Chapter 15 Capital-Budgeting Decision
Methods of Financing
15.1
(a) Equity Financing:
Let X denote the number of shares to be sold. The total flotation cost would be
15.2
(a) Equal repayment of the principal:
n
Repayment
Loan Balance
Interest
Principal
0
$500,000
1
$45,000
$83,333
$416,667
2
$37,500
$83,333
$333,333
3
$30,000
$83,333
$250,000
4
$22,500
$83,333
$166,667
5
$15,000
$83,333
6
$83,333
(b) Equal repayment of the interest:
n
Repayment
Loan Balance
Interest
Principal
0
$500,000
1
$45,000
$0
$500,000
2
$45,000
$500,000
3
$45,000
$0
$500,000
4
$45,000
$500,000
5
$45,000
$500,000
6
$45,000
(c) Equal annual installment:
$500,000( / ,9%,6) $111, 460A A P= =
n
Repayment
Loan Balance
Interest
Principal
0
$500,000
1
$45,000
$66,460
$433,540
15.3
(a) Equity Financing
Income Statement
0
1
2
3
4
Revenue
$100,000
$100,000
$100,000
$100,000
Expenses
Cash Flow Statement
Cash from operation
$104,660
2
$39,019
$72,441
$361,099
3
$32,499
$78,961
$282,138
4
$25,392
$86,068
$196,070
5
$17,646
$93,814
$102,257
6
(b) Debt Financing
Income Statement (Bank A)
0
1
2
3
4
Revenue
$100,000
$100,000
$100,000
$100,000
Expenses
Cash Flow Statement
Cash from operation
Net Income
$26,000
$13,650
$33,540
$54,262
Depreciation
$40,000
$64,000
$38,400
$11,520
Income Statement (Bank B)
0
1
2
3
4
Revenue
$100,000
$100,000
$100,000
$100,000
Expenses
Depreciation
$40,000
$64,000
$38,400
$11,520
$40,000
$19,276
$48,479
$79,323
$14,000
$16,968
$27,763
$12,529
$31,511
$51,560
$54,262
Cash Flow Statement
Cash from operation
Net Income
$26,000
$12,529
$31,511
$51,560
Depreciation
$40,000
$64,000
$38,400
$11,520
$30,000
(c) Best course of action: Adopt Bank B’s repayment plan
Interest
$20,000
$15,000
$10,000
$26,000
$13,650
$33,540
$54,262
15.4
(a) The total flotation costs to raise $65 million:
•Common stock:
amount of common stock ($65, 000,000)(0.45)
$29, 250, 000
=
=
(b) Number of shares or (bonds) to be sold to raise $65 million:
•Common stock:
(1 0.046)($32) $29, 250, 000
958,137 shares
S
S
X
X
−=
=
(c) Cash requirement to meet financing costs:
Cost of Capital
15.5 After-tax cost of debt:
(a)
(0.12)(1 0.25) 0.09 or 9%−=
15.6 In the absence of a bond maturity date, we need to assume that the 13% yield
to maturity represents the before-tax cost of debt after considering the flotation
cost as well as bond discounting. Let
13%
b
k=
. We compute the after-tax cost
of debt as follows:
15.8
(a) Flotation costs in percentage:
15.9
15.10
Given:
k
e
=0.30
(a)
i
e
=(55 / 55)(0.30) =0.3
i
d
=(1−0.40)[(10 / 30)(0.14) +(20 / 30)(0.12)] =0.076
k=(0.076)(0.30) +(0.3)(0.70) =0.2328
(a) Net equity flow method:
PW(18%)=$19,425 >0
, accept the project.
Income Statement
0
1
2
3
4
5
Revenue
$70,000
$70,000
$70,000
$70,000
$70,000
Expenses
O&M
$20,000
$20,000
$20,000
$20,000
$20,000
(b) Cost of capital method:
PW(13.87%)=$29,189 >0
, accept the project.
Income Statement
0
1
2
3
4
5
Revenue
$70,000
$70,000
$70,000
$70,000
$70,000
Expenses
O&M
$20,000
$20,000
$20,000
$20,000
$20,000
Depreciation
$17,148
$29,388
$20,988
$15,000
$5,352
.
