate the price of this bond when: a) The coupons are paid annually; b) The coupons are paid semi-annually Exercise 17. Calculate the NPV of the following project with r = 14% Year 0 1 2 3 4 5 -100 30 30 30 30 -15 Should one invest in this project? Exercise 18. FPT’s last dividend was $1.5. It is expected to grow at 22% per year for the next 3 years. After that, it grows at 6% forever. What is the PV of the stock if the interest rate is 15% (APR)? Exercise 19. Nga will retire 30 years from now. She plans to have $2 million in her retirement fund. How much does she need to put in the savings account at the end of each year if r = 4%? Exercise 20. A project has an initial cost of $6 billion with a 3-year life cycle. The projected cashflows are $2100 million, $2600 million and $2800 million in the next 3 years. What is the NPV at r = 15%? Exercise 21. A coupon bond has 1000 face value and an 8% coupon rate and is paid semi-annually. The first payment is after 6 months. The maturity is 12 years. a) What is the PV if the ytm = 8%? Two years later, after receiving the 4 th payment, the investor wishes to sell the bond. b) The ytm now rises to 9%. What is the price of the bond at this time? c) If someone buys this bond for $1000, should the investor sell or hold? Exercise 22. The dividend in year 1 of a stock is $1.5, in year 2 is $2.5 and in year 3 is $4. After that, the dividend grows at 6% a year. If the required rate of return is 10%, what is the present value of this stock? Exercise 23. Tam deposits 40 million VND at the end of each year for 4 years. Calculate the amount at the end of the 4 th year if the interest rate is 7% and compounded semi-annually. Exercise 24. Would you accept $1700 today or $2000 in two years at r = 7%? Exercise 25. ROC has just paid $4 as dividend last year. Its dividend is expected to grow at 4% forever. Calculate the price of the stock if the required rate of return for investors is 18%. Exercise 26. What is the present value of an annuity paying 1200 per year for 10 years with r = 14%? Exercise 27. A 5-year bond that pays annually has $1000 face value, 8% coupon rate and 6% yield to maturity. a) Calculate the Macaulay duration for this bond. b) If the ytm decreases from 6% to 5.5%, what is the price of this bond after the change?
REVIEW EXERCISES RMIT Classification: Trusted Exercise 28. What is the future value of this cashflow at the end of year 5? r = 10% Year 0 1 2 3 4 5 200 100 60 80 40 Exercise 29. A stock pays $3 as dividend in year 1, $5 as dividend in year 2 and then sold for $40. What is the current value of the stock if r = 8%? Exercise 30. The dividends in the next 3 years of a stock are $4, $3 and $8. From year 4, it pays $2 forever as a dividend. What is the PV of the stock if r = 12%? Exercise 31. A factory costs $800000. It would produce a net income of $140000 per year for 8 years. The opportunity cost is assumed equal 12%. What is the NPV? What is the value of this factory at the end of year 5? Exercise 32. A mortgage loan to borrow 150000 USD with r = 6% per year. Contract calls for equal quarterly payments for 20 years, what is the amount of each payment? Exercise 33. You have a prize of 52 mil. VND to be paid exactly after 3 years. You was offered 45 mil. Today as a consideration to sell the right to receive the prize. If r = 12% per year and compounded quarterly, should you accept the offer? Exercise 34. To save money for travel, I have to deposit 30 mil vnd at the end of each year for 3 years. Calculate the total money in the account at the end of year 3, if 4= 8% and compounded semi-annually. Exercise 35. Calculate the present value of CF of 9500 starting at the end of year 5 in perpetuity. a. Assuming a rate of return of 8.25% b. Assuming a rate of return of 8.25% and a constant growth rate of 3.5% Exercise 36. P&G just announced its next annual dividend is 1.50 usd with growth rate = 1.8%. How much will one share be worth 5 years from now if the required return is 15.5%?