Ross et al.: Fundamentals
of Corporate Finance, Sixth
Edition, Alternate EditionIII. Valuation of Future
Cash Flows- Discounted Cash Flow
Valuation
(^226) © The McGraw−Hill
Companies, 2002
- Calculating Present Value of Annuities Congratulations! You’ve just won
the $15 million first prize in the Subscriptions R Us Sweepstakes. Unfortunately,
the sweepstakes will actually give you the $15 million in $375,000 annual in-
stallments over the next 40 years, beginning next year. If your appropriate dis-
count rate is 11 percent per year, how much money did you really win? - Present Value and Multiple Cash Flows What is the present value of $1,000
per year, at a discount rate of 12 percent, if the first payment is received 8 years
from now and the last payment is received 20 years from now? - Variable Interest Rates A 10-year annuity pays $1,500 per month, and pay-
ments are made at the end of each month. If the interest rate is 15 percent com-
pounded monthly for the first four years, and 12 percent compounded monthly
thereafter, what is the present value of the annuity? - Comparing Cash Flow Streams You have your choice of two investment ac-
counts. Investment A is a 10-year annuity that features end-of-month $1,000
payments and has an interest rate of 11.5 percent compounded monthly. Invest-
ment B is an 8 percent continuously compounded lump-sum investment, also
good for 10 years. How much money would you need to invest in B today for it
to be worth as much as Investment A 10 years from now? - Calculating Present Value of a Perpetuity Given an interest rate of 6.5 per-
cent per year, what is the value at date t7 of a perpetual stream of $500 pay-
ments that begin at date t13? - Calculating EAR A local finance company quotes a 13 percent interest rate
on one-year loans. So, if you borrow $20,000, the interest for the year will be
$2,600. Because you must repay a total of $22,600 in one year, the finance com-
pany requires you to pay $22,600/12, or $1,883.33, per month over the next
12 months. Is this a 13 percent loan? What rate would legally have to be quoted?
What is the effective annual rate? - Calculating Future Values If today is Year 0, what is the future value of the
following cash flows five years from now? What is the future value 10 years
from now? Assume a discount rate of 9 percent per year. - Calculating Present Values A 5-year annuity of ten $8,000 semiannual pay-
ments will begin 9 years from now, with the first payment coming 9.5 years
from now. If the discount rate is 14 percent compounded monthly, what is the
value of this annuity five years from now? What is the value three years from
now? What is the current value of the annuity? - Calculating Annuities Due As discussed in the text, an ordinary annuity as-
sumes equal payments at the end of each period over the life of the annuity. An
annuity dueis the same thing except the payments occur at the beginning of each
period instead. Thus, a three-year annual annuity due would have periodic pay-
ment cash flows occurring at Years 0, 1, and 2, whereas a three-year annual or-
dinary annuity would have periodic payment cash flows occurring at Years 1, 2,
and 3.
Year Cash Flow
2 $30,000
3 50,000
5 85,000196 PART THREE Valuation of Future Cash Flows
Intermediate
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