Management Essay

2790 words - 12 pages

Chapter 4
Time Value of Money

Solutions to Problems
P4-1.

LG 1: Using a Time Line
Basic
(a), (b), and (c)
Compounding
Future

Value

–$25,000
$3,000
$6,000
$6,000
$10,000
$8,000
$7,000
|—————|—————|——————|——————|—————|——————|—>
0
1
2
3
4
5
6
End of Year

Present
Value

Discounting

(d) Financial managers rely more on present than future value because they typically make
decisions before the start of a project, at time zero, as does the present value calculation.

74

P4-2.

Part 2

Important Financial Concepts

LG 2: Future Value Calculation: FVn = PV × (1 + i)n
Basic
Case
A
B
C
D

P4-3.

FVIF12%,2 periods
FVIF6%,3 periods
...view middle of the document...

28

The PVIF for this 7-year annuity is obtained by summing together the PVIFs of 12% for periods 3 through 9.
This factor can also be calculated by taking the PVIFA12%,7 and multiplying by the PVIF12%,2.

(c) Harte should accept the series of payments offer. The present value of that mixed stream of
payments is greater than the $100,000 immediate payment.
P4-32. LG 5: Funding Budget Shortfalls
Intermediate
(a)
Year

Budget
Shortfall

×

PVIF8%,n

=

1

$5,000

×

0.926

=

$4,630

2

4,000

×

0.857

=

3,428

3

6,000

×

0.794

=

4,764

4

10,000

×

0.735

=

7,350

5

3,000

×

0.681

=

2,043

Present Value

$22,215
Calculator solution:

$22,214.03

A deposit of $22,215 would be needed to fund the shortfall for the pattern shown in the table.
(b) An increase in the earnings rate would reduce the amount calculated in part (a). The higher
rate would lead to a larger interest being earned each year on the investment. The larger
interest amounts will permit a decrease in the initial investment to obtain the same future
value available for covering the shortfall.

Chapter 4

Time Value of Money

P4-33. LG 4: Relationship between Future Value and Present Value-Mixed Stream
Intermediate
(a) Present Value
Year
CF

×

PVIF5%,n

=

Present Value

1

$800

×

0.952

=

$761.60

2

900

×

0.907

=

816.30

3

1,000

×

0.864

=

864.00

4

1,500

×

0.822

=

1,233.00

5

2,000

×

0.784

=

1,568.00
$5,242.90

Calculator Solution:

$5,243.17

(b) The maximum you should pay is $5,242.90.
(c) A higher 7% discount rate will cause the present value of the cash flow stream to be lower
than $5,242.90.
P4-34. LG 5: Changing Compounding Frequency
Intermediate
(1) Compounding Frequency: FVn = PV × FVIFi%/m,n×m
(a) Annual
12 %, 5 years
FV5 = $5,000 × (1.762)
FV5 = $8,810
Calculator solution: $8,811.71

Semiannual
12% ÷ 2 = 6%, 5 × 2 = 10 periods
FV5 = $5,000 × (1.791)
FV5 = $8,955
Calculator solution: $8,954.24

Quarterly
12% ÷ 4 = 3%, 5 × 4 = 20 periods
FV5 = $5,000 (1.806)
FV5 = $9,030
Calculator solution: $9,030.56
(b) Annual
16%, 6 years
FV6 = $5,000 (2.436)
FV6 = $12,180
Calculator solution: $12,181.98
Quarterly
16% ÷ 4 = 4%, 6 × 4 = 24 periods
FV6 = $5,000 (2.563)
FV6 = $12,815
Calculator solution: $12,816.52

Semiannual
16% ÷ 2 = 8%, 6 × 2 = 12 periods
FV6 = $5,000 (2.518)
FV6 = $12,590
Calculator solution: $12,590.85

89

90

Part 2

Important Financial Concepts

(c) Annual
20%, 10 years
FV10 = $5,000 × (6.192)
FV10 = $30,960
Calculator solution: $30,958.68

Semiannual
20% ÷ 2 = 10%, 10 × 2 = 20 periods
FV10 = $5,000 × (6.727)
FV10 = $33,635
Calculator solution: $33,637.50

Quarterly
20% ÷ 4 = 5%, 10 × 4 = 40 periods
FV10 = $5,000 × (7.040)
FV10 = $35,200
Calculator solution: $35,199.94
(2) Effective Interest...

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