1. Chapter 9 Accounting for Depreciation and Income Taxes
Asset Depreciation
Book Depreciation
Tax Depreciation
How to Determine “Accounting Profit”
Corporate Taxes

2. Depreciation Definition: Loss of value for a fixed asset
Example: You purchased a car worth $15,000 at the beginning of year 2005.
End of Year
Market
Value
Loss of 1 2 3 4 5
$15,000
10,000
8,000
6,000
5,000
4,000
$5,000
2,000
1,000
Depreciation

3. Why Do We Need to Consider Depreciation?
Business Expense: Depreciation is viewed as part of business expenses that reduce taxable income.
Gross Income -Expenses:
(Cost of goods sold)
(Depreciation)
(operating expenses)
Taxable Income
- Income taxes
Net income (profit)

4. Depreciation Concept Economic Depreciation
Purchase Price – Market Value
(Economic loss due to both physical deterioration and technological obsolescence)
Accounting Depreciation
A systematic allocation of cost basis over a period of time.

5. Cost Basis Cost of new hole-punching machine (Invoice price) $62,500
+ Freight
725
+ Installation labor
2,150
+ Site preparation
3,500
Cost basis to use in depreciation calculation
$68,875

6. Asset Depreciation Physical depreciation Economic depreciation
the gradual decrease in
utility in an asset with
use and time
Functional
depreciation
Depreciation
Book
depreciation
Accounting depreciation
The systematic allocation
of an asset’s value in
portions over its
depreciable life—often
used in engineering
economic analysis
Tax
depreciation

7. Matching Concept or in other words,
Allocate costs such that pattern of costs roughly matches pattern of service
or in other words,
A fraction of the cost of the asset is chargeable as an expense in each of the accounting periods in which the asset provides service to the firm, and each charge is meant to be a percentage of the whole cost which “matches” the percentage of the value utilized in the given period.
suggests that accounting depreciation allowance generally reflects to some extent the actual economic depreciation of the asset

8. Factors to Consider in Asset Depreciation
Depreciable life (how long?)
Salvage value (disposal value)
Cost basis (depreciation basis)
Method of depreciation (how?)

10. Depreciation Methods

13. Declining Balance Method
Principle:
A fixed asset as providing its service in a
decreasing fashion
Formula
Annual Depreciation
Book Value
where 0 < a < 2(1/N)
Note: if  is chosen to be the upper bound,  = 2(1/N),
we call it a 200% DB or double declining balance method.

14. Example – Declining Balance Method
Annual Depreciation
Book Value
$10,000
Total depreciation at end of life D1
$8,000
$6,000 D2 B1 n 1 2 3 4 5 Dn
$4,000
2,400
1,440
864
518 Bn
$10,000
6,000
3,600
2,160
1,296
778
$4,000 D3 B2 D4
$2,000 B3 D5 B5 B4 n
α=(1/5)(2)=40%

15. Salvage value must be estimated in the beginning of depreciation analysis.
Previous example: BN=S. What if not?

16. Example DB Switching to SL
Asset: Invoice Price $9,000
Freight
Installation
Depreciation Base $10,000
Salvage Value
Depreciation 200% DB
Depreciable life 5 years
SL Dep. Rate = 1/5
a (DDB rate) = (200%) (SL rate)
= 0.40

17. Case 1: S = 0 (a) Without switching (b) With switching to SL
Depreciation
Book
Value 1 2 3 4 5
10,000(0.4) = 4,000
6,000(0.4) = 2,400
3,600(0.4) = 1,440
2,160(0.4) =
1,296(0.4) =
$6,000
3,600
2,160
1,296
778 N
Book
Depreciation Value 1 2 3 4 5
10,000/5 = 2000 < 4,000 $6,000
6,000/4 = 1,500 < 2,400 3,600
3,600/3 = 1,200 < 1,440 2,160
2,160/2 = 1,080 > ,080
1,080/1 = 1,080 >
Note:Without switching, we haven’t depreciated the entire cost of the asset thus have not taken full advantage of depreciation’s tax deferring benefits.

18. Case 2: S = $2,000
End of Year
Depreciation
Book Value 1
0.4($10,000) = $4,000
$10,000 - $4,000 = $6,000 2
0.4(6,000) = 2,400
6,000 – 2,400 = 3,600 3
0.4(3,600) = 1,440
3,600 –1,440 = 2,160 4
0.4(2,160) = 864 > 160
2,160 – 160 = 2,000 5
2,000 – 0 = 2,000
Note: Tax law does not permit us to depreciate assets below
their salvage values.

