# Continuous compounding, FV, multiple cash flows, stock valuation

10. Continuous Compounding Compute the future value of $1,000 continuously compounded for

a. 5 years at a stated annual interest rate of 12 percent.

b. 3 years at a stated annual interest rate of 10 percent.

c. 10 years at a stated annual interest rate of 5 percent.

d. 8 years at a stated annual interest rate of 7 percent.

67. Future Value and Multiple Cash Flows An insurance company is offering a new policy to its customers. Typically the policy is bought by a parent or grandparent for a child at the child's birth. The details of the policy are as follows: The purchaser (say, the parent) makes the following six payments to the insurance company:

First birthday: $750

Second birthday: $750

Third birthday: $850

Fourth birthday: $850

Fifth birthday: $950

Sixth birthday: $950

After the child's sixth birthday, no more payments are made. When the child reaches age 65, he or she receives $250,000. If the relevant interest rate is 11 percent for the first six years and 7 percent for all subsequent years, is the policy worth buying?

Chapter 5

7. Stock Valuation Suppose you know that a company's stock currently sells for $70 per share and the required return on the stock is 12 percent. You also know that the total return on the stock is evenly divided between a capital gains yield and a dividend yield. If it's the company's policy to always maintain a constant growth rate in its dividends, what is the current dividend per share?

(Ross, Stephen A.. Corporate Finance, 8th Edition. Irwin/McGraw-Hill, 112006. 5.11).

1. Discuss the time value of money analysis, the process of compounding, discounting, and amortization of cash flows; and various applications of the concept of time value of money on financial management analysis and corporate finance.

2. Discuss bond valuation, stock valuation, the constant growth model and the dividend growth model.

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#### Solution Preview

10. Continuous Compounding Compute the future value of $1,000 continuously compounded for

a. 5 years at a stated annual interest rate of 12 percent.

b. 3 years at a stated annual interest rate of 10 percent.

c. 10 years at a stated annual interest rate of 5 percent.

d. 8 years at a stated annual interest rate of 7 percent.

A B C D E

=e^(C*B) =(A*D)

Present value Years Rate Future value interest factor Future value

1,000 5 12% 1.82 1,822.12

1,000 3 10% 1.35 1,349.86

1,000 10 5% 1.65 1,648.72

1,000 8 7% 1.75 1,750.67

67. Future Value and Multiple Cash Flows An insurance company is offering a new policy to its customers. Typically the policy is bought by a parent or grandparent for a child at the child's birth. The details of the policy are as follows: The purchaser (say, the parent) makes the following six payments to the insurance company:

First birthday: $750

Second birthday: $750

Third birthday: $850

Fourth birthday: $850

Fifth birthday: $950

Sixth birthday: $950

After the child's sixth birthday, no more payments are ...

#### Solution Summary

A dividend growth model for continuous compounding, FV, multiple cash flows and stock valuation are determined.