1 Time Value of Money #1 For all the problems: - Draw the cash flow diagram - Show the procedure for finding the solution (formulas or financial calculator input) - Underline the solution

Future value of a single cash flow 1.- How much money will you receive after 5 years if you put $40,000 in a savings account, with interest 10% per year ? Present value of a single cash flow

2.- Demi Moore is offered $1 million for selling the copyrights of her life. However, she is convinced that her popularity will grow even further and that she can expect to receive $2 million in 5 years from now. With an annual interest rate of 14%: a) what is the present value of the $2 million in 5 years from now? b) should she sell the rights now or wait ?

3.- A 15 year old boy wants to be a millionaire when he is 50 years old. How much money should he put in the bank now, if the annual interest rate is 8% ? What should he put in if the interest rate is 12% annual ? The concept of equivalence

4.- For which annual interest rate is $1,000 1 year ago the same as $2,500 in 6 years from now ?

5.- For which annual interest rate is $1,500 now the same as $2,200 in 4 years from now ? Future value of independent cash flows

6.- The Old-Students-from-Tec Club is 65 years old now. They plan to celebrate the 75th anniversary really big: the party is calculated to cost $25 million. To raise money they will raise money in this years reunion and in the reunion five years from now. The expectation is that this year they will get

$4 million, in 5 years they will get $8 million. If there is not enough money raised, the members will pay the rest at the time of the party (in 10 years from now). The money will be put in a bank account immediately, for an interest rate of 13% per year. Is there enough money for the party, or should the members pay additional money to reach the $25 million ? If so: how much ? Annuities: finding A when P is given

7.- 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

8.- 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

9.- 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

10.- 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?