19. Units-of-Production Method
Principle
Service units will be consumed in a non
time-phased fashion
Formula
Annual Depreciation
Dn = Service units consumed for year
total service units
(I - S)

20. Example: Pizza Company buys oven for $10000
Estimated life 7 years (500,000 pizzas)
Salvage value: $3000
Depreciation per unit
= ( )/500000=0.014
If pizzas are cooked this year,
depreciation expense for this year is
75000*0.014=1050

21. Depreciation Rates in Turkey

22. After-Tax Cash Flow
Investment decisions are based on net project cash flows (that is, cash flows after taxes).
If project revenues exceed project costs, then the project generates profit or income. Otherwise the project results in a loss.
Any profit generated will be taxed. After tax profit is called net income.

23. After-Tax Cash Flow
Project revenue is the income earned by a business as a result of providing products or services to customers (Note that the cash may be received in a different accounting period).
Project expenses are the cost of doing business to generate the revenues of the specified operating period (Note that the cash may be paid in a different accounting period).
Cost of goods sold (labor, material, inventory, supplies)
Depreciation
Salaries
Operating costs (cost of renting buildings, cost of insurance)
Income taxes

24. Treatment of Depreciation Expenses
The cost of capital assets are part of your business expenses. The accounting treatment of capital expenditures differs from the treatment of operating expenses. That is:
Capital expenditures must be capitalized: they must be systematically allocated as expenses over their depreciable lives. So,
When you acquire a property with productive life extending over several years, you cannot deduct the total costs from profits in the year the asset was purchased. A depreciation allowance is established over the life of the asset.

25. Taxable Income and Income Taxes
Item
Gross Income
Expenses
Cost of goods sold
Depreciation
Operating expenses
Taxable income
Income taxes
Net income

27. Example: Net Income Calculation
A company buys a NC machine for $28000 and uses it for 5 years. The depreciation deduction for the first year is $4000. Net income during the first year?
Item
Amount
Gross income (revenue)
$50,000
Expenses
Cost of goods sold
Depreciation
Operating expenses
20,000
4,000
6,000
Taxable income
Taxes (40%)
8,000
Net income
$12,000

28. Example Cont’d
The inclusion of depreciation ($4000) reflects the true cost of doing business. That expense is meant to match the amount of the total cost of the machine ($28000) that has been used up during the first year.
Inclusion of total cost would lead to dramatic variations in net income. Hence, net income would be a less accurate measure of the company performance.
On the other hand, if this cost is omitted, we would have a “false profit”.

29. Cash Flow vs. Net Income
Certain expenses are not really cash outflows. Example: Depreciation.
Deducted from revenue for tax purposes on a yearly basis, but no cash is paid to anyone, except when the asset was purchased.
Net income:
Net income is an accounting means of measuring a firm’s profitability based on the matching concept. Costs become expenses as they are matched against revenue. The actual timing of cash inflows and outflows are ignored.
Cash flow:
Given the time value of money, it is better
to receive cash now than later, because cash can be invested to earn more money.

30. Allowed depreciation expenses (not cash flow)
Capital Expenditure versus Depreciation Expenses 1 2 3 4 5 6 7 8
Capital expenditure
(actual cash flow)
$28,000 1 2 3 4 7 6 7 8
$1,250
$3,500
$2,500
$2,500
$2,500
$4,000
$4,900
$6,850
Allowed depreciation expenses (not cash flow)

31. Cash Flows are more important (than Net Income) for Project Evaluation
Example: Both companies (A & B) have the same amount of
net income and cash sum over 2 years, but Company A returns
$1 million cash yearly, while Company B returns $2 million
at the end of 2nd year. Company A can invest $1 million in year
1, while Company B has nothing to invest during the same period.
Company A
Company B
Year 1
Net income
Cash flow
$1,000,000
1,000,000
Year 2
2,000,000

