Day 78 examples u6f13
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This document provides examples of how to use logarithms to solve various financial and exponential growth problems. It includes examples of calculating how long it takes an investment to double at a given interest rate, determining the number of years it takes for one investment to equal another growing at different rates, calculating the number of monthly payments needed to reach a future value with compound interest, modeling population and radioactive decay with exponential functions, and converting between earthquake magnitude and intensity scales on a logarithmic scale.
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The document contains examples of applying logarithms and formulas to solve financial mathematics problems involving compound interest, loan repayment amounts, and calculating earthquake magnitudes on a logarithmic scale. It provides the formulas for future value of a lump sum, future value of an annuity, present value of an annuity, and converting between earthquake magnitude and intensity.
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This document discusses equations for sine and cosine wave functions that can be used to model periodic phenomena, with variables for amplitude (A), angular frequency (B), horizontal phase shift (C), and vertical shift (D), and notes that changing the coefficient of the angular frequency term (B) allows changing the period of the wave.
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MATH133 NAME:___Oscar Hernandez________
Individual Project Assignment
(Show your work for these calculations. Review http://www.purplemath.com/modules/mathtext.htmto see how to type mathematics using the keyboard symbols.)
Problem 1 – Photic Zone
Light entering water in a pond, lake, sea, or ocean will be absorbed or scattered by the particles in the water and its intensity will be attenuated by the depth of the water, x, in feet. Marine life in these ponds, lakes, seas, and oceans depend on microscopic plant life that exists in the photic zone. The photic zone is from the surface of the water down to a depth in that particular body of water where only 1% of the surface light remains unabsorbed or not scattered. The equation that models this light intensity is:
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a. Choose a value of kbetween 0.025 and 0.095.
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Page 1of 5
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1. This question is on the application of the Binomial option
1. This question is on the application of the Binomial option
pricing model.
PKZ stock is currently trading at 100. Over three-months it will either
go up by 6% or down by 5%. Interest rates are zero.
a. [25 marks] Using a two period binomial model to construct a delta-
hedged portfolio, price a six month European call option on PKZ
stock with a strike price of £105.
b. [3 Marks] Using your answer from the first part, together with the
put-call parity, price a put option on the same stock with same
strike and expiry.
COMP0041 SEE NEXT PAGE
2
2. This question is on the Binomial method in the limit δt → 0.
[40 Marks] The binomial model for pricing options leads to the for-
mula
V (S,t) = e−rδt [qV (US,t + δt) + (1 − q) V (DS,t + δt)]
where
U = eσ
√
δt, D = e−σ
√
δt, q =
erδt −D
U −D
.
V (S,t) is the option value, t is the time, S is the spot price, σ is volatil-
ity and r is the risk-free rate.
By carefully expanding U,D,q as Taylor series in δt or
√
δt (as appro-
priate) and then expanding V (US,t + δt) and V (DS,t + δt) as Taylor
series in both their arguments, deduce that to O (δt) ,
∂V
∂t
+
1
2
σ2S2
∂2V
∂S2
+ rS
∂V
∂S
− rV = 0.
COMP0041 SEE NEXT PAGE
3
3. This question is on probability and Monte Carlo
a. Consider theprobabilitydensity function p (x) fora randomvariable
X given by
p (x) =
{
µ exp (−µx) x ≥ 0
0 x < 0
where µ (> 0) is a constant.
i. [15 Marks] Show that for this probability density function
E
[
eθX
]
=
(
1 −
θ
µ
)−1
Hint: You may assume µ > θ in obtaining this result.
ii. [20 Marks] By expanding
(
1 −
θ
µ
)−1
as a Taylor series, show
that
E [xn] =
n!
µn
, n = 0, 1, 2, ....
iii. [15 Marks] Hence calculate the skew and kurtosis for X.
COMP0041 CONTINUED ON NEXT PAGE
4
b. [32 Marks] An Exchange Option gives the holder the right to
exchange one asset for another. The discounted payoff for this
contract V is
V = e−rT max (S1 (T) −S2 (T) , 0) .
The option price is then given by θ = E [V ] where
Si (t) = Si (0) e
(r−12σ
2
i )t+σiφi
√
t
for i = 1, 2, and φi ∼ N (0, 1) with correlation coeffi cient ρ.
Youmayassumethatauniformrandomnumbergenerator isavail-
able. Use a Cholesky factorisation method to show(
φ1
φ2
)
=
(
1 0
ρ
√
1 −ρ2
)(
x1
x2
)
,
where
(
x1
x2
)
is a vector of independent N (0, 1) variables and
has the same distribution as
(
φ1
φ2
)
.
Give a Monte Carlo simulation algorithm that makes use of anti-
thetic variates for the estimation of θ.
