The document discusses capital budgeting methods for evaluating investment projects, including payback period, net present value (NPV), internal rate of return (IRR), and modified internal rate of return (MIRR). It provides an example calculation of the payback period for Project A using a table of cash flows for Projects A and B over 4 time periods. The payback period for Project A is calculated to be 2.9 years.
Weighted average cost is the average of the costs of specific sources of capital employed in a business, properly weighted by the proportion they hold in the firm’s capital structure.
Book Value :
Value shown in the balance sheet is called book value. Weightage to each source of finance is given on the basis of book value as recorded in the balance sheet.
Market Value :
Market value represent prices of prevailing in the stock market for securities. So current market price are applied in ascertaining the weightage.
Capital structure decisions, cost of capital, weighted average cost of capita...Mohammed Jasir PV
Capital structure decisions — cost of capital — computation of cost of debt, preference shares, equity and retained earnings —weighted average cost of capital
Theories of capital structure — NI approach NOI approach -traditional — MM theory — indifference point — fair capitalization — over and under capitalization.
All related information about Cost of capital and investment theory for instance, weighted average cost of capital (WACC), cost of debt, cost of equity, investment theories and so on.
The presentation slide is on stock valuation. We have tried to present the various techniques to stock valuation under which different methods are discussed with illustrations. Key concepts:
Zero Growth Model
Balance sheet Technique
Constant Growth Model
Two-stage growth Model
Feel Free to comment.
Weighted average cost is the average of the costs of specific sources of capital employed in a business, properly weighted by the proportion they hold in the firm’s capital structure.
Book Value :
Value shown in the balance sheet is called book value. Weightage to each source of finance is given on the basis of book value as recorded in the balance sheet.
Market Value :
Market value represent prices of prevailing in the stock market for securities. So current market price are applied in ascertaining the weightage.
Capital structure decisions, cost of capital, weighted average cost of capita...Mohammed Jasir PV
Capital structure decisions — cost of capital — computation of cost of debt, preference shares, equity and retained earnings —weighted average cost of capital
Theories of capital structure — NI approach NOI approach -traditional — MM theory — indifference point — fair capitalization — over and under capitalization.
All related information about Cost of capital and investment theory for instance, weighted average cost of capital (WACC), cost of debt, cost of equity, investment theories and so on.
The presentation slide is on stock valuation. We have tried to present the various techniques to stock valuation under which different methods are discussed with illustrations. Key concepts:
Zero Growth Model
Balance sheet Technique
Constant Growth Model
Two-stage growth Model
Feel Free to comment.
Chapter 1 Introduction to Financial ManagementSafeer Raza
Chapter 1 of Financial Management by Van horn
Introduction to Financial management
Topics
Introduction
What is Financial Management
Investment Decision
Financing decision
Asset management Decision
Goal of the firm
Value creation or profit maximization
wealth maximization
Agency problems
Corporate Social Responsibility
Corporate governance
Organization of the financial management function
Chapter 1 Introduction to Financial ManagementSafeer Raza
Chapter 1 of Financial Management by Van horn
Introduction to Financial management
Topics
Introduction
What is Financial Management
Investment Decision
Financing decision
Asset management Decision
Goal of the firm
Value creation or profit maximization
wealth maximization
Agency problems
Corporate Social Responsibility
Corporate governance
Organization of the financial management function
Sheet4Assignment 1 LASA # 2—Capital Budgeting Techniques
Sheet1
Solution
:-A) Computation of WACC:-Cost of equity (Ke) will be calculated using dividend discount model which is as under:-Price of share (P0) = D1/(Ke-g)Ke = (D1/(P0*(1-f))) + gWhere,D1 = D0*(1+g)F = Flotation costKe = ((2.50*(1+6%))/(50*(1-10%))) + 6%Ke = 11.89%i) Equity financing and debt financing are two different sources of financing being used by the organizations to procure funds. Equity and debt are two different sources of financing, equity financing represents internal source of finance whereas debt financing represent external source of finance. Mixture of both is always used by the business organizations to procure funds and is most commonly known as target ratio or capital structure ratio. This ration varies from industry to industry and company and company depending upon various circumstances, equity financing can be raised only through issuing shares in market by the help of initial public offer whereas debt financing can be raise from many sources such as bonds, long term loans, money market instruments etc.Equity Financing has following advantages:1. The total cash flows generated can be used solely for investment purpose, rather than paying back the investors.2. Funds can be raised in shorter time as compared to other sources of funds.However, in equity financing, dilution of ownership easily occurs and more investors can lead to loss of Control.Cost of debt (Kd) will be calculated as follows:-Kd = Market rate of deb*(1-tax rate)Kd = 5%*(1-35%)Kd = 3.25%Debt is a more common source of finance used by most of the organizations, the reason for the same is as follows:-a. Debt is cheaper source of finance as compared to equity the reason being the cost associated with issuing the common stock like. Underwriters commission, legal expenses, various registration charges, issuing of prospectus, printing of various documents etc.b. Debt financing provide leverage to the company which will increase the Earning per Share (EPS) which in turn leads to increase in market value of share, this helps organization to maximize its market capitalization.However, if the expansion venture does not work in favour of the company, then these obligations of repayment of principal and interest may turnout to be a burden to the company. WACC = (Ke*We) + (Kd*Wd)WACC = (11.89%*70%) + (3.25%*30%)WACC = 9.30%B) Computation of NPV of project A:-Depreciation = Cost of the asset – salvage value Life of the asset = 1,500,000/ 3 = 500,000Calculation of cash flows:Revenue – 1,200,000Less Cost – 600,000Less Depreciation – 500,000Profit - 100,000Less taxes (35%) 35,000Profit after taxes .
BlueBookAcademy.com - Value companies using Discounted Cash Flow Valuationbluebookacademy
In this slideshow on valuing companies using discounted cash flows (DCF), we'll run through the most popular valuation tool used by investment bankers, traders and investors to compute the value of a company's shares and make stock recommendations.
As a fundamental concept in finance, DCF models have wider applications in valuing bonds (fixed income) and in project appraisal.
Monte Carl Simulation is a powerful and effective tool when used properly helps to navigate the expected Net Present Value NPV. This presentation helps to improve the pattern to ackowlege onthe Odessa Investment by Decision Dres.
What price will pi network be listed on exchangesDOT TECH
The rate at which pi will be listed is practically unknown. But due to speculations surrounding it the predicted rate is tends to be from 30$ — 50$.
So if you are interested in selling your pi network coins at a high rate tho. Or you can't wait till the mainnet launch in 2026. You can easily trade your pi coins with a merchant.
A merchant is someone who buys pi coins from miners and resell them to Investors looking forward to hold massive quantities till mainnet launch.
I will leave the telegram contact of my personal pi vendor to trade with.
@Pi_vendor_247
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Turin Startup Ecosystem 2024 - Ricerca sulle Startup e il Sistema dell'Innov...Quotidiano Piemontese
Turin Startup Ecosystem 2024
Una ricerca de il Club degli Investitori, in collaborazione con ToTeM Torino Tech Map e con il supporto della ESCP Business School e di Growth Capital
how can i use my minded pi coins I need some funds.DOT TECH
If you are interested in selling your pi coins, i have a verified pi merchant, who buys pi coins and resell them to exchanges looking forward to hold till mainnet launch.
