this is a lecture on time value of money which explains the topic time value of money in a very easy and simple way... it also explains some examples on the topic... plus definition of rate of return, real rate of return, inflation premium, nominal interest rate,market risk, maturity risk,liquidity risk,and default risk,
International Capital BudgetingReview of Domestic Capita.docxnormanibarber20063
International Capital Budgeting
Review of Domestic Capital Budgeting
1.Identify the SIZE and TIMING of all relevant cash flows on a time line.
2.Identify the RISKINESS of the cash flows to determine the appropriate discount rate.
3.Find NPV by discounting the cash flows at the appropriate discount rate.
4.Compare the value of competing cash flow streams at the same point in time.
Review of Domestic Capital Budgeting
The basic net present value equation is
Where:
T = economic life of the project in years.
CFt = expected incremental after-tax cash flow in year t,
TVT = expected after tax terminal value including return of net working capital,
C0 = initial investment at inception,
K = weighted average cost of capital.
K = (1 – )Kl + (1 – t)i
The NPV rule is to accept a project if NPV 0
and to reject a project if NPV 0
Review of Domestic Capital Budgeting
For our purposes it is necessary to expand the NPV equation.
Rt = incremental revenue
OCt = incremental operating costs
Dt = incremental depreciation
It = incremental interest expense
= the marginal tax rate
CFt = (Rt – OCt – Dt – It)(1 – t) + Dt + It (1 – t)
Review of Domestic Capital Budgeting
Alternative Formulations CFt
CFt = (Rt – OCt – Dt – It)(1 – t) + Dt + It (1 – t)
CFt = NIt + Dt + It(1 – t)
CFt = (Rt – OCt – Dt)(1 – t) + Dt
CFt = NOIt(1 – t) + Dt
CFt = (Rt – OCt)(1 – t) + t Dt
CFt = OCFt(1 – t) + t Dt
We can use CFt = (OCFt)(1 – t) + t Dt
to restate the NPV equation
as:
NPV =
S
t = 1
T
CFt
(1 + K)t
– C0
TVT
(1 + K)T
+
NPV =
S
t = 1
T
(OCFt)(1 – t) + t Dt
(1 + K)t
– C0
TVT
(1 + K)T
+
Review of Domestic Capital Budgeting
The Adjusted Present Value Model
Can be converted to adjusted present value (APV)
NPV =
S
t = 1
T
(OCFt)(1 – t)
(1 + K)t
C0
TVT
(1 + K)T
+
t Dt
(1 + K)t
+
–
S
t = 1
T
APV =
S
t = 1
T
(OCFt)(1 – t)
(1 + Ku)t
C0
TVT
(1 + Ku)T
+
t Dt
(1 + i)t
+
–
t It
(1 + i)t
+
The APV model is a value additivity approach to capital budgeting. Each cash flow that is a source of value to the firm is considered individually.
Note that with the APV model, each cash flow is discounted at a rate that is appropriate to the riskiness of the cash flow.
APV =
S
t = 1
T
(OCFt)(1 – t)
(1 + Ku)t
C0
TVT
(1 + Ku)T
+
t Dt
(1 + i)t
+
–
t It
(1 + i)t
+
The Adjusted Present Value Model
Domestic APV Example
Consider this project, the timing and size of the incremental after-tax cash flows for an all-equity firm are:
01 2 3 4
-$1,000 $125 $250 $375 $500
The unlevered cost of equity is r0 = 10%:
= –$1000
= $125
= $250
= $375
I
= 10
NPV
APV =
S
t = 1
T
(OCFt)(1 – t)
(1 + Ku)t
C0
TVT
(1 + Ku)T
+
t Dt
(1 + i)t
+
–
t It
(1 + i)t
+
?
=
CF0
CF1
CF2
CF3
CF4
= $500
Domestic APV Example
Now, imagine that the firm finances the project with $600 of debt at r = 8%.
The tax rate is 40%, so they have an interest tax shield worth t×I = .40×$600×.08 = $19.20 each year.
Fair valuation of participating life insurance contracts with jump riskAlex Kouam
A C++ based program which prices the fair value of a participating life insurance whereby the underlying follows a Kou process and the insurer's default occurs only at contract's maturity.
this is a lecture on time value of money which explains the topic time value of money in a very easy and simple way... it also explains some examples on the topic... plus definition of rate of return, real rate of return, inflation premium, nominal interest rate,market risk, maturity risk,liquidity risk,and default risk,
International Capital BudgetingReview of Domestic Capita.docxnormanibarber20063
International Capital Budgeting
Review of Domestic Capital Budgeting
1.Identify the SIZE and TIMING of all relevant cash flows on a time line.
2.Identify the RISKINESS of the cash flows to determine the appropriate discount rate.
3.Find NPV by discounting the cash flows at the appropriate discount rate.
4.Compare the value of competing cash flow streams at the same point in time.