COMP0041 SEE NEXT PAGE
5
4. This question is on finite differences
a. [30 Marks] Consider a forward difference operator, ∆, such that
∆V (S) = V (S + h) −V (S) , (4.1)
where h is an infinitessimal. By introducing the operators
D ≡
∂
∂S
; D2 ≡
∂2
∂S2
show that
∆ ≡ ehD −1 (4.2)
where 1 is the identity operator. Hint: start by doing a Taylor
expansion on V (S + h) .
By rearranging (4.2) show that
D =
1
h
(
∆ −
∆2
2
+
∆3
3
−
∆4
4
+ O
(
∆5
))
.
Hence obtain the second order approximation for
∂V
...
1. This question is on the application of the Binomial option
1. This question is on the application of the Binomial option
pricing model.
PKZ stock is currently trading at 100. Over three-months it will either
go up by 6% or down by 5%. Interest rates are zero.
a. [25 marks] Using a two period binomial model to construct a delta-
hedged portfolio, price a six month European call option on PKZ
stock with a strike price of £105.
b. [3 Marks] Using your answer from the first part, together with the
put-call parity, price a put option on the same stock with same
strike and expiry.
COMP0041 SEE NEXT PAGE
2
2. This question is on the Binomial method in the limit δt → 0.
[40 Marks] The binomial model for pricing options leads to the for-
mula
V (S,t) = e−rδt [qV (US,t + δt) + (1 − q) V (DS,t + δt)]
where
U = eσ
√
δt, D = e−σ
√
δt, q =
erδt −D
U −D
.
V (S,t) is the option value, t is the time, S is the spot price, σ is volatil-
ity and r is the risk-free rate.
By carefully expanding U,D,q as Taylor series in δt or
√
δt (as appro-
priate) and then expanding V (US,t + δt) and V (DS,t + δt) as Taylor
series in both their arguments, deduce that to O (δt) ,
∂V
∂t
+
1
2
σ2S2
∂2V
∂S2
+ rS
∂V
∂S
− rV = 0.
COMP0041 SEE NEXT PAGE
3
3. This question is on probability and Monte Carlo
a. Consider theprobabilitydensity function p (x) fora randomvariable
X given by
p (x) =
{
µ exp (−µx) x ≥ 0
0 x < 0
where µ (> 0) is a constant.
i. [15 Marks] Show that for this probability density function
E
[
eθX
]
=
(
1 −
θ
µ
)−1
Hint: You may assume µ > θ in obtaining this result.
ii. [20 Marks] By expanding
(
1 −
θ
µ
)−1
as a Taylor series, show
that
E [xn] =
n!
µn
, n = 0, 1, 2, ....
iii. [15 Marks] Hence calculate the skew and kurtosis for X.
COMP0041 CONTINUED ON NEXT PAGE
4
b. [32 Marks] An Exchange Option gives the holder the right to
exchange one asset for another. The discounted payoff for this
contract V is
V = e−rT max (S1 (T) −S2 (T) , 0) .
The option price is then given by θ = E [V ] where
Si (t) = Si (0) e
(r−12σ
2
i )t+σiφi
√
t
for i = 1, 2, and φi ∼ N (0, 1) with correlation coeffi cient ρ.
Youmayassumethatauniformrandomnumbergenerator isavail-
able. Use a Cholesky factorisation method to show(
φ1
φ2
)
=
(
1 0
ρ
√
1 −ρ2
)(
x1
x2
)
,
where
(
x1
x2
)
is a vector of independent N (0, 1) variables and
has the same distribution as
(
φ1
φ2
)
.
Give a Monte Carlo simulation algorithm that makes use of anti-
thetic variates for the estimation of θ.
COMP0041 SEE NEXT PAGE
5
4. This question is on finite differences
a. [30 Marks] Consider a forward difference operator, ∆, such that
∆V (S) = V (S + h) −V (S) , (4.1)
where h is an infinitessimal. By introducing the operators
D ≡
∂
∂S
; D2 ≡
∂2
∂S2
show that
∆ ≡ ehD −1 (4.2)
where 1 is the identity operator. Hint: start by doing a Taylor
expansion on V (S + h) .
By rearranging (4.2) show that
D =
1
h
(
∆ −
∆2
2
+
∆3
3
−
∆4
4
+ O
(
∆5
))
.
Hence obtain the second order approximation for
∂V
...
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The Nelson Company has $1,312,500 in current assets and $525,000 in current liabilities. Its initial inventory level is $375,000, and it will raise funds as additional notes payable and use them to increase inventory. How much can Nelson’s short-term debt (notes payable) increase without pushing its current ratio below 2.0? What will be the firm’s quick ratio after Nelson has raised the maximum amount of short-term funds?
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The Morris Corporation has $600,000 of debt outstanding, and it pays an interest rate of 8% annually. Morris’s annual sales are $3 million, its average tax rate is 40%, and its net profit margin on sales is 3%. If the company does not maintain a TIE ratio of at least 5 to 1, then its bank will refuse to renew the loan and bankruptcy will result. What is Morris’s TIE ratio?