Because the core team has announced that pi network will not be doing any pre-sale. The only way exchanges like huobi, bitmart and hotbit can get pi is by buying from miners.
Now a merchant stands in between these exchanges and the miners. As a link to make transactions smooth. Because right now in the enclosed mainnet you can't sell pi coins your self. You need the help of a merchant,
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@Pi_vendor_247
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Currently pi network is not tradable on binance or any other exchange because we are still in the enclosed mainnet.
Right now the only way to sell pi coins is by trading with a verified merchant.
What is a pi merchant?
A pi merchant is someone verified by pi network team and allowed to barter pi coins for goods and services.
Since pi network is not doing any pre-sale The only way exchanges like binance/huobi or crypto whales can get pi is by buying from miners. And a merchant stands in between the exchanges and the miners.
I will leave the telegram contact of my personal pi merchant. I and my friends has traded more than 6000pi coins successfully
Tele-gram
@Pi_vendor_247
how to sell pi coins in all Africa Countries.DOT TECH
Yes. You can sell your pi network for other cryptocurrencies like Bitcoin, usdt , Ethereum and other currencies And this is done easily with the help from a pi merchant.
What is a pi merchant ?
Since pi is not launched yet in any exchange. The only way you can sell right now is through merchants.
A verified Pi merchant is someone who buys pi network coins from miners and resell them to investors looking forward to hold massive quantities of pi coins before mainnet launch in 2026.
I will leave the telegram contact of my personal pi merchant to trade with.
@Pi_vendor_247
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when will pi network coin be available on crypto exchange.DOT TECH
There is no set date for when Pi coins will enter the market.
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Once they are available, users will be able to exchange other cryptocurrencies for Pi coins on designated exchanges.
But for now the only way to sell your pi coins is through verified pi vendor.
Here is the telegram contact of my personal pi vendor
@Pi_vendor_247
what is the best method to sell pi coins in 2024DOT TECH
The best way to sell your pi coins safely is trading with an exchange..but since pi is not launched in any exchange, and second option is through a VERIFIED pi merchant.
Who is a pi merchant?
A pi merchant is someone who buys pi coins from miners and pioneers and resell them to Investors looking forward to hold massive amounts before mainnet launch in 2026.
I will leave the telegram contact of my personal pi merchant to trade pi coins with.
@Pi_vendor_247
USDA Loans in California: A Comprehensive Overview.pptxmarketing367770
USDA Loans in California: A Comprehensive Overview
If you're dreaming of owning a home in California's rural or suburban areas, a USDA loan might be the perfect solution. The U.S. Department of Agriculture (USDA) offers these loans to help low-to-moderate-income individuals and families achieve homeownership.
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Find a USDA-Approved Lender: Not all lenders offer USDA loans, so it's essential to choose one approved by the USDA.
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USDA loans are an excellent option for those looking to buy a home in California's rural and suburban areas. With no down payment and flexible requirements, these loans make homeownership more attainable for many families. Explore your eligibility today and take the first step toward owning your dream home.
Greek trade a pillar of dynamic economic growth - European Business Review
Cost of Capital Learning
1. 1
The Cost
of Capital
For Deep Study of Cost of Capital, please visit
our website : http://www.svtuition.org
2. Learning Goals
• Sources of capital
• Cost of each type of funding
• Calculation of the weighted average cost of capital
(WACC)
• Construction and use of the marginal cost of capital
schedule (MCC)
2
For Deep Study of Cost of Capital, please visit
our website : http://www.svtuition.org
3. Factors Affecting the Cost of Capital
• General Economic Conditions
– Affect interest rates
• Market Conditions
– Affect risk premiums
• Operating Decisions
– Affect business risk
• Financial Decisions
– Affect financial risk
• Amount of Financing
– Affect flotation costs and market price of
security
3
For Deep Study of Cost of Capital, please visit
our website : http://www.svtuition.org
4. • Compute the cost of each source of capital
• Determine percentage of each source of
capital in the optimal capital structure
• Calculate Weighted Average Cost of Capital
(WACC)
4
Weighted Cost of Capital Model
For Deep Study of Cost of Capital, please visit
our website : http://www.svtuition.org
5. • Required rate of return for creditors
• Same cost found in Chapter 12 as yield to maturity
on bonds (kd).
• e.g. Suppose that a company issues bonds with a
before tax cost of 10%.
• Since interest payments are tax deductible, the true
cost of the debt is the after tax cost.
• If the company’s tax rate (state and federal
combined) is 40%, the after tax cost of debt
• AT kd = 10%(1-.4) = 6%.
5
1. Compute Cost of Debt1. Compute Cost of Debt
For Deep Study of Cost of Capital, please visit
our website : http://www.svtuition.org
6. • Cost to raise a dollar of preferred stock.
6
11.90%$5.00
$42.00
kp = =
The cost of preferred stock:
Example: You can issue preferred stock for a
net
price of $42 and the preferred stock pays a
$5 dividend.
Dividend (Dp)
Market Price (PP) - F
Required rate kp =
2. Compute Cost Preferred Stock2. Compute Cost Preferred Stock
7. • Two Types of Common Equity Financing
– Retained Earnings (internal common
equity)
– Issuing new shares of common stock
(external common equity)
7
3. Compute Cost of Common3. Compute Cost of Common
EquityEquity
For Deep Study of Cost of Capital, please visit
our website : http://www.svtuition.org
8. • Cost of Internal Common Equity
– Management should retain earnings only
if they earn as much as stockholder’s
next best investment opportunity of the
same risk.
– Cost of Internal Equity = opportunity
cost of common stockholders’ funds.
– Two methods to determine
• Dividend Growth Model
• Capital Asset Pricing Model
8
3. Compute Cost of Common Equity3. Compute Cost of Common Equity
9. • Cost of Internal Common Stock Equity
– Dividend Growth Model
9
D1
P0
kS = + g
3. Compute Cost of Common Equity3. Compute Cost of Common Equity
10. • Cost of Internal Common Stock Equity
– Dividend Growth Model
10
Example:
The market price of a share of common stock is
$60. The dividend just paid is $3, and the expected
growth rate is 10%.
3. Compute Cost of Common Equity3. Compute Cost of Common Equity
D1
P0
kS = + g
11. • Cost of Internal Common Stock Equity
– Dividend Growth Model
11
3(1+0.10)
60
kS = + .10 =.155 = 15.5%
Example:
The market price of a share of common stock is $60.
The dividend just paid is $3, and the expected growth
rate is 10%.
3. Compute Cost of Common Equity3. Compute Cost of Common Equity
D1
P0
kS = + g
12. • Cost of Internal Common Stock Equity
– Capital Asset Pricing Model (Chapter 7)
12
kS = kRF + β(kM – kRF)
3. Compute Cost of Common Equity3. Compute Cost of Common Equity
For Deep Study of Cost of Capital, please visit
our website : http://www.svtuition.org
13. • Cost of Internal Common Stock Equity
– Capital Asset Pricing Model (Chapter 7)
13
Example:
The estimated Beta of a stock is 1.2. The risk-free rate
is 5% and the expected market return is 13%.
