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# Penn State - RUS 100 - Annual Compounding 4 - Study Guide

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Penn State - RUS 100 - Annual Compounding 4 - Study Guide

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Annual Compounding 4.1 Compute the future value of \$1,000 compounded annually for a. 10 years at five percent b. 10 years at seven percent c. 20 years at five percent d. Why is the interest earned in part (c) not twice the amount earned in part (a)? 4.2 Calculate the present value of the following cash flows discounted at 10 percent.   a. \$1,000 received seven years from today. b. \$2,000 received one year from today. c. \$500 received eight years from today.  4.3 Would you rather receive \$1,000 today or \$2,000 in 10 years?  Assume a discount rate of eight
percent.
4.4 The government has issued a bond that will pay \$1,000 in 25 years.  The bond will pay no interim
coupon payments.  What is the present value of the bond if the discount rate is 10 percent?
4.5 A firm has an estimated pension liability of \$1.5 million due 27 years from today.  If the firm can
invest in a risk-free security with an interest rate of eight percent, how much must the firm invest
today to be able to make the \$1.5 million payment?
4.6 You have won the Florida state lottery.  Lottery officials offer you the choice of the following
alternative payouts:
Alternative 1: \$10,000,000 one year from now. Alternative 2: \$20,000,000 five years from now. Which alternative should you choose if the discount rate is: a. 0 percent? b. 10 percent? c. 20 percent? d. What discount rate makes the two alternatives equally attractive to you? 4.7 You are selling your house.  The Smiths have offered you \$115,000.  They will pay you
immediately.  The Joneses have offered you \$150,000, but they cannot pay you until three years
from today.  The interest rate is 10 percent.  Which offer should you choose?
4.8 Suppose you bought a bond that will pay \$1,000 in 20 years.  No intermediate coupon payments
will be made.  If the appropriate interest rate is eight percent,
a. what is the current price of the bond? b. what will the price be 10 years from today? c. what will the price be 15 years from today? Assume the interest rate does not change over the life of the bond.   4.9 Ann Woodhouse wants to invest in raw land.  She expects to own the property for 10 years and to
sell it at the end of the 10
th  year for \$5 million.  There are no other cash flows.  What is the most  she would be willing to pay for the property if the appropriate discount rate is 12 percent?   Copyright 2003, McGraw-Hill.  All rights reserved.
4.10 You have the opportunity to make an investment of \$900,000.  If you make this investment now,
you will receive \$120,000, \$250,000 and \$800,000 one, two and three years from today,
respectively.  The appropriate discount rate for this investment is 12 percent.
a. Should you make the investment? b. What is the net present value (NPV) of this opportunity? c. If the discount rate is 11 percent, should you invest?  Compute the NPV to support your
4.11 You have the opportunity to invest in a machine that costs \$340,000.  The machine generates
revenues of \$100,000 at the end of each year and requires maintenance costs of \$10,000 at the
beginning of each year.  The machine incurs a maintenance cost today because of start-up
expenses.  If the economic life of the machine is five years and the relevant discount rate is 10
percent, should you buy the machine?  What if the relevant discount rate is nine percent?
4.12 Today a firm signed a contract to sell a capital asset for \$90,000.  The firm will receive the
payment five years from today.  The asset costs \$60,000 to produce, payable immediately.
a. If the appropriate discount rate is 10 percent, what is the NPV of the contract? b. At what discount rate will the firm break even on the sale of the asset? 4.13 Your aunt owns an auto dealership.  She promised to pay you \$3,000 for your car when you
graduate one year from now.  However, your roommate offered you \$3,500 for the car now.  The
prevailing interest rate is 12 percent.  If the future value of the benefit from owning the car for one
additional year is \$1,000, should you accept your aunt’s offer?  You are not planning to buy
another car and will not need the car after you graduate.
4.14 You wish to purchase a new convertible 12 years from today.  At that time, the car will cost
\$80,000.  You currently have \$10,000 to invest.  What rate of interest must your investment earn
so that you can pay for the car?
4.15 Suppose you deposit \$1,000 in an account at the end of each of the next four years.  If the account
earns 12 percent annually, how much will be in the account at the end of seven years?
Compounding Periods 4.16 What is the future value three years hence of \$1,000 invested in an account with a stated annual
interest rate of eight percent,
a. compounded annually? b. compounded semiannually? c. compounded monthly? d. compounded continuously? e. Why does the future value increase as the compounding period shortens? 4.17 Compute the future value of \$1,000 continuously compounded for a. five years at a stated annual interest rate of 12 percent.   b. three years at a stated annual interest rate of 10 percent.  c. 10 years at a stated annual interest rate of five percent. d. eight years at a stated annual interest rate of seven percent. 4.18 Calculate the present value of \$5,000 received 12 years from today.  Assume a stated annual
interest rate of 10 percent, compounded quarterly.
Copyright 2003, McGraw-Hill.  All rights reserved.
4.19 Bank America offers a stated annual interest rate of 4.1 percent, compounded quarterly, while
Bank USA offers a stated annual interest rate of 4.05 percent, compounded monthly.  In which
bank should you deposit your money?
Perpetuities and Growing Perpetuities Annual Compounding  4.20 An investor purchasing a British consol is entitled to receive annual payments from the British
government forever.  What is the price of a consol that pays \$120 annually if the next payment
occurs one year from today?  The market interest rate is 15 percent.
4.21 Assuming an interest rate of 10 percent, calculate the present value of the following streams of
yearly payments:
a. \$1,000 per year, forever, with the first payment one year from today. b. \$500 per year, forever, with the first payment two years from today. c.  \$2,420 per year, forever, with the first payment three years from today. 4.22 Given an interest rate of 10 percent per year, what is the value at the end of year 5 of a perpetual
stream of \$120 annual payments starting at the end of year 9?
4.23 Harris, Inc., paid a \$3 dividend yesterday.  If the firm raises its dividend five percent every year
and the appropriate discount rate is 12 percent, what is the price of Harris stock?
4.24 In its most recent corporate report, Williams, Inc., apologized to its stockholders for not paying a
dividend.  The report states that management will pay a \$1 dividend next year.  That dividend will
grow at four percent every year thereafter.  If the discount rate is 10 percent, how much are you
willing to pay for a share of Williams, Inc.?
4.25 Mark Weinstein has been working on an advanced technology in laser eye surgery.  His
technology will be available in the near term.  He anticipates his first annual cash flow from the
technology to be \$200,000, received two years from today.  Subsequent annual cash flows will
grow at five percent, in perpetuity.  What is the present value of the technology if the discount rate
is 10 percent?
4.26 Barrett Pharmaceuticals is considering a drug project that costs \$100,000 today and is expected to
generate end-of-year annual cash flow of \$50,000, forever.  At what discount rate would Barrett be
indifferent between accepting or rejecting the project?
Compounding Periods 4.27 A prestigious investment bank designed a new security that pays a quarterly dividend of \$10 in
perpetuity.  The first dividend occurs one quarter from today.  What is the price of the security if
the stated annual interest rate is 12 percent, compounded quarterly?
4.28 World Transportation, Inc., is expected to initiate its quarterly dividend of \$1 five years from today
and the dividend is expected to remain constant, forever.  What is the price of World
Transportation stock if the stated annual interest rate is 15 percent, compounded quarterly?
Copyright 2003, McGraw-Hill.  All rights reserved.

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