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What is the future value of a 7%, 5-year ordinary annuity that pays $300 each year? If this were an annuity due, what would its future value be?
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What is the future v ...
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MATH133 .docx
MATH133 NAME:___Oscar Hernandez________
Individual Project Assignment
(Show your work for these calculations. Review http://www.purplemath.com/modules/mathtext.htmto see how to type mathematics using the keyboard symbols.)
Problem 1 – Photic Zone
Light entering water in a pond, lake, sea, or ocean will be absorbed or scattered by the particles in the water and its intensity will be attenuated by the depth of the water, x, in feet. Marine life in these ponds, lakes, seas, and oceans depend on microscopic plant life that exists in the photic zone. The photic zone is from the surface of the water down to a depth in that particular body of water where only 1% of the surface light remains unabsorbed or not scattered. The equation that models this light intensity is:
In this exponential function, is the intensity of the light at the surface of the water, k is a constant based on the absorbing or scattering materials in that body of water and is usually called the coefficient of extinction, e is the natural number e ≅2.718282, and is the light intensity at x feet below the surface of the water.
a. Choose a value of kbetween 0.025 and 0.095.
b. In a certain lake the value of k has been determined to be the value you chose above, which means that 100k% of the surface light is absorbed every foot of depth. For example, if you chose 0.062, then 6.2% of the light would be absorbed every foot of depth. What is the intensity of light at a depth of 10 feet if the surface intensity is foot candles? (Correctly round your answer to one decimal place and show the intermediate steps in your work.)
c. What is the depth of the photic zone for this lake? (Hint: , so ; solve this equation for x. Correctly round your answer to one decimal place and show the intermediate steps in your work.)
Problem 2 – Compound Interest
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Page 1of 5
A is the amount you will have after t years the money is invested, P is the principal (the initial amount of money invested), r is the decimal equivalent of the annual interest rate (divide the interest rate by 100), and n is the number of times the interest is compounded in ONE year. For the compounding continuously situation, the formula is:
A is the amount you will have after t years for principal, P, invested at r decimal equivalent annual interest rate compounded continuously.
Based on the first letter of your last name, choose values from the table below for P dollars and r percent.
If your last name begins
with the letter
Choose an investment amount,
P, dollars between ...
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The document discusses exponential growth and decay models. Exponential growth models take the form y = C(1+r)t, where C is the initial amount, r is the growth rate, and t is time. Exponential decay models take the form y = C(1-r)t, where C is the initial amount, r is the decay rate, and t is time. Examples are provided to demonstrate how to write the models, identify the key variables, and solve problems using exponential growth and decay equations.
Pre-Cal 40S Slides November 21(pm), 2007
Exponential growth refers to the rapid increase in the size of a quantity that is proportional to its current size. The document provides an example of a colony of flibberdejibbets that initially has 2 million members and increases by 20% every 4 hours. After treatment to slow the growth rate, it now takes 3 times as long for the colony to double in size. The question is how long will it take for the colony size to reach 12 million members after the treatment.
Continuosly compound interest and a comparison of exponential growth phenomena
The document discusses compound interest and continuous compound interest formulas. It provides examples of calculating balances with different compounding periods (annually, quarterly, monthly, etc.). It then introduces the continuous compounding formula A=Pe^rt and provides examples of using it to calculate balances over time at given interest rates. It compares exponential growth to polynomial and linear growth, showing that exponential functions eventually exceed other functions as x approaches infinity due to the power of compounding.
Estimating quantities
This document provides a summary of upcoming classroom activities and assignments:
1) A mid-unit summative exam on properties of exponents will take place.
2) MAP testing is scheduled for today at 10:00.
3) IXL online learning platform is now available for students to use.
4) There will be no school on September 4th or 7th.
5) Students should watch recording and submit assignment summaries if unable to attend class.
Exponential growth and decay
The document discusses exponential growth and decay models. Exponential growth models use the formula y = C(1 + r)t, where C is the initial amount, t is time, r is the growth rate, and (1 + r) is the growth factor. Exponential decay models use the formula y = C(1 - r)t, where (1 - r) is the decay factor and r is the decay rate. Examples are provided to demonstrate how to write, graph, and apply these models to problems involving compound interest, population growth, radioactive decay, and purchasing power.
Exponential growth and decay
The document discusses exponential growth and decay models. Exponential growth models use the formula y = C(1 + r)t, where C is the initial amount, t is time, r is the growth rate, and (1 + r) is the growth factor. Exponential decay models use the formula y = C(1 - r)t, where (1 - r) is the decay factor and r is the decay rate. Examples are provided to demonstrate how to write, graph, and apply these models to problems involving compound interest, population growth, radioactive decay, and purchasing power.