3. Compute Cost of Common Equity3. Compute Cost of Common Equity
kS = kRF + β(kM – kRF)
14. • Cost of Internal Common Stock Equity
– Capital Asset Pricing Model (Chapter 7)
14
kS = 5% + 1.2(13% – 5%) 14.6%
3. Compute Cost of Common Equity3. Compute Cost of Common Equity
=
Example:Example:
The estimated Beta of a stock is 1.2. The risk-free rate
is 5% and the expected market return is 13%.
kS = kRF + β(kM – kRF)
15. • Cost of New Common Stock
– Must adjust the Dividend Growth Model equation for
floatation costs of the new common shares.
15
3. Compute Cost of Common Equity3. Compute Cost of Common Equity
D1
P0 - F
kn = + g
16. • Cost of New Common Stock
– Must adjust the Dividend Growth Model equation
for floatation costs of the new common shares.
16
3. Compute Cost of Common Equity3. Compute Cost of Common Equity
Example:
If additional shares are issued floatation costs
will be 12%. D0 = $3.00 and estimated growth
is 10%, Price is $60 as before.
D1
P0 - F
kn = + g
17. • Cost of New Common Stock
– Must adjust the Dividend Growth Model equation for
floatation costs of the new common shares.
17
3. Compute Cost of Common Equity3. Compute Cost of Common Equity
3(1+0.10)
52.80
kn = + .10 = .1625 =
D1
P0 - F
kn = + g
16.25%
Example:Example:
If additional shares are issued floatation costs will
be 12%. D0 = $3.00 and estimated growth is 10%,
Price is $60 as before.
18. 18
Weighted Average Cost of CapitalWeighted Average Cost of Capital
Gallagher Corporation estimates the following
costs for each component in its capital structure:
Gallagher’s tax rate is 40%
Source of Capital Cost
Bonds kd = 10%
Preferred Stock kp = 11.9%
Common Stock
Retained Earnings ks = 15%
New Shares kn = 16.25%
19. 19
Weighted Average Cost of CapitalWeighted Average Cost of Capital
If using retained earnings to finance the
common stock portion the capital structure:
WACC= ka= (WTd x AT kd ) + (WTp x kp ) + (WTs x ks)
For Deep Study of Cost of Capital, please visit
our website : http://www.svtuition.org
20. 20
If using retained earnings to finance the
common stock portion the capital structure:
Weighted Average Cost of CapitalWeighted Average Cost of Capital
Assume that Gallagher’s desired capital
structure is 40% debt, 10% preferred and
50% common equity.
WACC= ka= (WTd x AT kd ) + (WTp x kp ) + (WTs x ks)
21. 21
Weighted Average Cost of CapitalWeighted Average Cost of Capital
WACC = .40 x 10% (1-.4) + .10 x 11.9%
+ .50 x 15% = 11.09%11.09%
WACC= ka= (WTd x AT kd ) + (WTp x kp ) + (WTs x ks)
If using retained earnings to finance the
common stock portion the capital structure:
Assume that Gallagher’s desired capital
structure is 40% debt, 10% preferred and
50% common equity.
22. 22
If using a new equity issue to finance the
common stock portion the capital structure:
Weighted Average Cost of CapitalWeighted Average Cost of Capital
WACC= ka= (WTd x AT kd ) + (WTp x kp ) + (WTs x ks)
For Deep Study of Cost of Capital, please visit
our website : http://www.svtuition.org
23. 23
Weighted Average Cost of CapitalWeighted Average Cost of Capital
WACC = .40 x 10% (1-.4) + .10 x 11.9%
+ .50 x 16.25% = 11.72%11.72%
If using a new equity issue to finance the
common stock portion the capital structure:
WACC= ka= (WTd x AT kd ) + (WTp x kp ) + (WTs x ks)
For Deep Study of Cost of Capital, please visit
our website : http://www.svtuition.org
24. Marginal Cost of CapitalMarginal Cost of Capital
• Gallagher’s weighted average cost will
change if one component cost of capital
changes.
• This may occur when a firm raises a
particularly large amount of capital such that
investors think that the firm is riskier.
• The WACC of the next dollar of capital raised
in called the marginal cost of capital (MCC).
24
25. Graphing the MCC curveGraphing the MCC curve
• Assume now that Gallagher Corporation
has $100,000 in retained earnings with
which to finance its capital budget.
• We can calculate the point at which they
will need to issue new equity since we
know that Gallagher’s desired capital
structure calls for 50% common equity.
25
26. Graphing the MCC curveGraphing the MCC curve
• Assume now that Gallagher Corporation
has $100,000 in retained earnings with
which to finance its capital budget.
• We can calculate the point at which they
will need to issue new equity since we
know that Gallagher’s desired capital
structure calls for 50% common equity.
26
Breakpoint = Available Retained Earnings
Percentage of Total
27. Graphing the MCC curveGraphing the MCC curve
27
Breakpoint = ($100,000)/.5 = $200,000
For Deep Study of Cost of Capital, please visit
our website : http://www.svtuition.org
28. Making Decisions Using MCC
28
WeightedCostofCapital
Total Financing
10%
11%
12%
13%
0 100,000 200,000 300,000 400,000
Marginal weighted cost of capital curve:
Using internal
common equity
Using internal
common equity
Using new
common equity
Using new
common equity
11.72%11.72%
11.09%11.09%
29. Making Decisions Using MCCMaking Decisions Using MCC
• Graph MIRRs of potential projects
29
WeightedCostofCapital
Total Financing
9%
10%
11%
12%
0 100,000 200,000 300,000 400,000
Marginal weighted cost of capital curve:
Project 1Project 1
MIRR =MIRR =
12.4%12.4%
Project 2Project 2
MIRR =MIRR =
12.1%12.1%
Project 3Project 3
MIRR =MIRR =
11.5%
30. Making Decisions Using MCCMaking Decisions Using MCC
• Graph IRRs of potential projects
30
WeightedCostofCapital
Total Financing
9%
10%
11%
12%
0 100,000 200,000 300,000 400,000
Marginal weighted cost of capital curve:
Project 1Project 1
IRR =IRR =
12.4%12.4%
Project 2Project 2
IRR =IRR =
12.1%12.1%
Project 3Project 3
IRR =IRR =
11.5%
Graph MCC Curve
11.09%11.09%
11.72%11.72%
31. Making Decisions Using MCCMaking Decisions Using MCC
• Graph IRRs of potential projects
• Graph MCC Curve
31
WeightedCostofCapital
Total Financing
9%
10%
11%
12%
0 100,000 200,000 300,000 400,000
Marginal weighted cost of capital curve:
Project 1Project 1
IRR = 12.4%IRR = 12.4% Project 2Project 2
IRR = 12.1%IRR = 12.1%
Project 3Project 3
IRR =IRR = 11.5%
Accept Projects #1 & #2Accept Projects #1 & #2
Choose projects whose IRR is above the weighted
marginal cost of capital
11.72%11.72%
11.09%11.09%
32. 32
Answer the following questions and do the following
problems and include them in you ECP Notes.
If the cost of new common equity is higher than the cost of internal equity, why would a
firm choose to issue new common stock?
Why is it important to use a firm’s MCC and not a firm’s initial WACC to evaluate
investments?
