Introduction to Corporate Finance

3: The Time Value of Money

P3-9 For the following questions, assume an ordinary annuity of $1,000 and a required return of 12%.

a What is the future value of a 10-year ordinary annuity?

b If you earned an additional year’s worth of interest on this annuity, what would be the future value?

c What is the future value of a 10-year annuity due?

d What is the relationship between your answers in parts (b) and (c)? Explain.

P3-10 Kim Edwards and Hiroshi Suzuki are both newly minted 30-year-old MBAs. Kim plans to invest
$1,000 per month into her defined contribution superannuation plan beginning next month.
Hiroshi intends to invest $2,000 per month in his superannuation plan, but he does not plan to
begin investing until 10 years after Kim begins investing. Both Kim and Hiroshi will retire at age 67,
and their superannuation plans average a 12% annual return. Who will have more superannuation
funds available at retirement?

P3-11 To supplement your planned retirement, you estimate that you need to accumulate $220,000 in
42 years. You plan to make equal annual end-of-year deposits into an account paying 8% annual
interest.
a How large must the annual deposits be to create the $220,000 fund in 42 years?
b If you can afford to deposit only $600 per year into the account, how much will you have
accumulated by the end of the 42nd year?

PRESENT VALUE OF CASH FLOW STREAMS

P3-12 Given the mixed streams of cash flows shown in the following table, answer parts (a) and (b) below.

Cash flow stream

Year A B

1 $ 50,000 $ 10,000

2 40,000 20,000

3 30,000 30,000

4 20,000 40,000

5 10,000 50,000

Totals $150,000 $150,000

a Find the present value of each stream, using a 15% per year discount rate.

b Compare the calculated present values, and discuss them in light of the fact that the

undiscounted total cash flows amount to $150,000 in each case.

P3-13 As part of your personal budgeting process, you have determined that at the end of each of the
next five years you will incur significant maintenance expenses on your home. You’d like to cover
these expenses by depositing a lump sum in an account today that earns 8% per year. You will
gradually draw down this account each year as maintenance bills come due.

End of year Expense

1 $ 5,000

2 4,000

3 6,000

4 10,000

5 3,000

a How much money must you deposit today to cover all of the expenses?

b What effect does an increase in the interest rate have on the amount calculated in part (a)? Explain.

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