4.6 Exponential Growth and Decay
This document discusses exponential growth and decay functions. It provides examples of how to set up and solve exponential equations to model population growth, fish population decline, world poultry production increase, and bacterial growth. It also explains how to calculate half-life and doubling time for exponential decay and growth. Examples are worked through to find the half-life of tritium decaying at 5.471% per year and a radioactive substance decaying at 11% per minute, and to determine the amount of radioactive substance remaining after 6 years given its half-life is 3 years. The document concludes with assignments for students.
1. This question is on the application of the Binomial option
1. This question is on the application of the Binomial option
pricing model.
PKZ stock is currently trading at 100. Over three-months it will either
go up by 6% or down by 5%. Interest rates are zero.
a. [25 marks] Using a two period binomial model to construct a delta-
hedged portfolio, price a six month European call option on PKZ
stock with a strike price of £105.
b. [3 Marks] Using your answer from the first part, together with the
put-call parity, price a put option on the same stock with same
strike and expiry.
COMP0041 SEE NEXT PAGE
2
2. This question is on the Binomial method in the limit δt → 0.
[40 Marks] The binomial model for pricing options leads to the for-
mula
V (S,t) = e−rδt [qV (US,t + δt) + (1 − q) V (DS,t + δt)]
where
U = eσ
√
δt, D = e−σ
√
δt, q =
erδt −D
U −D
.
V (S,t) is the option value, t is the time, S is the spot price, σ is volatil-
ity and r is the risk-free rate.
By carefully expanding U,D,q as Taylor series in δt or
√
δt (as appro-
priate) and then expanding V (US,t + δt) and V (DS,t + δt) as Taylor
series in both their arguments, deduce that to O (δt) ,
∂V
∂t
+
1
2
σ2S2
∂2V
∂S2
+ rS
∂V
∂S
− rV = 0.
COMP0041 SEE NEXT PAGE
3
3. This question is on probability and Monte Carlo
a. Consider theprobabilitydensity function p (x) fora randomvariable
X given by
p (x) =
{
µ exp (−µx) x ≥ 0
0 x < 0
where µ (> 0) is a constant.
i. [15 Marks] Show that for this probability density function
E
[
eθX
]
=
(
1 −
θ
µ
)−1
Hint: You may assume µ > θ in obtaining this result.
ii. [20 Marks] By expanding
(
1 −
θ
µ
)−1
as a Taylor series, show
that
E [xn] =
n!
µn
, n = 0, 1, 2, ....
iii. [15 Marks] Hence calculate the skew and kurtosis for X.
COMP0041 CONTINUED ON NEXT PAGE
4
b. [32 Marks] An Exchange Option gives the holder the right to
exchange one asset for another. The discounted payoff for this
contract V is
V = e−rT max (S1 (T) −S2 (T) , 0) .
The option price is then given by θ = E [V ] where
Si (t) = Si (0) e
(r−12σ
2
i )t+σiφi
√
t
for i = 1, 2, and φi ∼ N (0, 1) with correlation coeffi cient ρ.
Youmayassumethatauniformrandomnumbergenerator isavail-
able. Use a Cholesky factorisation method to show(
φ1
φ2
)
=
(
1 0
ρ
√
1 −ρ2
)(
x1
x2
)
,
where
(
x1
x2
)
is a vector of independent N (0, 1) variables and
has the same distribution as
(
φ1
φ2
)
.
Give a Monte Carlo simulation algorithm that makes use of anti-
thetic variates for the estimation of θ.
COMP0041 SEE NEXT PAGE
5
4. This question is on finite differences
a. [30 Marks] Consider a forward difference operator, ∆, such that
∆V (S) = V (S + h) −V (S) , (4.1)
where h is an infinitessimal. By introducing the operators
D ≡
∂
∂S
; D2 ≡
∂2
∂S2
show that
∆ ≡ ehD −1 (4.2)
where 1 is the identity operator. Hint: start by doing a Taylor
expansion on V (S + h) .
By rearranging (4.2) show that
D =
1
h
(
∆ −
∆2
2
+
∆3
3
−
∆4
4
+ O
(
∆5
))
.
Hence obtain the second order approximation for
∂V
...
1. This question is on the application of the Binomial option
1. This question is on the application of the Binomial option
pricing model.
PKZ stock is currently trading at 100. Over three-months it will either
go up by 6% or down by 5%. Interest rates are zero.
a. [25 marks] Using a two period binomial model to construct a delta-
hedged portfolio, price a six month European call option on PKZ
stock with a strike price of £105.
b. [3 Marks] Using your answer from the first part, together with the
put-call parity, price a put option on the same stock with same
strike and expiry.