Calculate the AT kd, ks, kn for the following information:
Loan rates for this firm = 9%
Growth rate of dividends = 4%
Tax rate = 30%
Common Dividends at t1 = $ 4.00
Price of Common Stock = $35.00
Flotation costs = 6%
Your firm’s ks is 10%, the cost of debt is 6% before taxes, and the tax rate is 40%. Given
the following balance sheet, calculate the firm’s after tax WACC:
Total assets = $25,000
Total debt = 15,000
Total equity = 10,000
33. 33
Your firm is in the 30% tax bracket with a before-tax required rate of return on its
equity of 13% and on its debt of 10%. If the firm uses 60% equity and 40% debt
financing, calculate its after-tax WACC.
Would a firm use WACC or MCC to identify which new capital budgeting projects
should be selected? Why?
A firm's before tax cost of debt on any new issue is 9%; the cost to issue new
preferred stock is 8%. This appears to conflict with the risk/return relationship. How
can this pricing exist?
What determines whether to use the dividend growth model approach or the CAPM
approach to calculate the cost of equity?
For Deep Study of Cost of Capital, please visit
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35. • The capital budgeting process.
• Calculation of payback, NPV, IRR, and MIRR for
proposed projects.
• Capital rationing.
• Measurement of risk in capital budgeting and
how to deal with it.
Learning Objectives
2
36. • Capital Budgeting is the process of
evaluating proposed investment projects for
a firm.
• Managers must determine which projects
are acceptable and must rank mutually
exclusive projects by order of desirability to
the firm.
The Capital Budgeting Process
3
37. Four methods:
• Payback Period
– years to recoup the initial investment
• Net Present Value (NPV)
– change in value of firm if project is under taken
• Internal Rate of Return (IRR)
– projected percent rate of return project will earn
• Modified Internal Rate of Return (MIRR)
The Accept/Reject Decision
4
38. • Consider Projects A and B that have the
following expected cashflows?
Capital Budgeting Methods
5
P R O J E C TP R O J E C T
TimeTime A BB
0 (10,000.) (10,000.)
1 3,500 500
2 3,500 500
3 3,500 4,600
4 3,500 10,000
39. • What is the payback for Project A?
Capital Budgeting Methods
6
P R O J E C TP R O J E C T
TimeTime A BB
0 (10,000.) (10,000.)
1 3,500 500
2 3,500 500
3 3,500 4,600
4 3,500 10,000
40. • What is the payback for Project A?
Capital Budgeting Methods
0 1 2 3 4
3,500
-6,500
3,500
-3,000
3,500
+500
3,500(10,000)
Cumulative CF
7
P R O J E C TP R O J E C T
TimeTime A BB
0 (10,000.) (10,000.)
1 3,500 500
2 3,500 500
3 3,500 4,600
4 3,500 10,000
41. • What is the payback for Project A?
Capital Budgeting Methods
Payback in
2.9 years
P R O J E C TP R O J E C T
TimeTime A BB
0 (10,000.) (10,000.)
1 3,500 500
2 3,500 500
3 3,500 4,600
4 3,500 10,000
8
0 1 2 3 4
3,500
-6,500
3,500
-3,000
3,500
+500
3,500(10,000)
Cumulative CF
0 1 2 3 4
3,500
-6,500
3,500
-3,000
3,500
+500
3,500(10,000)
Cumulative CF
42. • What is the payback for Project B?
Capital Budgeting Methods
9
0 1 2 3 4
500 500 4,600 10,000(10,000)
P R O J E C TP R O J E C T
TimeTime AA B
0 (10,000.) (10,000.)
1 3,500 500
2 3,500 500
3 3,500 4,600
4 3,500 10,000
43. Payback in
3.4 years
• What is the payback for Project B?
Capital Budgeting Methods
10
0 1 2 3 4
500
-9,500
500
-9,000
4,600
-4,400
10,000
+5,600
(10,000)
Cumulative CF
P R O J E C TP R O J E C T
TimeTime AA B
00 (10,000.) (10,000.)
11 3,500 500
22 3,500 500
33 3,500 4,600
44 3,500 10,000
44. • Accept project if payback is less than the
company’s predetermined maximum.
• If company has determined that it requires
payback in three years or less, then you
would:
– accept Project A
– reject Project B
Payback Decision Rule
11
45. • Present Value of all costs and benefits
(measured in terms of incremental cash
flows) of a project.
• Concept is similar to Discounted Cashflow
model for valuing securities but subtracts
the cost of the project.
Capital Budgeting Methods
Net Present ValueNet Present Value
12
46. • Present Value of all costs and benefits (measured in
terms of incremental cash flows) of a project.
• Concept is similar to Discounted Cashflow model for
valuing securities but subtracts of cost of project.
Capital Budgeting Methods
Net Present ValueNet Present Value
NPV = PV of Inflows - Initial InvestmentNPV = PV of Inflows - Initial Investment
NPV = + + – Initial
Investment
CF1
(1+ k)1
CF2
(1+ k)2 ….
CFn
(1+ k )n
13
47. What is the
NPV for
Project B?
14
P R O J E C TP R O J E C T
TimeTime AA B
0 (10,000) (10,000)
1 3,500 500
2 3,500 500
3 3,500 4,600
4 3,500 10,000
k=10%
0 1 2 3 4
500 500 4,600 10,000(10,000)
Capital Budgeting Methods
48. 455
$500
(1.10)1
What is the
NPV for
Project B?
15
P R O J E C TP R O J E C T
TimeTime AA B
0 (10,000.) (10,000.)
1 3,500 500
2 3,500 500
3 3,500 4,600
4 3,500 10,000k=10%
0 1 2 3 4
500 500 4,600 10,000(10,000)
Capital Budgeting Methods
49. 413
$500
(1.10) 2
What is the
NPV for
Project B?
16
P R O J E C TP R O J E C T
TimeTime AA B
0 (10,000.) (10,000.)
1 3,500 500
2 3,500 500
3 3,500 4,600
4 3,500 10,000
455
k=10%
0 1 2 3 4
500 500 4,600 10,000(10,000)
Capital Budgeting Methods
50. 3,456
$4,600
(1.10) 3
What is the
NPV for
Project B?
17
P R O J E C TP R O J E C T
TimeTime AA B
0 (10,000.) (10,000.)
1 3,500 500
2 3,500 500
3 3,500 4,600
4 3,500 10,000
413
$500
(1.10) 2
455
k=10%
0 1 2 3 4
500 500 4,600 10,000(10,000)
Capital Budgeting Methods
51. 6,830
$10,000
(1.10) 4
What is the
NPV for
Project B?
18
P R O J E C TP R O J E C T
TimeTime AA B
0 (10,000.) (10,000.)
1 3,500 500
2 3,500 500
3 3,500 4,600
4 3,500 10,000
3,456
$4,600
(1.10) 3413
$500
(1.10) 2
455
k=10%
0 1 2 3 4
500 500 4,600 10,000(10,000)
Capital Budgeting Methods
52. $11,154
What is the
NPV for
Project B?
19
P R O J E C TP R O J E C T
TimeTime A B
0 (10,000.) (10,000.)