32. Example: Cash Flow versus Net Income
Previous example: Assuming all sales are cash and all expenses except depreciation were paid during year one, how much cash would be generated from operations?
Item
Income
Cash Flow
Gross income (revenue)
$50,000
Expenses
Cost of goods sold
Depreciation
Operating expenses
20,000
4,000
6,000
-20,000
-6,000
Taxable income
Taxes (40%)
8,000
-8,000
Net income
$12,000
Net cash flow
$16,000

33. Net income versus net cash flow
Assuming that revenues are received and expenses are paid in cash:
Net cash flows = Net income + noncash expense (i.e., depreciation)
$50,000
Net income
Net
cash flow
$12,000
$40,000
Depreciation
$4,000
Income taxes
$8,000
$30,000
Gross
revenue
$6,000
Operating expenses
$20,000
$10,000
$20,000
Cost of goods sold $0

34. Corporate Taxes (U.S. Corporate Tax Rates)
Taxable income
0-$50,000
$50,001-$75,000
$75,001-$100,000
$100,001-$335,000
$335,001-$10,000,000
$10,000,001-$15,000,000
$15,000,001-$18,333,333
$18,333,334 and Up
Tax rate
15%
25%
34%
39%
35%
38%
Tax computation
$ (D)
$7, (D)
$13, (D)
$22, (D)
$113, (D)
$3,400, (D)
$5,150, (D)
$6,416, (D)
(D) denotes the taxable income in excess of the lower bound of each tax bracket

35. TURKISH INCOME TAXES (GELİR VERGİSİ TARİFESİ)
TL'ye kadar
% 15
TL'nin TL'si için TL, fazlası
% 20
TL'nin TL'si için TL, (ücret gelirlerinde TL'nin TL'si için TL), fazlası
% 27
TL'den fazlasının TL'si için TL, (ücret gelirlerinde TL'den fazlasının TL'si için TL), fazlası
Kurumlar vergisi oranı gelir miktarına bağlı olmaksızın, sabit %20 oranındadır.
% 35

36. Marginal and Effective (Average) Tax Rate for a Taxable Income of $16,000,000
Marginal Tax Rate
Amount of Taxes
Cumulative Taxes
First $50,000
15%
$7,500
Next $25,000
25%
6,250
13,750
34%
8,500
22,250
Next $235,000
39%
91,650
113,900
Next $9,665,000
3,286,100
3,400,000
Next $5,000,000
35%
1,750,000
5,150,000
Remaining $1,000,000
38%
380,000
$5,530,000

37. Example - Corporate Income Taxes
Facts:
Capital expenditure $100,000
(allowed depreciation) $58,000
Gross Sales revenue $1,250,000
Expenses:
Cost of goods sold $840,000
Depreciation $58,000
Leasing warehouse $20,000
Question: Taxable income?

38. Taxable income:
Gross income $1,250,000
- Expenses:
(cost of goods sold) $840,000
(depreciation) $58,000
(leasing expense) $20,000
Taxable income $332,000
Income taxes:
First 15% $7,500
25% $6,250
34% $8,500
39% $90,480
Total taxes $112,730

39. Average tax rate:
Total taxes = $112,730
Taxable income = $332,000
Marginal tax rate:
Tax rate that is applied to the last dollar earned
39%

41. Incremental Income Tax Rate
Before Undertaking Project
After Undertaking Project
The Effect
of Project
Gross revenue
$200,000
$240,000
$40,000
Expenses
130,000
150,000
20,000
Taxable income
$70,000
$90,000
$20,000
Income taxes
$12,500
$18,850
$6,350
Average tax rate % % %
6350/20000=31.75%
This is the rate we should use in evaluating the project in isolation from the rest of the operations

42. Regular income from operation
0.25($5,000/$20,000) ($15,000/$20,000) = 31.75%
Before
After
Incremental
Taxable income
$70,000
$90,000
$20,000
Income taxes
12,500
18,850
6,350
Average tax rate
17.86%
20.94%
Incremental tax rate
31.75%
$20,000 incremental
taxable income due to
undertaking project
Regular income from operation
$5,000
at 25%
$15,000
at 34%
Marginal tax rate
15%
25%
34% $0
$20,000
$40,000
$60,000
$80,000
$100,000

43. Example 1: Consider the following data on an asset:
Purchase cost of the asset: $25,000
Installation Cost: $5000
Useful Life: 4 years
Salvage Value: $1000
Compute the annual depreciation allowances and the resulting book values by using the DDB method switching to SL.