COMP0041 SEE NEXT PAGE
2
2. This question is on the Binomial method in the limit δt → 0.
[40 Marks] The binomial model for pricing options leads to the for-
mula
V (S,t) = e−rδt [qV (US,t + δt) + (1 − q) V (DS,t + δt)]
where
U = eσ
√
δt, D = e−σ
√
δt, q =
erδt −D
U −D
.
V (S,t) is the option value, t is the time, S is the spot price, σ is volatil-
ity and r is the risk-free rate.
By carefully expanding U,D,q as Taylor series in δt or
√
δt (as appro-
priate) and then expanding V (US,t + δt) and V (DS,t + δt) as Taylor
series in both their arguments, deduce that to O (δt) ,
∂V
∂t
+
1
2
σ2S2
∂2V
∂S2
+ rS
∂V
∂S
− rV = 0.
COMP0041 SEE NEXT PAGE
3
3. This question is on probability and Monte Carlo
a. Consider theprobabilitydensity function p (x) fora randomvariable
X given by
p (x) =
{
µ exp (−µx) x ≥ 0
0 x < 0
where µ (> 0) is a constant.
i. [15 Marks] Show that for this probability density function
E
[
eθX
]
=
(
1 −
θ
µ
)−1
Hint: You may assume µ > θ in obtaining this result.
ii. [20 Marks] By expanding
(
1 −
θ
µ
)−1
as a Taylor series, show
that
E [xn] =
n!
µn
, n = 0, 1, 2, ....
iii. [15 Marks] Hence calculate the skew and kurtosis for X.
COMP0041 CONTINUED ON NEXT PAGE
4
b. [32 Marks] An Exchange Option gives the holder the right to
exchange one asset for another. The discounted payoff for this
contract V is
V = e−rT max (S1 (T) −S2 (T) , 0) .
The option price is then given by θ = E [V ] where
Si (t) = Si (0) e
(r−12σ
2
i )t+σiφi
√
t
for i = 1, 2, and φi ∼ N (0, 1) with correlation coeffi cient ρ.
Youmayassumethatauniformrandomnumbergenerator isavail-
able. Use a Cholesky factorisation method to show(
φ1
φ2
)
=
(
1 0
ρ
√
1 −ρ2
)(
x1
x2
)
,
where
(
x1
x2
)
is a vector of independent N (0, 1) variables and
has the same distribution as
(
φ1
φ2
)
.
Give a Monte Carlo simulation algorithm that makes use of anti-
thetic variates for the estimation of θ.
COMP0041 SEE NEXT PAGE
5
4. This question is on finite differences
a. [30 Marks] Consider a forward difference operator, ∆, such that
∆V (S) = V (S + h) −V (S) , (4.1)
where h is an infinitessimal. By introducing the operators
D ≡
∂
∂S
; D2 ≡
∂2
∂S2
show that
∆ ≡ ehD −1 (4.2)
where 1 is the identity operator. Hint: start by doing a Taylor
expansion on V (S + h) .
By rearranging (4.2) show that
D =
1
h
(
∆ −
∆2
2
+
∆3
3
−
∆4
4
+ O
(
∆5
))
.
Hence obtain the second order approximation for
∂V
...
Day 7 examples
This document discusses compound interest problems and provides examples of calculations to solve for compound interest over time. It defines the general compound interest formula and explains that interest can be compounded annually or monthly. Three example problems are given to demonstrate calculating the time needed for an investment to double in value, the number of years for one investment to equal the value of another, and the number of monthly deposits needed to reach a future value, all using compound interest rates.
Day 7 examples
This document discusses compound interest problems and provides examples of calculations using the compound interest formula. It defines the general compound interest formula and explains annual and monthly compounding. Examples are given of calculating how long it would take an investment to double at a given interest rate, comparing the future values of different initial investments with different interest rates compounded annually, and calculating monthly investments needed to reach a future value at a given interest rate compounded monthly.
Principles of Macroeconomics
I am Ryan J. I am a Macroeconomics Homework Helper at economicshomeworkhelper.com/. I hold a PhD in M.S. Economics, University of Maine. I have been helping students with their homework for past 7 years. I solve assignments related to Macroeconomics Assignment.
Visit economicshomeworkhelper.com or email info@economicshomeworkhelper.com .
You can also call on +1 678 648 4277 for any assistance with Macroeconomics homework help.
The National Debt
The document discusses national debt and deficits. It notes that the US national debt in 2005 was $9.1 trillion, and provides comparisons to illustrate just how large that number is. It explains that deficits, which occur when government spending exceeds tax revenue, are added to the debt over time. While debt can be useful in some cases, like home mortgages, large deficits and growing debt are a concern because they require higher tax revenue or interest payments over time.
Real Money? Islamic Money?
Based on my own reading and understanding of the works of Prof. Kameel Mydin Meera and Thomas H. Greco on this important topic.