Taxable Income
$32,852
$20,612
$29,012
$35,000
$44,648
Income Taxes
$11,827
$7,420
$10,444
$12,600
Net Income
$21,025
$13,192
$18,568
$22,400
28,575
Cash from operation
Net Income
$21,025
$13,192
$18,568
$22,400
$28,575
Depreciation
$17,148
$29,388
$20,988
$15,000
Investment/Salvage
($120,000)
$30,000
Gains Tax
$765
Net cash flow
($120,000)
$38,173
$42,580
$39,556
$37,400
$64,692
Depreciation
$17,148
$29,388
$20,988
$15,000
Interest
Taxable Income
$27,092
$15,759
$25,174
$32,299
$43,221
Income Taxes
$11,628
$15,560
Net Income
Cash from operation
Net Income
Depreciation
$29,388
$20,988
$15,000
Investment/Salvage
$30,000
Gains Tax
Loan Repayment
Net cash flow
$26,931
$31,012
$17,621
$25,056
PW(18%) =
15.12
(a) Net equity flow method:
Income Statement
0
1
2
3
4
5
Revenue
$45,000
$45,000
$45,000
$45,000
$45,000
Expenses
Depreciation
$20,000
$32,000
$19,200
$11,520
$5,760
Interest (15%)
$9,000
$7,665
$6,130
$4,365
$2,335
(b) Cost of capital method:
ie=20%, id=(0.15)(1 −0.30) =0.105
k=(0.6)(0.105) +(0.4)(0.2) =14.3%
Income Statement
0
1
2
3
4
5
Revenue
$45,000
$45,000
$45,000
$45,000
$45,000
Expenses
Depreciation
$25,000
$13,000
$25,800
$33,480
$39,240
$17,500
$18,060
$23,436
$27,468
Cash Flow Statement
Cash from operation
Net Income
Depreciation
$30,000
$16,000
$5,335
$19,670
$29,115
$36,905
$4,800
$1,600
$5,901
$8,735
$11,072
$11,200
$3,734
$13,769
$20,381
$25,834
Cash Flow Statement
Cash from operation
$30,000
$60,000
$22,301
$25,501
$21,200
$18,366
$40,485
15.13
(a) Using
15%
e
i=
:
Machine A
Income Statement
0
1
2
3
4
5
6
Revenue
$20,000
$20,000
$20,000
$20,000
$20,000
$20,000
Cash Flow Statement
Cash from operation
Net Income
$1,820
($1,199)
$2,240
$4,359
$4,494
$6,140
Depreciation
$8,000
$12,800
$7,680
$4,608
$4,608
$2,304
$12,000
($1,555)
($1,711)
($1,882)
($2,070)
($2,277)
($2,505)
Machine B
Income Statement
0
1
2
3
4
5
6
Revenue
$28,000
$28,000
$28,000
$28,000
$28,000
$28,000
O&M
$10,000
$10,000
$10,000
$10,000
$10,000
$10,000
Interest (10%)
$1,800
$1,567
$1,310
$1,028
$2,730
($1,798)
$3,360
$6,539
$6,741
$9,209
Cash Flow Statement
Cash from operation
Net Income
$2,730
($1,798)
$3,360
$6,539
$6,741
$9,209
Depreciation
$12,000
$19,200
$11,520
$6,912
$6,912
$3,456
$8,000
$12,397
$14,835
$12,058
$10,346
$10,237
$14,108
O&M
$8,000
$8,000
$8,000
$8,000
$8,000
$8,000
Interest(10%)
$1,200
$1,044
$2,800
($1,844)
$3,447
$6,707
$6,914
$9,446
$1,820
($1,199)
$2,240
$4,359
$4,494
$6,140
(b) Using
12.45%k=
:
Machine A
Income Statement
0
1
2
3
4
5
6
Revenue
$20,000
$20,000
$20,000
$20,000
$20,000
$20,000
Expenses
Cash Flow Statement
Cash from operation
Net Income
$2,600
($520)
$2,808
$4,805
$4,805
$6,302
$12,800
Machine B
Income Statement
0
1
2
3
4
5
6
Revenue
$28,000
$28,000
$28,000
$28,000
$28,000
$28,000
Expenses
O&M
Depreciation
$6,912
$6,912
$3,456
$6,000
$6,480
$2,100
($420)
$2,268
$3,881
$3,881
$5,090
Cash Flow Statement
Cash from operation
Net Income
$3,900
($780)
$4,212
$7,207
$7,207
$9,454
$12,000
$19,200
$11,520
$8,000
∴ Machine B should still be better.
