Future Value of Annuity | Assignment

Running head: QUESTION
Question
Name of the Student:
Name of the University:
Author Note:

1QUESTION
Table of Contents
Answer 1:...................................................................................................................................2
Part a:.....................................................................................................................................2
Part b:.....................................................................................................................................3
Part c:.....................................................................................................................................3
Answer 2:...................................................................................................................................4
Part a:.....................................................................................................................................4
Part b:.....................................................................................................................................5
Part c:.....................................................................................................................................5
Answer 3:...................................................................................................................................6
Part a:.....................................................................................................................................6
Part b:.....................................................................................................................................7
Part c:.....................................................................................................................................7
Answer 4:...................................................................................................................................8
Part a:.....................................................................................................................................8
Part b:.....................................................................................................................................8
Part c:...................................................................................................................................10

2QUESTION
Answer 1:
Part a:
The calculation of the monthly payments would require the use of the following formula
which is presented below in the following steps,
Step 1: Calculation of future Value
The future value of the house would be calculated using the following formula,
FV =Current price∗(1+Growth Rate )n
FV =$ 1000000∗(1+5 %)10
FV =$ 1000000∗1.6288946
FV =$ 1628894.62
PMT = $ 371990.6075
6.14456
PMT =$ 60539.75
The solution has also been calculated in excel which is represented in the following figure,
Figure 1: Answer 1 Part a

3QUESTION
Part b:
Wealth maximization of the company is the policy is to increase the value of the stock
of the company. This is the long term goal of the company to maximize the wealth which is
achieved by the improving the factors such as sales, Products and services. The company
expands its operations which leads to the creation of wealth of the stakeholders by investing
in profitable projects. This is a long term strategy of the company and ultimately benefits the
shareholders of the company.
The profits maximization is the short term goal of the company, as it aims to increase
the profits for one financial year. The company would report positive figures for one financial
year ignoring the risk and value of money. It is concerned with the growth of the company in
the existing business environment.
The decision of whether to focus on profit maximization or wealth maximization, the
company should focus on the maximization of the wealth in the company. The profit
maximization is a short term strategy which is necessary for the company to survive in the
business environment. However, this requires overlooking the risk in the short term which is
not possible for the company to do in the long term. The company would focus on the
maximization of the wealth taking the concern of all the stakeholders. The wealth
maximization ensures the building block in the future growth and expansion of the company
which should be undertaken.
Part c:
The calculation of the yearly instalment would first require the calculation of the future value
of the loan after 4 years. This would be done by the following formula in the following steps,
Step 1: Calculation of Future Value after 4 years,
FV =Current value∗(1+interest rate)n

4QUESTION
FV =$ 10000∗(1+8 %)4
FV =$ 10000∗1.36048
FV =$ 13604.88
Step 2: The 2nd step for the payment to be made each year is calculated in excel which is
presented in the following figure,
Figure 2: Answer 1 Part c
Answer 2:
Part a:
The present value of all the cash flows is calculated in the following figure using the
excel PV function. The amount of the present value which is calculated is $ 73734.81, while
the inventor is receiving $100000 for selling the invention today. Thus, the present value of
all the future cash flow is less than the cash flow which can be received. Hence the inventor
should sell the invention today at $100000

5QUESTION
Figure 3: Answer 2 Part a
Part b:
The present value of all the future cash flow which is received by the Kate is
$811089.58.
Figure 4: Answer 2 Part b
Part c:
The nominal interest rate of the Property Trust Bank which is 8% needs to be
converted to effective interest rate which is done by the following formula,
Effective interest rate=¿ 1+ Nominal rate / period of compounding) ^ period of
compounding) – 1
Effective interest rate=¿ 1+ 8% / 2) ^ 2) - 1
Effective interest rate=8.16 %
This effective interest rate which is calculated for the Property Trust Bank needs to be
converted to Nominal interest rate for the Mortgage trust bank by the following formula,
Nominal rate=Period∗( ( 1+ Effective Rate ) ¿¿ 1/ period)−1 ¿
Nominal rate=4∗( ( 1+ 8.16 % )¿ ¿1 /4)−1 ¿
Nominal rate=7.92%

6QUESTION
Thus the Mortgage Trust bank should charge 7.92% per annum on quarterly
compounding basis.
Answer 3:
Part a:
The calculation of the monthly instalment of the loan would require 1st to calculate the
loan amount which is taken by the individual. The calculation is presented in the steps below,
Step 1: The calculation of Loan amount
The price of the house is $1200000 million, while the loan to value ratio provided by
the bank is 90%. Hence the loan amount which is taken is
= $1200000*90% = $1080000
Step 2: Calculation of the monthly instalment of the loan.
The monthly instalment of the loan is calculated by the following formula which is
presented in the equation below,
Installment= ( Loan amount∗Rate per month∗( 1+ Rate per month ) period ) /¿ ((1+Rate per
month)^ N) – 1)
Installment= (1080000∗0.5 %∗( 1+0.5 % )360 ) /¿ ((1+0.5%)^ 360) – 1)
Installment=32521.91/¿ (6.022575 – 1)
Installment=32521.91/¿ (5.022575)
Installment=$ 6475.15