Pre-Cal 40S Slides April 12, 2007
The document discusses exponential modeling using different bases. It provides examples of modeling population growth, bacterial colony growth, radioactive decay, compound interest, and more. Exponential functions are used to model situations where a quantity changes by a constant factor over equal time periods. The base represents the common factor by which the quantity is multiplied each period.
(2-3)Income StatementMolteni Motors Inc. recently reported $6 mi.docx
(2-3)Income Statement
Molteni Motors Inc. recently reported $6 million of net income. Its EBIT was $13 million, and its tax rate was 40%. What was its interest expense? (Hint: Write out the headings for an income statement, and then fill in the known values. Then divide $6 million net income by 1 − T = 0.6 to find the pre-tax income. The difference between EBIT and taxable income must be the interest expense. Use this procedure to work some of the other problems.)
(2-5)Net Cash Flow
Kendall Corners Inc. recently reported net income of $3.1 million and depreciation of $500,000. What was its net cash flow? Assume it had no amortization expense.
(2-6) Statement of Retained Earnings
In its most recent financial statements, Del-Castillo Inc. reported $70 million of net income and $900 million of retained earnings. The previous retained earnings were $855 million. How much in dividends did the firm pay to shareholders during the year?
(3-2) Debt Ratio
Vigo Vacations has $200 million in total assets, $5 million in notes payable, and $25 million in long-term debt. What is the debt ratio?
(3-4) Price/Earnings Ratio
Reno Revolvers has an EPS of $1.50, a cash flow per share of $3.00, and a price/cash flow ratio of 8.0. What is its P/E ratio?
(3-5) ROE
Needham Pharmaceuticals has a profit margin of 3% and an equity multiplier of 2.0. Its sales are $100 million and it has total assets of $50 million. What is its ROE?
(3-8) Profit Margin and Debt Ratio
Assume you are given the following relationships for the Haslam Corporation:
Sales/total assets 1.2
Return on assets (ROA) 4%
Return on equity (ROE) 7%
Calculate Haslam’s profit margin and liabilities-to-assets ratio. Suppose half its liabilities are in the form of debt. Calculate the debt-to-assets ratio.
(3-9) Current and Quick Ratios
The Nelson Company has $1,312,500 in current assets and $525,000 in current liabilities. Its initial inventory level is $375,000, and it will raise funds as additional notes payable and use them to increase inventory. How much can Nelson’s short-term debt (notes payable) increase without pushing its current ratio below 2.0? What will be the firm’s quick ratio after Nelson has raised the maximum amount of short-term funds?
(3-10) Times-Interest-Earned Ratio
The Morris Corporation has $600,000 of debt outstanding, and it pays an interest rate of 8% annually. Morris’s annual sales are $3 million, its average tax rate is 40%, and its net profit margin on sales is 3%. If the company does not maintain a TIE ratio of at least 5 to 1, then its bank will refuse to renew the loan and bankruptcy will result. What is Morris’s TIE ratio?
(4-6) Future Value: Ordinary Annuity versus Annuity Due
What is the future value of a 7%, 5-year ordinary annuity that pays $300 each year? If this were an annuity due, what would its future value be?
(4-10) Present and Future, Values of Single Cash, Flows for Different, Interest Rates
What is the future v ...
The National Debt
The document discusses national debt and deficits. It notes that the US national debt was $5.6 trillion in 1999 and $12.8 trillion in 2010. It explains that debt is the accumulation of yearly deficits and surpluses, with deficits added to the debt and surpluses reducing it. The document also discusses "pork barrel" spending projects by Congress and debates around taxation and proportional versus progressive tax systems.
Similar to Day 78 examples u6f13 (19)
Continuosly compound interest and a comparison of exponential growth phenomena
Continuosly compound interest and a comparison of exponential growth phenomena
1. This question is on the application of the Binomial option
1. This question is on the application of the Binomial option
1. This question is on the application of the Binomial option
1. This question is on the application of the Binomial option
(2-3)Income StatementMolteni Motors Inc. recently reported $6 mi.docx
(2-3)Income StatementMolteni Motors Inc. recently reported $6 mi.docx
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Combs perms review pascals
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Permutations refer to arrangements of objects in a definite order. Some key points:
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- Permutations are used to calculate possibilities like license plates, phone numbers, and locker combinations.
- Restrictions like starting/ending conditions or requiring alternating arrangements reduce the number of possible permutations.
- Objects that are identical only count once toward the total number of permutations rather than being distinguishable.
Day 2 examples u7w14
Factorial notation represents the product of all positive integers less than or equal to the given number. For example, 5! = 5 x 4 x 3 x 2 x 1 and 8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1. The document also provides examples of simplifying factorials without a calculator by using properties such as 5! + 4! = 6 x 4! and (k + 1)! + k! = (k + 2)k!.