(c) Both methods provide the same decision.
O&M
$8,000
$8,000
$8,000
$8,000
$8,000
$8,000
Depreciation
$8,000
$7,680
$4,608
$4,608
$2,304
$4,000
($800)
$4,320
$7,392
$7,392
$9,696
$1,400
($280)
$1,512
$2,587
$2,587
$3,394
11 | Page
Capital Budgeting
15.14 Based on the investment opportunity curve below, the firm’s optimal capital
budget would be $177 million, if there is no restriction on the firm’s debt limit.
However, with a budget limit of $100 million, the firm may select projects 5
90%
5
80%
3
15.15
(a)
Rate of Return
JProjects Required.Investment
1 0 5$.. ..
2 A 100.00$.. ..
3 C 100.00$.. ..
4 D 300.00$.. ..
5 F 150.00$.. ..
6AC 200.00$.. ..
(b) Optimal capital budget = $750, select ALT 20
The IRR for each project exceeds its cost of capital k, all projects
should be considered in the budget.
0!
1!
2!
3!
IRR!
k”
A!
)100!
40!
60!
40!
19%!
14.5%!
B!
)200!
150!
100!
30!
25%!
16.0%!
C!
)100!
30!
80!
60!
29%!
14.5%!
D!
)300!
200!
120!
150!
28%!
16.0%!
E!
)200!
100!
100!
150!
31%!
16.0%!
)150!
50!
70!
80!
15%!
14.5%!
Compute the net present worth for each alternative at its cost of
capital and select the alternative with the largest net present value.
The optimal capital budget is found at $750 with ALT 20.
0 1 2 3 IRR k
PW(k)
1 0 0 0 0 0
2+100 40 60 40 19% 14.5% 7.35$44444444
3+100 30 80 60 29% 14.5% 27.19$444444
4+300 200 120 150 28% 16.0% 57.69$444444
5+150 50 70 80 15% 14.5% 0.35$44444444
6+200 70 140 100 24% 16.0% 28.45$444444
7+400 240 180 190 26% 17.5% 51.75$444444
(c)
Select ALT 20
Note: The same selection would be found by applying the incremental IRR
analysis as illustrated in Example 15.12.
Short Case Studies
ST 15.1
(a)
•Total market value = Present value of its expected future net cash flows +
the value of current assets (5M)
(b)
Income before tax = $3.5M
Earnings = $2.1M
Income before tax (1-tax rate) = Earnings
Tax rate = 40%
(c)
•The case when the financing source is known, we use interest rate of equity (
ie
) as MARR, MARR =
ie
•The case when the financing source is unknown, we use k (WACC) as MARR,
MARR= k
d e
d e
d e d e
c c
k i i
c c c c
= +
+ +
(d)
The current stock price*(shares outstanding) = $18(1M)
PW of increasing profit after installing and operating the new machine =
$7,021K
Finally, the most likely estimate for Games’ stock price may be $ $18.2.
Note) The income statement and cash flows of most likely case are like below:
Income statement
(1000US$)
Inflation
012
10%
$48,400 $53,240
10%
$38,720 $31,944
Depreciation
$1,445 $1,061
Cash flow statement
(1000US$)
012
Operating activities
Net income $4,701 $11,901
Depreciation $1,445 $1,061
Investment activities
Expense
Revenue
(e) Not provided
ST 15.2
(a) There are 58 alternatives.