Review of Domestic Capital Budgeting
The basic net present value equation is
Where:
T = economic life of the project in years.
CFt = expected incremental after-tax cash flow in year t,
TVT = expected after tax terminal value including return of net working capital,
C0 = initial investment at inception,
K = weighted average cost of capital.
K = (1 – )Kl + (1 – t)i
The NPV rule is to accept a project if NPV 0
and to reject a project if NPV 0
Review of Domestic Capital Budgeting
For our purposes it is necessary to expand the NPV equation.
Rt = incremental revenue
OCt = incremental operating costs
Dt = incremental depreciation
It = incremental interest expense
= the marginal tax rate
CFt = (Rt – OCt – Dt – It)(1 – t) + Dt + It (1 – t)
Review of Domestic Capital Budgeting
Alternative Formulations CFt
CFt = (Rt – OCt – Dt – It)(1 – t) + Dt + It (1 – t)
CFt = NIt + Dt + It(1 – t)
CFt = (Rt – OCt – Dt)(1 – t) + Dt
CFt = NOIt(1 – t) + Dt
CFt = (Rt – OCt)(1 – t) + t Dt
CFt = OCFt(1 – t) + t Dt
We can use CFt = (OCFt)(1 – t) + t Dt
to restate the NPV equation
as:
NPV =
S
t = 1
T
CFt
(1 + K)t
– C0
TVT
(1 + K)T
+
NPV =
S
t = 1
T
(OCFt)(1 – t) + t Dt
(1 + K)t
– C0
TVT
(1 + K)T
+
Review of Domestic Capital Budgeting
The Adjusted Present Value Model
Can be converted to adjusted present value (APV)
NPV =
S
t = 1
T
(OCFt)(1 – t)
(1 + K)t
C0
TVT
(1 + K)T
+
t Dt
(1 + K)t
+
–
S
t = 1
T
APV =
S
t = 1
T
(OCFt)(1 – t)
(1 + Ku)t
C0
TVT
(1 + Ku)T
+
t Dt
(1 + i)t
+
–
t It
(1 + i)t
+
The APV model is a value additivity approach to capital budgeting. Each cash flow that is a source of value to the firm is considered individually.
Note that with the APV model, each cash flow is discounted at a rate that is appropriate to the riskiness of the cash flow.
APV =
S
t = 1
T
(OCFt)(1 – t)
(1 + Ku)t
C0
TVT
(1 + Ku)T
+
t Dt
(1 + i)t
+
–
t It
(1 + i)t
+
The Adjusted Present Value Model
Domestic APV Example
Consider this project, the timing and size of the incremental after-tax cash flows for an all-equity firm are:
01 2 3 4
-$1,000 $125 $250 $375 $500
The unlevered cost of equity is r0 = 10%:
= –$1000
= $125
= $250
= $375
I
= 10
NPV
APV =
S
t = 1
T
(OCFt)(1 – t)
(1 + Ku)t
C0
TVT
(1 + Ku)T
+
t Dt
(1 + i)t
+
–
t It
(1 + i)t
+
?
=
CF0
CF1
CF2
CF3
CF4
= $500
Domestic APV Example
Now, imagine that the firm finances the project with $600 of debt at r = 8%.
The tax rate is 40%, so they have an interest tax shield worth t×I = .40×$600×.08 = $19.20 each year.
Fair valuation of participating life insurance contracts with jump riskAlex Kouam
A C++ based program which prices the fair value of a participating life insurance whereby the underlying follows a Kou process and the insurer's default occurs only at contract's maturity.
[Note: This is a partial preview. To download this presentation, visit:
https://www.oeconsulting.com.sg/training-presentations]
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Leading companies such as Nike, Toyota, and Siemens are prioritizing sustainable innovation in their business models, setting an example for others to follow. In this Sustainability training presentation, you will learn key concepts, principles, and practices of sustainability applicable across industries. This training aims to create awareness and educate employees, senior executives, consultants, and other key stakeholders, including investors, policymakers, and supply chain partners, on the importance and implementation of sustainability.
LEARNING OBJECTIVES
1. Develop a comprehensive understanding of the fundamental principles and concepts that form the foundation of sustainability within corporate environments.
2. Explore the sustainability implementation model, focusing on effective measures and reporting strategies to track and communicate sustainability efforts.
3. Identify and define best practices and critical success factors essential for achieving sustainability goals within organizations.
CONTENTS
1. Introduction and Key Concepts of Sustainability
2. Principles and Practices of Sustainability
3. Measures and Reporting in Sustainability
4. Sustainability Implementation & Best Practices
To download the complete presentation, visit: https://www.oeconsulting.com.sg/training-presentations
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133chapter102002.ppt
1. Valuation and Rates of Return
(Chapter 10)
Valuation of Assets in General
Bond Valuation
Preferred Stock Valuation
Common Stock Valuation
2. Valuation of Assets in General
The following applies to any financial asset:
V = Current value of the asset
Ct = Expected future cash flow in period (t)
k = Investor’s required rate of return
Note: When analyzing various assets (e.g., bonds,
stocks), the formula below is simply modified
to fit the particular kind of asset being
evaluated.