Day 1 examples u7w14
This document provides examples and explanations of the fundamental counting principle and addition counting principle to solve combinatorics problems. It gives 8 examples of using the fundamental counting principle to count the number of possible outcomes of independent events. These include counting the number of volleyball shoe combinations, outfits that can be created from different clothing items, ways to select committees from groups of people, and 3-digit numbers with no repeating digits. It also provides 5 examples of using the addition counting principle to count outcomes when events are dependent, such as selecting a president and vice president of opposite sexes from a group.
Day 7 examples u6w14
This document discusses graphing composite functions. It provides examples of determining the composite functions f(g(x)) and g(f(x)) for various functions f(x) and g(x), sketching the graphs of the composite functions, and stating their domains. It also gives examples of determining possible functions f(x) and g(x) that satisfy given composite functions.
Day 5 examples u6w14
1. The document discusses composite functions, which involve combining two functions f(x) and g(x) where the output of one is used as the input of the other. It provides examples of evaluating composite functions using tables and graphs.
2. Key steps for evaluating composite functions are: 1) Substitute the inner function into the outer function and 2) Simplify the expression. Order matters as f(g(x)) and g(f(x)) may have different values.
3. Examples are worked through to find composite functions given basic functions like f(x) = x + 1 and g(x) = 2x as well as more complex rational functions.
Day 4 examples u6w14
The graph is a linear function with a domain of all real numbers and a range of real numbers greater than or equal to 3. The graph is a line with a y-intercept of 3 that increases at a rate of 1 as x increases.
Day 3 examples u6w14
Rational functions are functions of the form f(x) = p(x)/q(x) where p(x) and q(x) are polynomials. For example, comparing rational functions like 2x/(x^2 - 4) and (x-1)/(x+1). Horizontal asymptotes of rational functions occur when the degree of the polynomial in the numerator is less than the degree of the polynomial in the denominator.
Day 2 examples u6w14
This document discusses combining functions by graphing. When two functions f(x) and g(x) are combined, their graphs are overlayed on the same coordinate plane. The result is a new combined function where the output is determined by applying both functions f(x) and g(x) to the same input x.
Day 1 examples u6w14
This document discusses how to find the sum, difference, product, and quotient of functions. The sum of functions is found by adding the y-coordinates of each function. The difference is found by subtracting the y-coordinates. The product is represented as h(x) = f(x)g(x) and the quotient is represented as h(x) = f(x)/g(x). Examples are provided for adding and subtracting functions.
Mental math test outline
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Day 8 examples u5w14
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Day 7 examples u5w14
The document provides 3 polynomial word problems: 1) finding the equation for a polynomial given its graph f(x) = -(x - 2)2(x + 1), 2) determining the polynomial P(x) when divided by (x - 3) with a quotient of 2x^2 + x - 6 and remainder of 4, and 3) finding the value of a if (x - 2) is a factor of ax^3 + 4x^2 + x - 2. It also gives a 4th problem of determining the value of k when 2x^3 + kx^2 - 3x + 2 is divided by x - 2 with a remainder of 4.
Day 5 examples u5w14
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一比一原版新西兰奥塔哥大学毕业证（otago毕业证）如何办理
一模一样【微信：A575476】【新西兰奥塔哥大学毕业证（otago毕业证）成绩单Offer】【微信：A575476】（留信学历认证永久存档查询）采用学校原版纸张、特殊工艺完全按照原版一比一制作（包括：隐形水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠，文字图案浮雕，激光镭射，紫外荧光，温感，复印防伪）行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备，十五年致力于帮助留学生解决难题，业务范围有加拿大、英国、澳洲、韩国、美国、新加坡，新西兰等学历材料，包您满意。
【业务选择办理准则】
一、工作未确定，回国需先给父母、亲戚朋友看下文凭的情况，办理一份就读学校的毕业证【微信：A575476】文凭即可
二、回国进私企、外企、自己做生意的情况，这些单位是不查询毕业证真伪的，而且国内没有渠道去查询国外文凭的真假，也不需要提供真实教育部认证。鉴于此，办理一份毕业证【微信：A575476】即可
三、进国企，银行，事业单位，考公务员等等，这些单位是必需要提供真实教育部认证的，办理教育部认证所需资料众多且烦琐，所有材料您都必须提供原件，我们凭借丰富的经验，快捷的绿色通道帮您快速整合材料，让您少走弯路。
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
→ 【关于价格问题（保证一手价格）
我们所定的价格是非常合理的，而且我们现在做得单子大多数都是代理和回头客户介绍的所以一般现在有新的单子 我给客户的都是第一手的代理价格，因为我想坦诚对待大家 不想跟大家在价格方面浪费时间
对于老客户或者被老客户介绍过来的朋友，我们都会适当给一些优惠。
选择实体注册公司办理，更放心，更安全！我们的承诺：可来公司面谈，可签订合同，会陪同客户一起到教育部认证窗口递交认证材料，客户在教育部官方认证查询网站查询到认证通过结果后付款，不成功不收费！
Part 2 Deep Dive: Navigating the 2024 Slowdown
Introduction
The global retail industry has weathered numerous storms, with the financial crisis of 2008 serving as a poignant reminder of the sector's resilience and adaptability. However, as we navigate the complex landscape of 2024, retailers face a unique set of challenges that demand innovative strategies and a fundamental shift in mindset. This white paper contrasts the impact of the 2008 recession on the retail sector with the current headwinds retailers are grappling with, while offering a comprehensive roadmap for success in this new paradigm.
