978-1259277160 Chapter 9 Solution Manual Part 8

9-46. Solution:

PV of college costs five years from today (Part 1)

4

1

1(1 )

1

1(1.10)

$17,000 .10

$17,000 (3.170)

$53,887.71

n

A

i

PV A i

PV

–+

= ´

–

= ´

=

Accumulation of $2,000 per year for 10 years (Part 2)

10

(1 ) 1

(1.10) 1

$2,000 .10

$2,000 (15.937)

$31,874.85

n

A

i

FV A i

FV

+ –

= ´

–

= ´

=

Part 1 minus Part 2

Additional contribution required for next five years

5

(1 ) 1

$22,012.86

(1.10) 1

.10

$22,012.86

6.105

$3,605.65

n

A

n

i

FV A i

FV

Ai

i

A

+ –

= ´

=+ –

=–

=

Calculator Solution:

Present value of college costs

N I/Y PV PMT FV

Answer: $53,887.71

Accumulation based on investing $2,000 per year for 10 years.

N I/Y PV PMT FV

Answer: $31,874.85

N I/Y PV PMT FV

Present value of college costs

Appendix D

A IFA

PV = A × PV (10%, 4 periods)

= $17,000 × 3.170

= $53,890

Accumulation based on investing $2,000 per year for 10 years.

Appendix C

A IFA

FV = A × FV (10%, 10 periods)

= $2,000 × 15.937

= $31,874

Additional funds required five years from now.

Added contribution for the next five years

Appendix C

A IFA

A = FV /FV (10%, 5 periods)

= $22,016/6.105

= $3,606.22

Connect-Only Problem

47. Special consideration of annuities and time periods (LO9-4) Your parents have

accumulated a $120,000 nest egg. They have been planning to use this money to pay college

costs to be incurred by you and your sister, Courtney. However, Courtney has decided to forgo

college and start a nail salon. Your parents are giving Courtney $15,000 to help her get started,

and they have decided to take year-end vacations costing $10,000 per year for the next four

years.

How much money will your parents have at the end of four 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 $26,353 per year, approximately how long will you be able to stay in school based

on these funds? Use 9 percent as the appropriate interest rate throughout this problem. Round all

values to whole numbers.

9.47. Solution:

Funds available after Nail Salon

PV of vacations

4

1

1(1 )

1

1(1.09)

$10,000 .09

$10,000 (3.2397)

$32,397

n

A

i

PV A i

PV

–+

= ´

–

= ´

=

Funds available after vacations

Funds four years later for graduate school

4

(1 )

$72,603 (1.09)

$102, 485

n

FV PV i

FV

= ´ +

= ´

=

Number of years of graduate school

1

1(1 )

1

1(1 )

(1.09)

1.6500

n

A

n

A

n

i

PV A i

PV

i

i A

–+

= ´

–+=

– =-

Funds available after the nail salon

N I/Y PV PMT FV

Less present value of vacation

Funds available four years later for graduate school:

N I/Y PV PMT FV

Answer: $102,485

Number of years of graduate education

N I/Y PV PMT FV

Answer: Three years

of McGraw-Hill Education.

$120,000 Funds available

Funds available after the nail salon

Less present value of vacation

Appendix D

A IFA

PV A PV (9%, 4 periods)

$10,000 3.240 = $32,400

= ´

$105,000

– 32,400

$72,600 Remaining funds for graduate school

Available funds after four years.

Appendix A

IF

FV PV FV (9%, 4 periods)

$72,600 1.412

$102,511 Funds available for starting graduate school

= ´

=

Number of years of graduate education

Appendix D

A

IFA

PV

PV (9%)

A

$102,511 3.890 (rounded)

$26,353

=

= =

COMPREHENSIVE PROBLEM

Medical Research Corporation (Comprehensive time value of money) Dr. Harold Wolf of

Medical Research Corporation (MRC) was thrilled with the response he had received from drug

companies for his latest discovery, a unique electronic stimulator that reduces the pain from

arthritis. The process had yet to pass rigorous Federal Drug Administration (FDA) testing and

was still in the early stages of development, but the interest was intense. He received the three

offers described following this paragraph. (A 10 percent interest rate should be used throughout

this analysis unless otherwise specified.)

Offer I – $1,000,000 now plus $200,000 from year 6 through 15. Also, if the product did over

$100 million in cumulative sales by the end of year 15, he would receive an additional

$3,000,000. Dr. Wolf thought there was a 70 percent probability this would happen.

Offer II – Thirty percent of the buyer’s gross profit on the product for the next four years. The

buyer in this case was Zbay Pharmaceutical. Zbay’s gross profit margin was 60 percent. Sales in

year one were projected to be $2 million and then expected to grow by 40 percent per year.

Offer III – A trust fund would be set up for the next eight years. At the end of that period, Dr.

Wolf would receive the proceeds (and discount them back to the present at 10 percent). The trust

fund called for semiannual payments for the next eight years of $200,000 (a total of $400,000 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 an annuity

due in the tables, add 1 to n (16 + 1) and subtract 1 from the value in the table. Assume the

annual interest rate on this annuity is 10 percent annually (5 percent semiannually). Determine

the present value of the trust fund’s final value. Hint: See page 280for a discussion of calculating

an annuity due.

Required: Find the present value of each of the three offers and indicate which one has the

highest present value.

CP 9-1. Solution:

Medical Research Corporation

Offer I

Year Sales (60% of Sales) of Gross Profit

Appendix B

Year Payment PV Factor PV

Offer III

Future value of an annuity due (Appendix C)

8 years – semiannually

A IFA

FV A FV

$200,000 24.840

$4,968,000 value of trust fund after eight years

= ´

=

Present value of trust fund (Appendix B)

of McGraw-Hill Education.

IF

PV A PV (10%, 8 years)

$4,968,000 .467

$2,320,056 Total value of offer III

 



CP 9-1. (Continued)

Summary