V
C
k
t
t
t
n
( )
1
1
3. Valuation of Assets (Continued)
Determining Intrinsic Value:
– The intrinsic value of an asset (the perceived
value by an individual investor) is determined
by discounting all of the future cash flows back
to the present at the investor’s required rate of
return (i.e., Given the Ct’s and k, calculate V).
Determining Expected Rate of Return:
– Find that rate of discount at which the present
value of all future cash flows is exactly equal to
the current market value. (i.e., Given the Ct’s
and V, calculate k).
5. Bond Valuation
Pb = Price of the bond
It = Interest payment in period (t)
(Coupon interest)
Pn = Principal payment at maturity (par value)
Y = Bondholders’ required rate of return or
yield to maturity
Annual Discounting:
n
t
n
n
t
t
b
Y
P
Y
I
P
1 )
1
(
)
1
(
6. Bond Valuation (Continued)
Semiannual Discounting:
– Divide the annual interest payment by 2
– Divide the annual required rate of return by 2
– Multiply the number of years by 2
n
n
n
t
t
t
b
)
Y/
(
P
)
Y/
(
/
I
P 2
2
1 2
1
2
1
2
7. Determining Intrinsic Value
– The investor’s perceived value
– Given It, Pn, and Y, solve for Pb
Determining Yield to Maturity
– Expected rate of return
– Given It, Pn, and Pb, solve for Y
8. Calculating Yield to Maturity
Trial and Error: Keep guessing until you find
the rate whereby the present value of the interest
and principal payments is equal to the current
price of the bond. (necessary procedure without a
financial calculator or computer).
Easiest Approach: Use a computer or financial
calculator. Note, however, that it is extremely
important to understand the mechanics that go into
the calculations.
9. Relationship Between Interest Rates,
Time to Maturity, and Bond Prices
For both bonds shown below, the coupon rate is
10% (i.e., It = $100 and Pn = $1,000).
0
200
400
600
800
1000
1200
1400
1600
0 5 10 15 20 25
Bond Price
Yield to Maturity (Y) - Percent
5 year bond
20 year bond
10. Relationship Between Coupon Rate and
Yield to Maturity (Y) or Current
Interest Rates
1: When Y = coupon rate, Pb = Pn
2. When Y < coupon rate, Pb >Pn
– (Bond sells at a premium)
3. When Y > coupon rate, Pb < Pn
– (Bond sells at a discount)
Also Note: If interest rates (Y) go up, bond prices
drop, and vice versa. Furthermore, the longer the
maturity of the bond, the greater the price change
for any given change in interest rates.
11. Preferred Stock Valuation
Ordinary preferred stock usually represents a perpetuity (a
stream of equal dividend payments expected to continue
forever).
Pp = Price of the preferred stock
Dp = Annual dividend (a constant amount)
kp = Required rate of return
Determining Intrinsic Value:
2)
(Equation
k
D
P
)
k
(1
D
...
)
k
(1
D
)
k
(1
D
P
1)
(Equation
)
k
(1
D
P
p
p
p
p
p
2
p
p
1
p
p
p
1
t
t
p
p
p
12. Preferred Stock (Continued)
Algebraic proof that Equation 1 is equal to
Equation 2 on the previous slide when the
dividend is a constant amount can be found in
many finance texts.
Determining Expected Rate of Return:
p
p
p
P
D
k
13. Common Stock Valuation
1
t
t
e
t
0
e
t
0
)
k
(1
D
P
:
Model
Basic
return
of
rate
Required
k
(t)
year
in
expected
Dividends
D
price
stock
Common
P
14. Common Stock Valuation Continued
dividends.
future
of
function
a
is
P
that
however,
Note,
)
k
(1
P
)
k
(1
D
P
:
Period
Holding
Year
One
1
e
1
e
1
0
n
e
n
n
e
n
2
e
2
e
1
0
)
k
(1
P
)
k
(1
D
...
)
k
(1
D
)
k
(1
D
P
:
Years
(n)
of
Period
Holding
15. Constant Growth Rate Model
texts.
finance
many
in
found
be
can
equations
above
the
of
proof
Algebraic
:
Note
g
P
D
k
:
Return
of
Rate
Expected
g
k
g)
(1
D
g
k
D
P
:
Value
Intrinsic
0
1
e
e
0
e
1
0
16. Valuing Common Stock
Using Valuation Ratios
Price Per Share = (EPS)(P/E)
Price Per Share = (BV Per Share)(Price/Book)
Price Per Share = (Sales Per Share)(Price/Sales)