Best Forex Brokers Comparison in INDIA 2024
Navigating the world of forex trading can be challenging, especially for beginners. To help you make an informed decision, we have comprehensively compared the best forex brokers in India for 2024. This article, reviewed by Top Forex Brokers Review, will cover featured award winners, the best forex brokers, featured offers, the best copy trading platforms, the best forex brokers for beginners, the best MetaTrader brokers, and recently updated reviews. We will focus on FP Markets, Black Bull, EightCap, IC Markets, and Octa.
Digital Transformation Frameworks: Driving Digital Excellence
[To download this presentation, visit:
https://www.oeconsulting.com.sg/training-presentations]
This presentation is a curated compilation of PowerPoint diagrams and templates designed to illustrate 20 different digital transformation frameworks and models. These frameworks are based on recent industry trends and best practices, ensuring that the content remains relevant and up-to-date.
Key highlights include Microsoft's Digital Transformation Framework, which focuses on driving innovation and efficiency, and McKinsey's Ten Guiding Principles, which provide strategic insights for successful digital transformation. Additionally, Forrester's framework emphasizes enhancing customer experiences and modernizing IT infrastructure, while IDC's MaturityScape helps assess and develop organizational digital maturity. MIT's framework explores cutting-edge strategies for achieving digital success.
These materials are perfect for enhancing your business or classroom presentations, offering visual aids to supplement your insights. Please note that while comprehensive, these slides are intended as supplementary resources and may not be complete for standalone instructional purposes.
Frameworks/Models included:
Microsoft’s Digital Transformation Framework
McKinsey’s Ten Guiding Principles of Digital Transformation
Forrester’s Digital Transformation Framework
IDC’s Digital Transformation MaturityScape
MIT’s Digital Transformation Framework
Gartner’s Digital Transformation Framework
Accenture’s Digital Strategy & Enterprise Frameworks
Deloitte’s Digital Industrial Transformation Framework
Capgemini’s Digital Transformation Framework
PwC’s Digital Transformation Framework
Cisco’s Digital Transformation Framework
Cognizant’s Digital Transformation Framework
DXC Technology’s Digital Transformation Framework
The BCG Strategy Palette
McKinsey’s Digital Transformation Framework
Digital Transformation Compass
Four Levels of Digital Maturity
Design Thinking Framework
Business Model Canvas
Customer Journey Map
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Day 78 examples u6f13
- 1. Applications of Logarithms Ex) If you invest any amount of money at 11.25% compounded quarterly, how long will it take to DOUBLE? r A = P(1 + n )nt
- 2. Ex) Craig invests $1000 in a mutual fund which is supposed to grow at 10% compounded annually. Laura has concerns about the stock market so she buys $2000 worth of bonds paying 5% compounded annually. After how many years will Craig's investment be equal in value to Laura's?
- 3. Ex) Determine how many monthly investments of $200 would have to be made into an account that pays 6% annual interest, compounded monthly, for the future value to be $100,000. FV = R[(1 + i)n - 1] i
- 4. Ex) A person borrows $15000 to buy a car. The person can afford to pay $300 a month. The loan will be repaid with equal monthly payments at 6% annual interest, compounded monthly. How many monthly payments will the person make? PV = R[1 - (1 + i)-n] i
- 5. Continuous Growth + Decay Problems Ex) The population of a certain country is 28 million and grows continuously at a rate of 3% annually. How many years will it take for the population to reach 40 million? A = Pert
- 6. Ex) A radioactive substance decays so that the amount present is "P" grams after "t" years according to the following: P = 50e-0.135t. What is the half life of the substance? Half life = the amount of time it takes for the substance to decay to half its original amount.
- 7. Logarithmic Scale Problems Ex) The most intense earthquake ever recorded was in Chile in May 1960, with magnitude 9.5. In January 2010, Haiti experienced an earthquake with magnitude 7.0. a) Calculate the intensity of the Haiti earthquake in terms of a standard earthquake. b) Calculate the intensity of the Chile earthquake in terms of a standard earthquake. c) How many times as intense as the Haiti earthquake was the Chile earthquake? Give answer to the nearest whole number. M = log( I ) S