For all the problems: Draw the cash flow diagram Show the procedure for finding the solution (formulas or Excel input) Underline the solution Deferred annuity (paragraph 3.11) 1.- A 55 year old employee wants to retire in 5 years from now. Then he wants $40,000 per year, for a period of 25 years. He just inherited $1,000,000. The interest rate is 11% per year. He wants to put in the bank just enough to have his pension arranged. He wants to spend the money that is not necessary (if any) on some trips and parties. How much money (if any) can he spend now? Unequal cash flows (paragraph 3.12) 2.- A company has just developed a new product and the future looks bright. In the first years sales will not be so high, but the management is sure that after three years from now it will take off. The projected (end-of- year) cash flows are: year 1: $1 million year 2: $2 million year 3: $2.5 million year 4 to 10: $6 million (per year) With an interest rate of 14%, what is the Present Value of the projected cash flows ? 3.- A company is using a new machine which generates annual cash flows of $3 million per year (at the end of the year). The machine can be used for another 6 years, then it will be worthless. At the end of the 3rd year replacement of some parts has to take place, which will cost $4 million. The interest rate will be 7% during the next 6 years. a) What is the Present Value of all the cash flows that the machine generates ? b) What is the Future Value ? Annuities: finding A when P is given 4.- A company just bought a new machine for $7 million. They want to pay in parts: in 6 years time, each year an equal amount so that at the end the whole debt will be paid off. The first payment is due one year after the purchase. The selling company demands an interest of 14% annual. What yearly amount does the company pay? Annuities: finding A when F is given 5.- A 55 year old employee wants to buy a yacht to sail around the world when he retires. He has exactly 10 years to get the $100,000 that he needs. What does he have to save per year if the interest rate is 9% per year ? (the first deposit will be made in 1 year from now) Annuities: finding P when A is given 6.- An employee receives a monthly constant salary of $5,000 (which is being paid at the end of each month). He plans to buy a house and wants to pay this completely in cash. Unfortunately he hasn't got enough. Therefore he asks his employer to give him the Present Value of the salary for the next five years. What will he get if the interest rate is 1% monthly ? Annuities: finding F when A is given 7.- A company retains a constant part ($100,000) of its earnings every year, starting exactly one year from now. This money is invested for an interest rate of 15% per year. In ten years, the proceeds will be used to buy new machinery. The new machinery will cost approximately $2 million. Do you think the proceeds will be enough? For all the problems: Draw the cash flow diagram Show the procedure for finding the solution (formulas or Excel input) Underline the solution Deferred annuity (paragraph 3.11) 1.- A 55 year old employee wants to retire in 5 years from now. Then he wants $40,000 per year, for a period of 25 years. He just inherited $1,000,000. The interest rate is 11% per year. He wants to put in the bank just enough to have his pension arranged. He wants to spend the money that is not necessary (if any) on some trips and parties. How much money (if any) can he spend now? Unequal cash flows (paragraph 3.12) 2.- A company has just developed a new product and the future looks bright. In the first years sales will not be so high, but the management is sure that after three years from now it will take off. The projected (end-of- year) cash flows are: year 1: $1 million year 2: $2 million year 3: $2.5 million year 4 to 10: $6 million (per year) With an interest rate of 14%, what is the Present Value of the projected cash flows ? 3.- A company is using a new machine which generates annual cash flows of $3 million per year (at the end of the year). The machine can be used for another 6 years, then it will be worthless. At the end of the 3rd year replacement of some parts has to take place, which will cost $4 million. The interest rate will be 7% during the next 6 years. a) What is the Present Value of all the cash flows that the machine generates ? b) What is the Future Value ? Annuities: finding A when P is given 4.- A company just bought a new machine for $7 million. They want to pay in parts: in 6 years time, each year an equal amount so that at the end the whole debt will be paid off. The first payment is due one year after the purchase. The selling company demands an interest of 14% annual. What yearly amount does the company pay? Annuities: finding A when F is given 5.- A 55 year old employee wants to buy a yacht to sail around the world when he retires. He has exactly 10 years to get the $100,000 that he needs. What does he have to save per year if the interest rate is 9% per year ? (the first deposit will be made in 1 year from now) Annuities: finding P when A is given 6.- An employee receives a monthly constant salary of $5,000 (which is being paid at the end of each month). He plans to buy a house and wants to pay this completely in cash. Unfortunately he hasn't got enough. Therefore he asks his employer to give him the Present Value of the salary for the next five years. What will he get if the interest rate is 1% monthly ? Annuities: finding F when A is given 7.- A company retains a constant part ($100,000) of its earnings every year, starting exactly one year from now. This money is invested for an interest rate of 15% per year. In ten years, the proceeds will be used to buy new machinery. The new machinery will cost approximately $2 million. Do you think the proceeds will be enough