1 3,500 500
2 3,500 500
3 3,500 4,600
4 3,500 10,000
6,830
3,456
413
455
k=10%
0 1 2 3 4
500 500 4,600 10,000(10,000)
Capital Budgeting Methods
53. PV Benefits > PV Costs
$11,154 > $ 10,000
What is the
NPV for
Project B?
20
P R O J E C TP R O J E C T
TimeTime A B
0 (10,000.) (10,000.)
1 3,500 500
2 3,500 500
3 3,500 4,600
4 3,500 10,000
$11,154
6,830
3,456
413
455
k=10%
0 1 2 3 4
500 500 4,600 10,000(10,000)
54. NPV > $0
$1,154 > $0
- $10,000 =- $10,000 = $1,154$1,154 == NPVNPV
What is the
NPV for
Project B?
21
P R O J E C TP R O J E C T
TimeTime AA B
0 (10,000.) (10,000.)
1 3,500 500
2 3,500 500
3 3,500 4,600
4 3,500 10,000
PV Benefits > PV Costs
$11,154 > $ 10,000
$11,154$11,154
6,830
3,456
413
455
k=10%
0 1 2 3 4
500 500 4,600 10,000(10,000)
55. 22
• Additional Keys used to enter
Cash Flows and compute the
Net Present Value (NPV)
Financial Calculator:
56. NPV IRR
P/YR
CF
N I/Y PV PMT FV
Key used to enter expected cash flows in order of
their receipt.
NoteNote:: the initial investment (CF0) must be
entered as a negative number since it is an
outflow.
23
• Additional Keys used to
enter Cash Flows and
compute the Net
Present Value (NPV)
Financial Calculator:
57. NPV IRR
P/YR
CF
N I/Y PV PMT FV
• Additional Keys used to
enter Cash Flows and
compute the Net Present
Value (NPV)
Financial Calculator:
Key used to calculate the net present value of
the cashflows that have been entered in the
calculator.
24
58. NPV IRR
P/YR
CF
N I/Y PV PMT FV
• Additional Keys used
to enter Cash Flows
and compute the Net
Present Value (NPV)
Financial Calculator:
Key used to calculate the internal rate of return
for the cashflows that have been entered in the
calculator. 25
59. Calculate the NPV for Project B with calculator.
26
NPV IRR
P/YR
CF
N I/Y PV PMT FV
P R O J E C TP R O J E C T
Time ATime A B
0 (10,000.) (10,000.)
1 3,500 500
2 3,500 500
3 3,500 4,600
4 3,500 10,000
60. NPV IRR
P/YR
CF
N I/Y PV PMT FV
Calculate the NPV for Project B with calculator.
Keystrokes for TI BAII PLUS:
CFCF00 = -10,000= -10,000
27
CF 10000 +/- ENTER
61. NPV IRR
P/YR
CF
N I/Y PV PMT FV
Calculate the NPV for Project B with calculator.
C01 =C01 = 500500
500 ENTER
28
CF 10000 +/- ENTER
Keystrokes for TI BAII PLUS:
62. NPV IRR
P/YR
CF
N I/Y PV PMT FV
Calculate the NPV for Project B with calculator.
F01 =F01 = 22
F stands for “frequency”. Enter 2 since there
are two adjacent payments of 500 in periods 1 and 2.
29
2 ENTER
500 ENTER
CF 10000 +/- ENTER
Keystrokes for TI BAII PLUS:
63. NPV IRR
P/YR
CF
N I/Y PV PMT FV
Calculate the NPV for Project B with calculator.
C02 =C02 = 46004600
4600 ENTER
30
2 ENTER
500 ENTER
CF 10000 +/- ENTER
Keystrokes for TI BAII PLUS:
64. NPV IRR
P/YR
CF
N I/Y PV PMT FV
Calculate the NPV for Project B with calculator.
F02 =F02 = 11
1 ENTER
31
4600 ENTER
2 ENTER
500 ENTER
CF 10000 +/- ENTER
Keystrokes for TI BAII PLUS:
65. NPV IRR
P/YR
CF
N I/Y PV PMT FV
Calculate the NPV for Project B with calculator.
C03 =C03 = 1000010000
10000 ENTER
32
1 ENTER
4600 ENTER
2 ENTER
500 ENTER
CF 10000 +/- ENTER
Keystrokes for TI BAII PLUS:
66. NPV IRR
P/YR
CF
N I/Y PV PMT FV
Calculate the NPV for Project B with calculator.
F03 =F03 = 11
1 ENTER
33
10000 ENTER
1 ENTER
4600 ENTER
2 ENTER
500 ENTER
CF 10000 +/- ENTER
Keystrokes for TI BAII PLUS:
67. NPV IRR
P/YR
CF
N I/Y PV PMT FV
Calculate the NPV for Project B with calculator.
I =I = 1010
k = 10%
34
Keystrokes for TI BAII PLUS:
10 ENTERNPV
68. NPV IRR
P/YR
CF
N I/Y PV PMT FV
Calculate the NPV for Project B with calculator.
NPV = 1,153.95
CPT
The net present value of Project B = $1,154
as we calculated previously.
35
10 ENTERNPV
Keystrokes for TI BAII PLUS:
69. • Accept the project if the NPV is greater
than or equal to 0.
Example:
NPVA = $1,095
NPVB = $1,154
NPV Decision Rule
> 0> 0
> 0> 0
AcceptAccept
AcceptAccept
•If projects are independent, accept both projects.
•If projects are mutually exclusive, accept the project
with the higher NPV.
36
70. • IRR (Internal Rate of Return)
– IRR is the discount rate that forces the NPV to equal
zero.
– It is the rate of return on the project given its initial
investment and future cash flows.
• The IRR is the rate earned only if all CFs are reinvested at the
IRR rate.
Capital Budgeting Methods
37
71. Calculate the IRR for Project B with calculator.
39
NPV IRR
P/YR
CF
N I/Y PV PMT FV
P R O J E C TP R O J E C T
Time ATime A B
0 (10,000.) (10,000.)
1 3,500 500
2 3,500 500
3 3,500 4,600
4 3,500 10,000
72. Enter CFs as for NPV
NPV IRR
P/YR
CF
N I/Y PV PMT FV
Calculate the IRR for Project B with calculator.
IRR =IRR = 13.5%13.5%
40
P R O J E C TP R O J E C T
TimeTime A B
0 (10,000.) (10,000.)
1 3,500 500
2 3,500 500
3 3,500 4,600
4 3,500 10,000
IRRIRR CPTCPT
73. • Accept the project if the IRR is greater than or
equal to the required rate of return (k).
• Reject the project if the IRR is less than the
required rate of return (k).
Example:
k = 10%
IRRA = 14.96%
IRRB = 13.50%
IRR Decision Rule
> 10%> 10%
> 10%> 10%
AcceptAccept
AcceptAccept
41
74. • MIRR (Modified Internal Rate of Return)
– This is the discount rate which causes the project’s PV of
the outflows to equal the project’s TV (terminal value) of
the inflows.
– Assumes cash inflows are reinvested at k, the safe re-
investment rate.
– MIRR avoids the problem of multiple IRRs.
– We accept if MIRR > the required rate of return.
Capital Budgeting Methods
PVPVoutflowoutflow ==
TVinflows
(1 + MIRR)n
42
75. What is the
MIRR for
Project B?