7QUESTION
Part b:
The value of the mortgage amount which remains after the 60th payment is provided
by the following equation,
Remaining Mortgage=Loan amount∗( ( 1+Rate ) Period ) −¿) / ( ( 1+Rate )Period )−1
Remaining Mortgage=1080000∗( ( 1+ 0.5 % )360 )−¿)/( ( 1+0.5 % )360 )−1
Remaining Mortgage=5047623.1/5.0225
Remaining Mortgage=$ 1004987.1
Part c:
The time to completely pay the loan would be 120 months which means around 10
more years. This is on the assumption that the monthly payment for the loan instalment is
$6475.15. The calculation is done using the excel function of NPER which determines the
period of payment. The calculated period is provided in the figure below,
Figure 5: Answer 3 Part c
Answer 4:
Part a:
The expected return for each of the stock is presented in the table below for the company
ABC limited,

8QUESTION
Return % Probability % Expected Return = Return *
Probability
16% 50% = 0.16 * 0.5 = 8%
12% 30% = 0.12* 0.3 = 3.6%
10% 20% = 0.1 * 0.2 = 2%
The total expected return from the stock is 8%+3.6%+2% = 13.6%
The expected return for each of the stock is presented in the table below for the company
XYZ limited,
Return % Probability % Expected Return = Return *
Probability
18% 30% = 0.18 * 0.3 = 5.4%
10% 20% = 0.1* 0.2 = 2%
8% 50% = 0.08 * 0.5 = 4%
The total expected return from the stock is 5.4%+4%+2% = 11.4%
Part b:
Return % (A) Return Squared
(B)
Probability %
( C)
( A*C) (B *C)
16% 0.0256 50% = 0.16 * 0.5 =
8%
= 0.0256*0.5 =
1.28%
12% 0.0144 30% = 0.12* 0.3 =
3.6%
0.0144*0.3 =
0.432%
10% 0.01 20% = 0.1 * 0.2 = = 0.01*0.2 =

9QUESTION
2% 0.20%
The variance of the stock ABC is calculated in the table below,
The variance of the stock is (1.28%+0.432%+0.2%)-(8%+3.6%+2%)^2=1.91%-
1.85%=0.06%
The Standard deviation of the stock is = 0.06%^0.5 = 2.45%
The variance of the stock XYZ is calculated in the table below,
Return % Return Squared
(B)
Probability %
( C)
( A*C) (B *C)
18% 0.0324 30% = 0.18 * 0.3 =
5.4%
= 0.0324*0.3 =
0.97%
10% 0.01 20% = 0.1* 0.2 = 2% 0.01*0.2 =
0.2%
8% 0.0064 50% = 0.08 * 0.5 =
4%
= 0.0064*0.5 =
0.32%
The variance of the stock is (0.97%+0.2%+0.32%)-(5.4%+2%+4%)^2=1.49%-
1.30%=0.1904%
The Standard deviation of the stock is = 0.1904%^0.5 = 4.36%
Part c:
The return from the portfolio is calculated in the table below for the two stocks ABC
limited and XYZ limited using the following formula,

10QUESTION
Portfolio Return=Stock a ( Expected Return∗weight ) + Stock b( Expected Return∗weight)
Stock Returns Weight Returns * Weight
ABC 13.6% 60% 13.6%*60% = 8.16%
XYZ 11.4% 40% 11.4%*40% =4.56%
The total expected return from the portfolio of the two stocks is 8.16%+4.56% = 12.72%
The standard deviation of the portfolio is given by the following equation which is
being presented below,
Portfolio S . D= √ ( W A2∗VarianceA ) + ( W B2∗Variance B ) +¿
Portfolio S . D= √ ( 0.62∗0.0 00 6 ) + ( 0.42∗0. 001904 ) +¿
Portfolio S . D= √(0.0216+0.0304−0.15)
Portfolio S . D= √ ( −0.1 ) =3.19 %
The expected return which is calculate for the portfolio is 12.72% while the risk
reported by the portfolio is 3.19%. The return which was provided from the stock of ABC
limited is 13.6% while the risk is 2.45%. Also the return from the stock of the company XYZ
limited is 11.4% and the risk is 4.36%. Thus the portfolio has provided a risk adjusted return
to the portfolio which it does by reducing the unsystematic risk from the portfolio and the
investor is rewarded for the systematic risk from the portfolio.