44. Example 2:
Compute the 150% DB depreciation schedule for an asset with the following data:
Cost = 12000
Useful Life = 5 years
Salvage Value = 3000
a)What is the value of alpha?
b)What is the amount of depreciation for the first full year of use?
c)What is the book value of the asset at the end of the fourth year?

45. Example 3:
Quick Printing Company had the following data during tax year one.
Sales revenue: $1,250,000 Labor expenses: 550,000
Material Costs: 150,000 Depreciation Expenses: 30,000
Interest Income on deposits: 10,000 Bond Interest Income: 5,000
Interest Expenses: 12,000 Rental Expenses: 45,000
Proceeds from the sale of old equipment : 23000
(that had a book value of 20,000)
Find the taxable income for the company
What is the marginal and effective(average) tax rate?
What is the net cash flow after tax?

46. Chapter 10 – Cash Flow Analysis General Cost Terms
Manufacturing Costs
Direct materials
Direct labor
Mfg. Overhead
Non-manufacturing Costs
Overhead
Marketing
Administrative

47. Elements of Investment Decision
Identification of Investment Opportunities
Generation of Cash Flows
Measures of Investment Worth
Project Selection
Project Implementation
Project-Control/Post-Audit
Our focus in this chapter is to develop the format of after-tax cash flow statements.

48. Types of Cash Flow Elements in Project Analysis

49. Cash Flows from Operating Activities
Approach 1
Income Statement Approach
Approach 2
Direct Cash Flow Approach
Operating revenues
Cost of goods sold
Depreciation
Operating expenses
Interest expenses
Taxable income
Income taxes
Net income + Depreciation
- Cost of goods sold
- Operating expenses
- Interest expenses
- Income taxes
Cash flow from operation

50. A Typical Format used for Presenting Cash Flow Statement
+ Net income
+Depreciation
Capital investment
+ Proceeds from sales of
depreciable assets
Gains tax
Investments in working
capital
+ Working capital recovery
+ Borrowed funds
Repayment of principal
Net cash flow
Operating
activities
Income statement
Revenues
Expenses
Cost of goods sold
Depreciation
Debt interest
Operating expenses
Taxable income
Income taxes
Net income +
Investing
activities +
Financing
activities

51. Example: When Projects Require only Operating and Investing Activities
Project Nature: Installation of a new computer control system
Financial Data:
Investment: $125,000
Project life: 5 years
Working capital investment: $23,331
Sale value at the 5th year: $50,000
Annual labor savings: $100,000
Annual additional expenses:
Labor: $20,000
Material: $12,000
Overhead: $8,000
Income tax rate: 40%
MARR: 15%

52. Questions (a) Develop the project’s cash flows over its project life.
(b) Is this project justifiable at a MARR of 15%?
(c) What is the internal rate of return of this project?

53. When Projects Require Working Capital Investments
Working capital means the amount carried in cash, accounts receivable, and inventory that is available to meet day-to-day operating needs.
How to treat working capital investments: just like a capital expenditure except that no depreciation is allowed.

54. Allowed Depreciation Amount
(a) Step 1: Depreciation Calculation
Cost Base = $125,000 N
Depreciation Rates
Depreciation Amount
Allowed Depreciation Amount 1
14.29%
$17,863 2
24.49%
$30,613 3
17.49%
$21,863 4
12.49%
$15,613 5
8.93%
$11,150
$5,575 6
8.92% 7 8
4.46%

55. (a) Step 2: Gains (Losses) associated with Asset Disposal
Salvage value = $50,000
Book Value (year 5) = Cost Base – Total Depreciation
= $125,000 - $ 91,525
= $ 33,475
Taxable gains = Salvage Value – Book Value
= $50,000 - $ 33,475
= $16,525
Gains taxes = (Taxable Gains)(Tax Rate)
= $16,525 (0.40)
= $6,610

56. Step 3 – Create an Income Statement1 2 3 4 5
Revenues
$100,000
Expenses:
Labor
20,000
Material
12,000
Overhead
8,000
Depreciation
17,863
30,613
21,863
15,613
5,581
Taxable Income
$42,137
$29,387
$38,137
$44,387
$54,419
Income Taxes (40%)
16,855
11,755
15,255
17,755
21,768
Net Income
$25,282
$17,632
$22,882
$26,632
$32,651