P R O J E C TP R O J E C T
Time ATime A B
0 (10,000.) (10,000.)
1 3,500 500
2 3,500 500
3 3,500 4,600
4 3,500 10,000
Safe =2%
0 1 2 3 4
500500 500500 4,6004,600 10,00010,000(10,000)(10,000)
(10,000)(10,000)
10,000(1.02)0
10,000
4,600(1.02)1
500(1.02)2
500(1.02)3
4,692
520
531
15,74310,000 =
15,743
(1 + MIRR)4
(10,000)/(1.02)0
MIRR = .12 = 12%MIRR = .12 = 12%
43
76. NPV IRR
P/YR
CF
N I/Y PV PMT FV
Calculate the MIRR for Project B with calculator.
10000 ENTER
1 ENTER
1 ENTER
4600 ENTER
2 ENTER
500 ENTER
CF 0 +/- ENTER
Keystrokes for TI BAII PLUS:
Step 1. Calculate NPV using cash inflows
44
77. NPV IRR
P/YR
CF
N I/Y PV PMT FV
Calculate the MIRR for Project B with calculator.
NPV = 14,544NPV = 14,544
CPT
The net present value of Project B cash inflows = $14,544
(use as PV)
45
2 ENTERNPV
Keystrokes for TI BAII PLUS:
Step 1. Calculate NPV using cash inflowsStep 1. Calculate NPV using cash inflows
78. NPV IRR
P/YR
CF
N I/Y PV PMT FV
Calculate the MIRR for Project B with calculator.
FV =FV = 15,74315,743
46
Step 2. Calculate FV of cash inflows using previous NPV
This is the Terminal Value
Calculator Enter:
N = 4
I/YR = 2
PV = -14544
PMT= 0
CPT FV = ?
79. NPV IRR
P/YR
CF
N I/Y PV PMT FV
Calculate the MIRR for Project B with calculator.
MIRRMIRR 12.0112.01
47
Step 3. Calculate MIRR using PV of outflows and calculated
Terminal Value.
Calculator Enter:
N = 4
PV = -10000
PMT = 0
FV = 15,743
CPT I/YR = ??
80. • Capital rationing is the practice of placing
a dollar limit on the total size of the
capital budget.
• This practice may not be consistent with
maximizing shareholder value but may be
necessary for other reasons.
• Choose between projects by selecting the
combination of projects that yields the
highest total NPV without exceeding the
capital budget limit.
What is capital rationing?
54
81. • Calculate the coefficient of variation of
returns of the firm’s asset portfolio with the
project and without it.
• This can be done by following a five step
process. Observe the following example.
Measurement of Project Risk
55
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82. • Step 1:Step 1: Find the CV of the Existing Portfolio
– Assume Company X has an existing rate of return
of 6% and standard deviation of 2%.
Measurement of Project Risk
56
Standard Deviation
Mean, or expected valueCV=
= .02
.06
= .3333, or 33.33%
83. • Step 2:Step 2: Find the Expected return of the New
Portfolio (Existing plus Proposed)
– Assume the New Project (Y) has an IRR of 5.71%
and a Standard Deviation of 2.89%
– Assume further that Project Y will account for 10%
of X’s overall investment.
Measurement of Project Risk
57
(wx x E(Rx)) + (wy x E(Ry))
= (.10 x .0571) + (.90 x .06)
= .00571 + .05400
= .05971, or 5.971%
E(Rp) =
84. • Step 3:Step 3: Find the Standard Deviation of the New
Portfolio (Existing plus Proposed).
– Assume the proposed is uncorrelated with the
existing project. rxy = 0
Measurement of Project Risk
58
[wx
2
σx
2
+ wy
2
σy
2
+ 2wxwyrxyσxσy]1/2
= [(.102
)(.02892
) + (.902
)(.022
) + (2)(.10)(.90)(0.0)(.0289)(02)]1/2
= [(.01)(.000835) + (.81)(.0004) + 0]1/2
= .0182, or 1.82%
= [.00000835 + .000324]1/2
= [.00033235]1/2
σp =
85. • Step 4:Step 4: Find the CV of the New Portfolio
(Existing plus Proposed)
Measurement of Project Risk
59
Standard Deviation
Mean, or expected valueCV=
= .0182
.05971
= .3048, or 30.48%
86. • Step 5:Step 5: Compare the CV of the portfolio
with and without the Proposed Project.
– The difference between the two coefficients
of variation is the measure of risk of the
capital budgeting project.
Measurement of Project Risk
60
CV without Y Change in CVCV with Y
33.33% -2.8530.48%
87. • Firms often compensate for risk by
adjusting the discount rate used to
calculate NPV.
– Higher risk, use a higher discount rate.
– Lower risk, use a lower discount rate
• The risk adjusted discount rate (RADR) can
also be used as a risk adjusted hurdle rate
for IRR comparisons.
Comparing risky projects using risk
adjusted discount rates (RADRs)
61
88. • Non-simple projects have one or
more negative future cash flows
after the initial investment.
Non-simple Projects
62
89. • How would a negative cash flow in year 4
affect Project Z’s NPV?
Non-simple projects
Project Z should be rejected in this case.
63
8,336
-4,098
3,757
4,132
4,545
k=10%
0 1 2 3 4
5,000 5,000 5,000 -6,000(10,000)
- $10,000 = -$1,664 NPV
90. • Mutually exclusive projects with unequal
project lives can be compared by using two
methods:
– Replacement Chain
– Equivalent Annual Annuity
Mutually Exclusive Projects With
Unequal Lives
68
91. • Assumes each project can be replicated until a
common period of time has passed, allowing
the projects to be compared.
• Example
– Project Cheap Talk has a 3-year life, with an NPV
of $4,424.
– Project Rolles Voice has a 12-year life, with an
NPV of $4,510.
Replacement Chain Approach
69
92. • Project Cheap Talk could be repeated four
times during the life of Project Rolles Voice.
• The NPVs of Project Cheap Talk, in years t3, t6,
and t9,are discounted back to year t0.
Replacement Chain Approach
70
93. • The NPVs of Project Cheap Talk, in years t3,
t6, and t9,are discounted back to year t0,which
results in an NPV of $12,121.
Replacement Chain Approach
3,324
12,121
2,497
1,876
0 3 6 9
4,424 4,424 4,4244,424
k=10%
71
94. • Amount of the annuity payment that
would equal the same NPV as the actual
future cash flows of a project.
• EAA = NPV
PVIFAk,n
Equivalent Annual Annuity
72
96. ECP HomeworkECP Homework
1. The following net cash flows are projected for two separate projects. Your required rate
of return is 12%.
Year Project A Project B
0 ($150,000) ($400,000)
1 $30,000 $100,000
2 $30,000 $100,000
3 $30,000 $100,000
4 $30,000 $100,000
5 $30,000 $100,000
6 $30,000 $100,000
a. Calculate the payback period for each project.
b. Calculate the NPV of each project.
c. Calculate the MIRR of each project.
d. Which project(s) would you accept and why?
97. 2. What is meant by risk adjusted discount rates?
