Introduction to Corporate Finance

PART 1: INTRODUCTION

P3-22 Consider the following three investments of equal risk. Which offers the greatest rate of return?

Investment

End of year A B C

0 –$10,000 –$20,000 –$25,000

1 0 9,500 20,000

2 0 9,500 30,000

3 24,600 9,500 –12,600

ADVANCED APPLICATIONS OF TIME VALUE

P3-23 You plan to invest $2,000 in an individual retirement arrangement (IRA) today at a stated interest

rate of 8%, which is expected to apply to all future years.

a How much will you have in the account at the end of 10 years if interest is compounded as follows?

i Annually

ii Semiannually

iii Daily (assume a 365-day year)

iv Continuously

b What is the effective annual rate (EAR) for each compounding period in part (a)?

c How much greater will your IRA account balance be at the end of 10 years if interest is

compounded continuously rather than annually?

d How does the compounding frequency affect the future value and effective annual rate for a

given deposit? Explain in terms of your findings in parts (a)–(c).

P3-24 Binh Tran has shopped around for the best interest rates for his investment of $10,000 over the

next year.

Stated rate Compounding

6.10% Annual

5.90% Semiannual

5.85% Monthly

a Which investment offers Binh the highest effective annual rate of return?

b Assume that Binh wants to invest his money for only six months, and the annual compounded

rate of 6.10% is not available. Which of the remaining opportunities should Binh choose?

P3-25 Tara Cutler is newly married and preparing a surprise gift of a trip to Europe for her husband on

their tenth anniversary. Tara plans to invest $5,000 per year until that anniversary, and to make her

first $5,000 investment on their first anniversary. If she earns an 8% annual rate on her investments,

how much will she have saved for their trip if the interest is compounded in each of the following

ways?

a Annually

b Quarterly

c Monthly

P3-26 Find the present value of a three-year, $20,000 ordinary annuity deposited into an account that

pays 12% annual interest, compounded monthly. Solve for the present value of the annuity in the

following ways:

a as three single cash flows discounted at the stated annual rate of interest

b as three single cash flows discounted at the appropriate effective annual rate of interest

c as a three-year annuity discounted at the effective annual rate of interest.