978-0133546408 Chapter 5 Solution Manual Part 2

P5-14. Time value: Present value of a lump sum

LG 2; Intermediate

N  6, I  8%, FV  $100

Solve for PV  $63.02

P5-15. Personal finance: Time value and discount rates

LG 2; Intermediate

(3) N  10, I  12%, FV  $1,000,000

b. (1) N  15, I  6%, FV  $1,000,000 (2)

(3) N  15, I  12%, FV  $1,000,000

c. As the discount rate increases, the present value decreases. This decrease is due to the higher

opportunity cost associated with the higher rate. Also, the longer the time until the lottery payment is

P5-16. Personal finance: Time value comparisons of single amounts

LG 2; Intermediate

a. AN  3, I  11%, FV  $28,500 BN  9, I  11%, FV  $54,000

CN  20, I  11%, FV  $160,000

P5-17. Personal finance: Cash flow investment decision

LG 2; Intermediate

AN  5, I  10%, FV  $30,000 BN  20, I  10%, FV  $3,000

CN  10, I  10%, FV  $10,000 DN  40, I  10%, FV  $15,000

Purchase Do Not Purchase

2 Gitman/Zutter Principles of Managerial Finance, Brief, Seventh Edition

P5-18. Calculating deposit needed

LG 2; Challenge

Step 1: Determination of future value of initial investment

Step 2: Determination of future value of second investment

Step 3: Calculation of initial investment

P5-19. Future value of an annuity

LG 3; Intermediate

a. Future value of an ordinary annuity vs. annuity due

(1) Ordinary Annuity (2) Annuity Due

b. The annuity due results in a greater future value in each case. By depositing the payment at the

P5-20. Present value of an annuity

LG 3; Intermediate

a. Present value of an ordinary annuity vs. annuity due

(1) Ordinary Annuity (2) Annuity Due

b. The annuity due results in a greater present value in each case. By depositing the payment at the

Chapter 3: Financial Statements and Ratio Analysis 3

P5-21. Personal finance: Time value—annuities

LG 3; Challenge

a. Annuity C (Ordinary) Annuity D (Due)

b. (1) At the end of year 10, at a rate of 10%, Annuity C has a greater value ($39,843.56 vs.

c. Annuity C (Ordinary) Annuity D (Due)

(1) N  10, I  10%, PMT  $2,500 N  10, I  10%, PMT  $2,200

(2) N  10, I  20%, PMT  $2,500 N  10, I  20%, PMT  $2,200

e. Annuity C, with an annual payment of $2,500 made at the end of the year, has a higher present value at

P5-22. Personal finance: Retirement planning

LG 3; Challenge

a. N  40, I  10%, PMT  $2,000 b. N  30, I  10%, PMT  $2,000

c. By delaying the deposits by 10 years the total opportunity cost is $556,197. This difference is due to

d. Annuity Due:

4 Gitman/Zutter Principles of Managerial Finance, Brief, Seventh Edition

Annuity Due Adjustment: $328,988.05  1.10  $361,886.85

Both deposits increased due to the extra year of compounding from the beginning-of-year deposits

P5-23. Personal finance: Value of a retirement annuity

LG 3; Intermediate

P5-24. Personal finance: Funding your retirement

LG 2, 3; Challenge

a. N  30, I  11%, PMT  $20,000 b. N  20, I  9%, FV  $173.875.85

c. Both values would be lower. In other words, a smaller sum would be needed in 20 years for the

d. N  30, I  10%, PMT  $20,000 b. N  20, I  10%, FV  $188,538.29

More money will be required to support the $20,000 annuity in retirement, because the initial amount

P5-25. Personal finance: Value of an annuity vs. a single amount

LG 2, 3; Intermediate

a. N  25, I  5%, PMT  $40,000

Solve for PV  $563,757.78

b. N  25, I  7%, PMT  $40,000

Solve for PV  $466,143.33

c. View this problem as an investment of $500,000 to get a 25-year annuity of $40,000. The discount

P5-26. Perpetuities

LG 3; Basic

Case Equation Value

Chapter 3: Financial Statements and Ratio Analysis 5

P5-27. Personal finance: Creating an endowment

LG 3; Intermediate

a. 6% interest rate

b. 9% percent interest rate

P5-28. Value of a mixed stream

LG 4; Challenge

a.

Cash Flow

Stream Year

Number of Years

to Compound Cash flow

Interest

Rate Future Value

B1 4 $30,000  $ 47,205.58

C1 3 $ 1,200  $1,685.91

b. If payments are made at the beginning of each period the present value of each of the end-of-period

cash flow streams will be multiplied by (1  i) to get the present value of the beginning- of-period cash

flows.

P5-29. Personal finance: Value of a single amount vs. a mixed stream

LG 4; Intermediate

Lump-Sum Deposit

6 Gitman/Zutter Principles of Managerial Finance, Brief, Seventh Edition

Mixed Stream of Payments

Beginning of

Year

Number of Years

to Compound Cash Flow Interest Rate Future Value

P5-30. Value of mixed streams

LG 4; Basic

Project A

Project B

Project C

P5-31. Present value—Mixed streams

LG 4; Intermediate

a. Stream A

b. Cash flow stream A, with a present value of $109,856, is higher than cash flow stream B’s present

P5-32. Value of a mixed stream

LG 1, 4; Intermediate

a.

Chapter 3: Financial Statements and Ratio Analysis 7

P5-33. Personal finance: Funding budget shortfalls

LG 4; Intermediate

a. CF1  $5,000, CF2  $4,000, CF3  $6,000, CF4  $10,000, CF5  $3,000

b. An increase in the earnings rate would reduce the amount calculated in part a. The higher rate would

P5-34. Relationship between future value and present value-mixed stream

LG 4; Intermediate

a. CF1  $800, CF2  $900, CF3  $1,000, CF4  $1,500, CF5  $2,000

P5-35. Relationship between future value and present value-mixed stream

LG 4; Intermediate

Step 1: Calculation of present value of known cash flows

Year CFtPV @ 4%

Step 2: Identify difference between total amount and sum in Step 1.

8 Gitman/Zutter Principles of Managerial Finance, Brief, Seventh Edition

P5-36. Changing compounding frequency

LG 5; Intermediate

a. Compounding frequency

(1) Annual Semiannual

(2) Annual Semiannual

(3) AnnualSemiannual

b. Effective interest rate: ieff  (1  r/m)m – 1

(1) Annual Semiannual

Quarterly

(2) Annual Semiannual

Quarterly

Chapter 3: Financial Statements and Ratio Analysis 9

(3) Annual Semiannual

Quarterly