Corporate finance

1. The continuously compounded interest rate is 12%.

a. You invest $1,000 at this rate. What is the investment worth after five years?

b. What is the PV of $5 million to be received in eight years?

c. What is the PV of a continuous stream of cash flows, amounting to $2,000 per year, starting immediately and continuing for 15 years?

2. You are quoted an interest rate of 6% on an investment of $10 million. What is the value of your investment after four years if interest is compounded: a.Annually? b.Monthly? or c.Continuously?

3. If the interest rate is 7%, what is the value of the following three investments?

a. An investment that offers you $100 a year in perpetuity with the payment at the end of each year.

b. A similar investment with the payment at the beginning of each year.

c. A similar investment with the payment spread evenly over each year.

4. Several years ago The Wall Street Journal reported that the winner of the Massachusetts State Lottery prize had the misfortune to be both bankrupt and in prison for fraud. The prize was $9,420,713, to be paid in 19 equal annual installments. (There were 20 installments, but the winner had already received the first payment.) The bankruptcy court judge ruled that the prize should be sold off to the highest bidder and the proceeds used to pay off the creditors.

a. If the interest rate was 8%, how much would you have been prepared to bid for the prize?