3. Explain why the NPV method of capital budgeting is preferable over the payback method.
4. A firm has a net present value of zero. Should the project be rejected? Explain.
5. You have estimated the MIRR for a new project with the following probabilities:
Possible MIRR Value Probability
4% 5%
7% 15%
10% 15%
11% 50%
14% 15%
a. Calculate the expected MIRR of the project.
b. Calculate the standard deviation of the project.
c. Calculate the coefficient of variation.
d. Calculate the expected MIRR of the new portfolio with the new project. The current
portfolio has an expected MIRR of 9% and a standard deviation of 3% and will
represent 60% of the total portfolio.
ECP HomeworkECP Homework
99. Learning Objectives
• Understand the importance of business valuation.
• Understand the importance of stock and bond
valuation.
• Learn to compute the value and yield to maturity of
bonds.
• Learn to compute the value and expected yield on
preferred stock and common stock.
• Learn to compute the value of a complete business.
99
100. General Valuation Model
• To develop a general model for valuing a
business, we consider three factors that affect
future earnings:
– Size of cash flows
– Timing of cash flows
– Risk
• We then apply the factors to the Discounted Cash
Flow (DCF) Model (Equation 12-1)
100
101. Bond Valuation Model
• Bond Valuation is an application of time value
model introduced in chapter 8.
• The value of the bond is the present value of
the cash flows the investor expects to
receive.
• What are the cashflows from a bond
investment?
101
102. Bond Valuation Model
• 3 Types of Cash Flows
– Amount paid to buy the bond (PV)
– Coupon interest payments made to the
bondholders (PMT)
– Repayment of Par value at end of Bond’s life
(FV).
102
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103. Bond Valuation Model
• 3 Types of Cash Flows
– Amount paid to buy the bond (PV)
– Coupon interest payments made to the
bondholders (PMT)
– Repayment of Par value at end of Bond’s life
(FV).
103
Discount rate (I/YR)
• Bond’s time to maturity (N)
104. 104
Cur Net
Bonds Yld Vol Close Chg
AMR6¼24 cv 6 91¼ -1½
ATT 8.35s25 8.3 110 102¾ +¼
IBM 63
/8 05 6.6 228 965
/8 -1
/8
Kroger 9s99 8.8 74 1017
/8 -¼
IBM 63
/8 09 6.6 228 965
/8 -1
/8
IBM Bond Wall Street Journal Information:
For Deep Study of Cost of Capital, please visit
our website : http://www.svtuition.org
105. 105
Suppose IBM makes annual coupon payments. The
person who buys the bond at the beginning of 2005 for
$966.25 will receive 5 annual coupon payments of
$63.75 each and a $1,000 principal payment in 5 years
(at the end of 2009). Assume t0 is the beginning of
2005.
Suppose IBM makes annual coupon payments. The
person who buys the bond at the beginning of 2005 for
$966.25 will receive 5 annual coupon payments of
$63.75 each and a $1,000 principal payment in 5 years
(at the end of 2009). Assume t0 is the beginning of
2005.
IBM Bond Wall Street Journal
Information:
Cur Net
Bonds Yld Vol Close Chg
AMR6¼24 cv 6 91¼ -1½
ATT 8.35s25 8.3 110 102¾ +¼
IBM 63
/8 05 6.6 228 965
/8 -1
/8
Kroger 9s99 8.8 74 1017
/8 -¼
IBM 63
/8 09 6.6 228 965
/8 -1
/8
106. 106
IBM Bond Timeline:
0 1 2 3 4 5
2005 2006 2007 2008 2009
63.75 63.75 63.75 63.75 63.75
1000.00
Suppose IBM makes annual coupon payments. The person
who buys the bond at the beginning of 2005 for $966.25 will
receive 5 annual coupon payments of $63.75 each and a
$1,000 principal payment in 5 years (at the end of 2009).
Suppose IBM makes annual coupon payments. The person
who buys the bond at the beginning of 2005 for $966.25 will
receive 5 annual coupon payments of $63.75 each and a
$1,000 principal payment in 5 years (at the end of 2009).
Cur Net
Bonds Yld Vol Close Chg
AMR6¼24 cv 6 91¼ -1½
ATT 8.35s25 8.3 110 102¾ +¼
IBM 63
/8 05 6.6 228 965
/8 -1
/8
Kroger 9s99 8.8 74 1017
/8 -¼
IBM 63
/8 09 6.6 228 965
/8 -1
/8
107. 107
Compute the Value for the IBM Bond given that you require anCompute the Value for the IBM Bond given that you require an
8% return on your investment.8% return on your investment.
Compute the Value for the IBM Bond given that you require anCompute the Value for the IBM Bond given that you require an
8% return on your investment.8% return on your investment.
0 1 2 3 4 5
2005 2006 2007 2008 2009
63.75 63.75 63.75 63.75 63.75
1000.00
IBM Bond Timeline:IBM Bond Timeline:
108. 108
$63.75 Annuity for 5 years$63.75 Annuity for 5 years$63.75 Annuity for 5 years$63.75 Annuity for 5 years
VB = (INT x PVIFAk,n) + (M x PVIFk,n )
$1000 Lump Sum in 5 years$1000 Lump Sum in 5 years$1000 Lump Sum in 5 years$1000 Lump Sum in 5 years
0 1 2 3 4 5
2005 2006 2007 2008 2009
63.75 63.75 63.75 63.75 63.75
1000.00
IBM Bond Timeline:IBM Bond Timeline:
109. 109
VB = (INT x PVIFAk,n) + (M x PVIFk,n )
= 63.75(3.9927) + 1000(.6806)
= 254.53 + 680.60 = 935.13
$63.75 Annuity for 5 years$63.75 Annuity for 5 years$63.75 Annuity for 5 years$63.75 Annuity for 5 years $1000 Lump Sum in 5 years$1000 Lump Sum in 5 years$1000 Lump Sum in 5 years$1000 Lump Sum in 5 years
0 1 2 3 4 5
2005 2006 2007 2008 2009
63.75 63.75 63.75 63.75 63.75
1000.00
IBM Bond Timeline:IBM Bond Timeline:
110. 110
.01 rounding
differenceN I/YR PV PMT FV
––935.12935.12
5 8 ? 63.75 1,000
IBM Bond Timeline:IBM Bond Timeline:
$63.75 Annuity for 5 years$63.75 Annuity for 5 years$63.75 Annuity for 5 years$63.75 Annuity for 5 years
0 1 2 3 4 5
2005 2006 2007 2008 2009
63.75 63.75 63.75 63.75 63.75
1000.00
$1000 Lump Sum in 5 years$1000 Lump Sum in 5 years$1000 Lump Sum in 5 years$1000 Lump Sum in 5 years
111. 111
Most Bonds Pay Interest Semi-Annually:
e.g. semiannual coupon bond with 5 years
to maturity, 9% annual coupon rate.
Instead of 5 annual payments of $90, the bondholder
receives 10 semiannual payments of $45.
0 1 2 3 4 5
2005 2006 2007 2008 2009
45 45
1000
45 45 45 45 45 45 45 45
112. 112
Compute the value of the bond given that you
require a 10% return on your investment.
Compute the value of the bond given that you
require a 10% return on your investment.
