Chapter 09: Time Value of Money
9-45. (Continued)
Subtract this value from $200,000 to determine how much you
need to accumulate on the next 14 payments.
$200,000
88,203
$111,797
−
Determine the revised semi-annual payment necessary to
accumulate this sum after 14 periods at 5%.
Appendix C
46. Annuity consideration (LO4) Your younger sister, Brittany, will start college in five
years. She has just informed your parents that she wants to go to Eastern State U., which
will cost $30,000 per year for four years (cost assumed to come at the end of each year).
Anticipating Brittany’s ambitions, your parents started investing $5,000 per year five years
ago and will continue to do so for five more years.
How much more will your parents have to invest each year for the next five years to
have the necessary funds for Brittany’s education? Use 10 percent as the appropriate
interest rate throughout this problem (for discounting or compounding). Round all values to
whole numbers.
9-46. Solution:
Present value of college costs
Appendix D
Chapter 09: Time Value of Money
9-29
A IFA
PV = A × PV (10%, 4 periods)
= $30,000 × 3.170
= $95,100
Accumulation based on investing $5,000 per year for 10 years.
Appendix C
A IFA
FV = A × FV (10%, 10 periods)
= $5,000 × 15.937
= $79,685
Additional funds required 5 years from now when Brittany starts
college.
Additional annual contribution required between now and the
time Brittany starts college in 5 years.
9-46. (Continued)
Appendix C
A IFA
A = FV / FV (10%, 5 periods)
= $15,415 / 6.105
= $2,525
Chapter 09: Time Value of Money
9-30
47. Special consideration of annuities and time periods (LO4) Brittany (from problem 46) is
now 18 years old (five years have passed), and she wants to get married instead of going to
college. Your parents have accumulated the necessary funds for her education.
Instead of her schooling, your parents are paying $10,000 for her current wedding and
plan to take year-end vacations costing $3,000 per year for the next three years.
How much money will your parents have at the end of three years to help you with
graduate school, which you will start then? You plan to work on a master’s and perhaps a
PhD. If graduate school costs $32,600 per year, approximately how long will you be able to
stay in school based on these funds? Use 10 percent as the appropriate interest rate
throughout this problem. (Round all values to whole numbers.
9-47. Solution:
Funds available after the wedding
$95,100 Funding available before the wedding
Less present value of vacation
Appendix D
A IFA
PV A PV (10%, 3 periods)
$3,000 2.487 = $7,461
=
=
$85,100
Chapter 09: Time Value of Money
9-31
9-47. (Continued)
Appendix A
IF
FV PV (10%, 3 periods)
$77,639 1.331
$103,338 Funds available for starting graduate school
=
=
=
Number of years of graduate education
Appendix D
A
IFA
PV
PV (10%)
A
$103,338 3.170 (rounded)
$32,600
=
==
COMPREHENSIVE PROBLEM
Modern Weapons, Inc. (Comprehensive time value of money) Mr. Rambo, President of
Modern Weapons, Inc., was pleased to hear that he had three offers from major defense
companies for his latest missile firing automatic ejector. He will use a discount rate of 12 percent
to evaluate each offer.
Chapter 09: Time Value of Money
Offer I
$500,000 now plus $120,000 from the end of years 6 through 15. Also if the product
goes over $50 million in cumulative sales by the end of year 15, he will receive an
additional $1,500,000. Rambo thought there was a 75 percent probability this would
happen.
Offer II
Twenty-five percent of the buyer’s gross margin for the next four years. The buyer
in this case is Air Defense, Inc. (ADI). Its gross margin is 65 percent. Sales for year
1 are projected to be $1 million and then grow by 40 percent per year. This amount
is paid today and is not discounted.
Offer III
A trust fund would be set up for the next nine years. At the end of that period,
Rambo would receive the proceeds (and discount them back to the present at
12 percent). The trust fund called for semiannual payments for the next nine years of
$80,000 (a total of $160,000 per year). The payments would start immediately. Since
the payments are coming at the beginning of each period instead of the end, this is
an annuity due. To look up the future value of the annuity due in the tables, add 1 to
n (18 + 1) and subtract 1 from the value in the table. Assume the annual interest rate
on this annuity is 12 percent annually (6 percent semiannually). Determine the
present value of the trust fund’s final value.
Required: Find the present value of each of the three offers and then indicate which
one has the highest present value.
CP 9–1. Solution:
Modern Weapons, Inc.
Offer I
$500,000 now plus:
Appendix D
A IFA
PV = A × PV (12%, 10 years)
= $120,000 × 5.650
= $678,000 (present value at the beginning of
year 6, i.e., the end of year 5)
Appendix B
IF
PV FV PV (12%, 5 years)
$678,000 .567 $384,426
=
= =
Chapter 09: Time Value of Money
9-33
Probability of bonus = 75%
Appendix B
IF
PV FV PV (12%, n 15)
$1,125,000 .183 $205,875
= =
= =
Total value of Offer I
$500,000 Payment today
CP 9–1. (Continued)
Offer II
Sales Gross Profit Payment 25%
Year (40% Growth) (65% of Sales) of Gross Profit
1 $1,000,000 $ 650,000 $162,500
2 1,400,000 910,000 227,500
Offer III
Future value of an annuity due (Appendix C)
9 years – semiannually
Chapter 09: Time Value of Money
9-34
N = 18 + 1 = 19
A IFA
FV A FV
$80,000 32.760
$2,620,800 Value of trust fund after 9 years
=
=
=
Present value of trust fund (Appendix B)
IF
PV FV PV (12%, 9 years)
$2,620,800 .361 $946,109
=
= =
CP 9-1. (Continued)
Summary
Value of Offer I $1,090,301
Select Offer II.