(b) Only 10 alternatives are feasible.
j
Projects
j
Projects
1
1
6
1, 7
2
2
7
4
9
2, 6
5
2, 7
ST 15.3
(a) Select A and C with FW(10%) = $4,894. Since there are $500 left over after
selecting A and C, this left-over is lent out at 10% for 3 periods. Therefore, the
total amount available for lending at the end of period 3 is calculated as
follows:
ST 15.4
(a) The debt repayment schedule for the loan from the equipment manufacturer:
n
Loan Repayment
Loan Balance
Interest
Principal
0
$2,000,000
1
$200,000
$125,491
$1,874,509
2
$187,451
$138,040
$1,736,469
3
$173,647
$151,844
$1,584,625
4
$158,463
$167,028
$1,417,597
5
$141,760
$183,731
$1,233,866
6
$123,387
$202,104
$1,031,762
7
$103,176
$222,315
$809,447
8
$244,546
$564,901
9
$269,001
$295,901
$295,901
(b) The flotation costs and the number of common stocks to raise $8,500,000:
number of shares =
$8,500,000 205,537 shares
(1 0.081)($45)
=
−
(c) The floatation costs and the number of $1,000 bonds to raise $10.5 million:
ST 15.5 (a) The net cash flow the cogeneration project with bond financing
0 1 2 3 4 5 6 7 8 9 10 11 12
Revenue
$6,120,000 $6,120,000 $6,120,000 $6,120,000 $6,120,000 $6,120,000 $6,120,000 $6,120,000 $6,120,000 $6,120,000 $6,120,000 $6,120,000
$480,000 $480,000 $480,000 $480,000 $480,000 $480,000 $480,000 $480,000 $480,000 $480,000 $480,000 $480,000
Expenses
O&M $500,000 $500,000 $500,000 $500,000 $500,000 $500,000 $500,000 $500,000 $500,000 $500,000 $500,000 $500,000
.
$2,143,230 $1,633,230 $292,230 $1,915,630 $1,992,630 $591,430 $2,152,730 $2,743,230 $1,243,230 $2,743,230 $2,743,230 $2,743,230
Net Income $1,371,667 $1,045,267 $187,027 $1,226,003 $1,275,283 $378,515 $1,377,747 $1,755,667 $795,667 $1,755,667 $1,755,667 $1,755,667
$1,371,667 $1,045,267 $187,027 $1,226,003 $1,275,283 $378,515 $1,377,747 $1,755,667 $795,667 $1,755,667 $1,755,667 $1,755,667
Unit $500,000 $950,000 $855,000 $770,000 $693,000 $623,000 $590,500 $590,501 $590,502 $590,503 $590,504 $295,000
Depreciation
Taxable Income
Cash Flow Statement
Cash from operation
Net Income
Income State ment
Electricity Bill
Excess power
(b) The maximum annual lease amount that ACC is willing to pay is $1,183,771. (By Excel Goal Seek)
Cash from operation
0 1 2 3 4 5 6 7 8 9 10 11 12
Revenue
$6,120,000 $6,120,000 $6,120,000 $6,120,000 $6,120,000 $6,120,000 $6,120,000 $6,120,000 $6,120,000 $6,120,000 $6,120,000 $6,120,000
$480,000 $480,000 $480,000 $480,000 $480,000 $480,000 $480,000 $480,000 $480,000 $480,000 $480,000 $480,000
$1,183,771 $1,183,771 $1,183,771 $1,183,771 $1,183,771 $1,183,771 $1,183,771 $1,183,771 $1,183,771 $1,183,771 $1,183,771 $1,183,771
.
$2,629,829 $2,629,829 $2,629,829 $2,629,829 $2,629,829 $2,629,829 $2,629,829 $2,629,829 $2,629,829 $2,629,829 $2,629,829 $2,629,829
$946,738 $946,738 $946,738 $946,738 $946,738 $946,738 $946,738 $946,738 $946,738 $946,738 $946,738 $946,738
Net Income $1,683,090 $1,683,090 $1,683,090 $1,683,090 $1,683,090 $1,683,090 $1,683,090 $1,683,090 $1,683,090 $1,683,090 $1,683,090 $1,683,090
Income Taxes (36%)
Income Statement
Electricity Bill
Excess power
Lease
Taxable Income