Since interest is received every 6 months, we need to use
semiannual compounding
VB = 45( PVIFA10 periods,5%) + 1000(PVIF10 periods, 5%)
10%
2
10%
2
Semi-Annual
Compounding
Most Bonds Pay Interest Semi-Annually:Most Bonds Pay Interest Semi-Annually:
0 1 2 3 4 5
2005 2006 2007 2008 2009
45 45
1000
45 45 45 45 45 45 45 45
113. 113
Most Bonds Pay Interest Semi-Annually:
= 45(7.7217) + 1000(.6139)
= 347.48 + 613.90 = 961.38
Compute the value of the bond given that youCompute the value of the bond given that you
require a 10% return on your investment.require a 10% return on your investment.
Compute the value of the bond given that youCompute the value of the bond given that you
require a 10% return on your investment.require a 10% return on your investment.
Since interest is received every 6 months, we need to use
semiannual compounding
VB = 45( PVIFA10 periods,5%) + 1000(PVIF10 periods, 5%)
0 1 2 3 4 5
2005 2006 2007 2008 2009
45 45
1000
45 45 45 45 45 45 45 45
115. Yield to Maturity
• If an investor purchases a 6.375% annual coupon
bond today for $966.25 and holds it until maturity
(5 years), what is the expected annual rate of
return ?
115
-966.25
??
0 1 2 3 4 5
2005 2006 2007 2008 2009
63.75 63.75 63.75 63.75 63.75
1000.00
+ ??
966.25966.25
116. Yield to Maturity
116
VB = 63.75(PVIFA5, x%) + 1000(PVIF5,x%)
Solve by trial and error.
• If an investor purchases a 6.375% annual coupon
bond today for $966.25 and holds it until maturity
(5 years), what is the expected annual rate of
return ?
-966.25
??
0 1 2 3 4 5
2005 2006 2007 2008 2009
63.75 63.75 63.75 63.75 63.75
1000.00
+ ??
966.25966.25
118. Yield to Maturity
118
If YTM > Coupon Rate bond Sells at a DISCOUNT
If YTM < Coupon Rate bond Sells at a PREMIUM
-966.25
0 1 2 3 4 5
2005 2006 2007 2008 2009
63.75 63.75 63.75 63.75 63.75
1000.00
119. Interest Rate Risk
• Bond Prices fluctuate over Time
– As interest rates in the economy change,
required rates on bonds will also change
resulting in changing market prices.
119
Interest
Rates
VVBB
120. Interest Rate Risk
120
• Bond Prices fluctuate over Time
– As interest rates in the economy change,
required rates on bonds will also change
resulting in changing market prices.
Interest
Rates
VVBBInterest
Rates VVBB
121. Valuing Preferred Stock
121
P0 = Value of Preferred Stock
= PV of ALL dividends discounted at investor’s
Required Rate of Return
52 Weeks Yld Vol Net
Hi Lo Stock Sym Div % PE 100s Hi Lo Close Chg
s 42½ 29 QuakerOats OAT 1.14 3.3 24 5067 35 34¼ 34¼ -¾
s 36¼ 25 RJR Nabisco RN .08p ... 12 6263 29¾ 285
/8 287
/8 -¾
237
/8 20 RJR Nab pfB 2.31 9.7 ... 966 24 235
/8 23¾ ...
7¼ 5½ RJR Nab pfC .60 9.4 ... 2248 6½ 6¼ 63
/8 -1
/8
0 1 2 3 ∞
P0=23.75 D1=2.31 D2=2.31 D3=2.31 D∞ =2.31
237
/8 20 RJR Nab pfB 2.31 9.7 ... 966 24 235
/8 23¾ ...
124. Valuing Individual Shares of Common
Stock
124
P0 = PV of ALL expected dividends discounted at investor’s
Required Rate of Return
Not like Preferred Stock since D0 = D1 = D2 = D3 = DN , therefore the cash
flows are no longer an annuity.
Not like Preferred Stock since D0 = D1 = D2 = D3 = DN , therefore the cash
flows are no longer an annuity.
P0 = + + +···∞
D1
(1+ ks )
D2
(1+ ks )2
D3
(1+ ks )3
D1 D2 D3
P0 D∞
0 1 2 3 ∞
125. Valuing Individual Shares of Common
Stock
125
P0 = PV of ALL expected dividends discounted at investor’s
Required Rate of Return
Investors do not know the values of
D1, D2, .... , DN. The future dividends must be
estimated.
Investors do not know the values of
D1, D2, .... , DN. The future dividends must be
estimated.
D1 D2 D3
P0 D∞
0 1 2 3 ∞
P0 = + + +···∞
D1
(1+ ks )
D2
(1+ ks )2
D3
(1+ ks )3
126. Constant Growth Dividend Model
126
Assume that dividends grow at a constant rate (g).
D1=D0 (1+g)D0
D2=D0 (1+g)2
D3=D0 (1+g)3
D∞=D0 (1+g)∞
0 1 2 3 ∞
127. Constant Growth Dividend Model
127
Requires
ks > g
Requires
ks > g
Reduces to:
P0 = + + + ··· +
D0 (1+ g)
(1+ ks )
D0 (1+ g)2
(1+ ks )2
D0 (1+ g)3
(1+ ks )3 ∞
P0 = =
D0(1+g)
ks – g
D1
ks – g
Assume that dividends grow at a constant rate (g).
D1=D0 (1+g)D0
D2=D0 (1+g)2
D3=D0 (1+g)3
D∞=D0 (1+g)∞
0 1 2 3 ∞
128. Constant Growth Dividend Model
128
P0 = = $30.50
1.14(1+.07)
.11 – .07
What is the value of a share of common stock if the
most recently paid dividend (D0) was $1.14 per share and
dividends are expected to grow at a rate of 7%?
Assume that you require a rate of return of 11%
on this investment.
P0 = =
D0(1+g)
ks – g
D1
ks – g
129. Valuing Total Stockholders’ Equity
• The Investor’s Cash Flow DCF Model
– Investor’s Cash Flow is the amount that is
“free” to be distributed to debt holders,
preferred stockholders and common
stockholders.
– Cash remaining after accounting for
expenses, taxes, capital expenditures and
new net working capital.
129
131. 131
ECP Homework
1. Indicate which of the following bonds seems to be reported incorrectly with respect to discount, premium,
or par and explain why.
Bond Price Coupon Rate Yield to Maturity
A 105 9% 8%
B 100 6% 6%
C 101 5% 4.5%
D 102 0% 5%
2. What is the price of a ten-year $1,000 par-value bond with a 9% annual coupon rate and a 10% annual
yield to maturity assuming semi-annual coupon payments?
3. You have an issue of preferred stock that is paying a $3 annual dividend. A fair rate of return on this
investment is calculated to be 13.5%. What is the value of this preferred stock issue?
4. Total assets of a firm are $1,000,000 and the total liabilities are $400,000. 500,000 shares of common
stock have been issued and 250,000 shares are outstanding. The market price of the stock is $15 and net
income for the past year was $150,000.
a.. Calculate the book value of the firm.
b. Calculate the book value per share.
c. Calculate the P/E ratio.
5. A firm’s common stock is currently selling for $12.50 per share. The required rate of return is 9% and the
company will pay an annual dividend of $.50 per share one year from now which will grow at a constant rate
for the next several years. What is the growth rate?
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