57. Step 4 – Develop a Cash Flow Statement1 2 3 4 5
Operating Activities:
Net Income
$25,282
$17,632
$22,882
$26,632
$32,651
Depreciation
17,863
30,613
21,863
15,613
5,581
Investment Activities:
Investment
(125,000)
Salvage Value
50,000
Gains Tax
(6,610)
Working capital
(23,331)
23,331
Net Cash Flow
($148,331)
$43,145
$48,245
$44,745
$42,245
$104,950

58. Excel
Worksheet

59. Example - Net Cash Flow TableD E F G H I J
Year End
Investment & Salvage Value
Revenue
Labor
Expenses Materials
Overhead
Depreciation
Taxable Income
Income Taxes
Net Cash Flow
-$125,000
-23,331
-$125, ,331 1
$100,000
20,000
12,000
8,000
$17,863
42,137
16,855
$43,145 2
100,000
30,613
29,387
11,755
$48,245 3
21,863
38,137
15,255
$44,745 4
15,613
44,387
17,755
$42,245 5
50,000*
23,331
5,581
54,419 16,525
21,678 6,613
$38,232 43,387
*Salvage value
Note that
H = C-D-E-F-G
I = 0.4 * H
J= B+C-D-E-F-I
Information required to
calculate the income taxes

60. Cash Flow Diagram including Working Capital
$23,331
Working capital
recovery
$44,745
$48,245
$81,619
$43,145
$42,245 1 2 3 4 5
$125,000 Investment in
physical assets
$23,331
$23,331
Investment in
working capital 1 2 3 4 5
Years
$23,331
Working capital recovery cycles

61. Question (b): Is this investment justifiable at a MARR of 15%?
PW(15%) = -$148, $43,145(P/F, 15%, 1) $104,950 (P/F, 15%, 5)
= $31,420 > 0
Yes, Accept the Project !
$104,950
$48,245
$44,745
$42,245
$43,145 1 2 3 4 5
Years
$148,331

63. When Projects are Financed with Borrowed Funds
Key issue: Interest payment is a tax-deductible expense.
What Needs to Be Done: Once loan repayment schedule is known, separate the interest payments from the annual installments.
What about Principal Payment? As the amount of borrowing is NOT viewed as income to the borrower, the repayment of principal is NOT viewed as expenses either– NO tax effect.

64. Loan Repayment Schedule (Example 9.2)
Amount financed: $62,500, or 50% of total capital expenditure
Financing rate: 10% per year
Annual installment: $16,487 or, A = $62,500(A/P, 10%, 5)
End of
Year
Beginning
Balance
Interest Payment
Principal Payment
Ending 1
$62,500
$6,250
$10,237
$52,263 2
52,263
5,226
11,261
41,002 3
4,100
12,387
28,615 4
2,861
13,626
14,989 5
1,499
14,988
$16,487

65. Table
Additional
entries related
to debt financing

66. When Projects Result in Negative Taxable Income
Handling Project Loss
Negative taxable income (project loss) means you can reduce your taxable income from regular business operation by the amount of loss, which results in a tax savings.
Regular Business
Project
Combined Operation
Taxable income
Income taxes (35%)
$100M
$35M
(10M) ?
$90M
$31.5M
Tax savings
Tax Savings = $35M - $31.5M
= $3.5M
Or (10M)(0.35) = -$3.5M

67. Effects of Inflation on Project Cash Flows
Item
Effects of Inflation
Depreciation expense
Depreciation expense is charged to taxable income in dollars of declining values; taxable income is overstated, resulting in higher taxes
Note: Depreciation expenses are based on historical costs and
always expressed in actual dollars

68. Item
Effects of Inflation
Salvage value
Inflated salvage value combined with book values based on historical costs results in higher taxable gains.

69. Item
Effects of Inflation
Loan repayments
Borrowers repay historical loan amounts with dollars of decreased purchasing power, reducing the debt-financing cost.

70. Item
Effects of Inflation
Working capital requirement
Known as working capital drain, the cost of working capital increases in an inflationary environment.

71. PW(20.75%)=23441>0 (compare with 31420 without inflation)
20.75%= (0.15)(0.05)

72. ROR based on actual dollars: 22.2%
22.2%>20.75% justifiable project
Real (inflation-free) ROR:
16.38%>15% justifiable project

73. Example: Applying Specific Inflation Rates

74. Cost of Capital – What is it?
Cost of capital is the risk-adjusted discount rate (k) to be used in computing a project’s NPV.
Used for selection of an appropriate MARR

75. Methods of Financing
Equity Financing – Capital is coming from either retained earnings or funds raised from an issuance of stock
Debt Financing – Money raised through loans or by an issuance of bonds
Capital Structure – Well managed firms establish a target capital structure and strive to maintain the debt ratio

76. Equity Financing
Flotation (discount) Costs: the expenses associated with issuing stock
Types of Equity Financing:
Retained earnings
Common stock
Preferred stock
Retained earnings +
Preferred stock +
Common stock

77. Debt Financing Bond Financing: Term Loan: Incur floatation cost +
Pay only interests at the end of each period (usually semi-annually)
Pay the entire principal (face value) in a lump sum when the bond matures
Term Loan:
Involve an equal repayment arrangement.
May incur origination fee
Allow terms to be negotiated directly between the borrowing company and a financial institution
Bond Financing +
Term Loans

78. Cost of Capital
Cost of Equity (ie) – Opportunity cost associated with using shareholders’ capital
Cost of Debt (id) – Cost associated with borrowing capital from creditors
Cost of Capital (k) – Weighted average of ie and id
Cost of Debt
Cost of Capital
Cost of Equity

79. 1. Calculating the after-tax Cost of Debt

80. 2. Calculating the Cost of Equity
Cost of Retained Earnings (kr)
Cost of issuing New Common Stock(ke)
Cost of Preferred Stock (kp)
Cost of equity: weighted average of kr ke, and kp

81. Calculating Cost of Equity Based on Financing Sources
Where Cr = amount of equity financed
from retained earnings,
Cc = amount of equity financed from
issuing new stock,
Cp = amount of equity financed from
issuing preferred stock, and
Ce = Cr + Cc + Cp

82. 3. Calculating the Weighted after-tax Cost of Capital
Cd= Total debt capital(such as bonds) in dollars,
Ce=Total equity capital in dollars,
V = Cd+ Ce,
ie= Average equity interest rate per period considering
all equity sources,
id = After-tax average borrowing interest rate per
period considering all debt sources, and
k = Tax-adjusted weighted-average cost of capital.

83. Fraction of Total Equity
Practice Problem
Source
Amount
Fraction
Interest rate
Term Loan
Bond
$1.33M
$2.67M
0.333
0.667
12%
10.74%
Alpha Corporation needs to raise $10 million and has decided to finance $4 million by securing a term loan and issuing a 20‑year $1,000 par bonds for the following condition. The remaining funds would be raised through equity financing as in the table
Alpha’s marginal tax rate is 38%, and it is expected to remain constant in the future. What is the after-tax cost of debt?
Source
Amount
Interest Rate
Fraction of Total Equity
Retained earnings
$1 M
20.50%
0.167
New common stock
$4 M
22.27%
0.666
Preferred stock
10.08%

84. Marginal Cost of Capital
Comments: This 14.74% would be the marginal cost
of capital that a company with this financial structure
would expect to pay to raise $10 million.

85. Summary
Identifying and estimating relevant project cash flows is perhaps the most challenging aspect of engineering economic analysis. All cash flows can be organized into one of the following three categories:
1. Operating activities
2. Investing activities
3. Financing activities

86. Cash Items
1. New investment and disposal of existing assets
2. Salvage value (or net selling price)
3. Working capital
4. Working capital release
5. Cash revenues/savings
6. Manufacturing, operating, and maintenance costs.
7. Interest and loan payments
8. Taxes and tax credits

87. Non-cash items
Depreciation expenses
The income statement approach is typically used in organizing project cash flows. This approach groups cash flows according to whether they are operating, investing, or financing functions.

88. Methods of financing:
1. Equity financing uses retained earnings or funds raised from an issuance of stock to finance a capital.
2. Debt financing uses money raised through loans or by an issuance of bonds to finance a capital investment.

89. The selection of an appropriate MARR depends generally upon the cost of capital—the rate the firm must pay to various sources for the use of capital.
The cost of the capital formula is a composite index reflecting the cost of funds raised from different sources. The formula is

90. The marginal cost of capital is defined as the cost of obtaining another dollar of new capital. The marginal cost rises as more and more capital is raised during a given period.