Answer To: Value: 20% Due Date: 01-Sep-2019 Return Date: 20-Sep-2019 Submission method options: Alternative...
Payal answered on Aug 30 2021
Assessment 2 – Question 1
(a) Your daughter has expressed a wish to attend university when she finishes school in five (5) years. You anticipate the cost will be $60,000 at the time she commences university. If your financial institution is offering you 4% pa (compounded monthly), how much do you need to deposit in your account each month in order to save the required amount before your daughter commences university? (5 marks)
Solution to 1 a)
Annuity is series of equal cashflows that occur at equal time intervals for a specified number of time periods. Future value of an annuity of ‘C’ dollars per period at the interest rate of ‘r’ percent per period for n periods is given below: -
FVAn = Future value of an annuity
C = Annuity payment i.e. constant payment
r = interest rate, rate of return per period
n = number of periods (not necessarily one year)
Time value problems (TVM) has total five variables; if three or more values are known; value for any one variable can easily be calculated. Here, FVAn, no. of years and rate of interest is known. So, annuity payments can easily be calculated.
Annuity payment for college fees in 5 years is given below: -
Annuity payments can be calculated by substituting following values in the above formula. C =? r = 0.04/12 per period, n = 5*12= 60 periods, FV = $60,000
Therefore, total amount to be saved each month for University fees is $904.99
(b) You have been offered the opportunity to purchase a start-up company building electric cars for the Australian market called Green Motors P/L. Your initial investment is $22,000,000. The term of the project is 5 years. The project has an expected rate of return of 10% pa. All expected cash flows for the project are below and you have an expected rate of return of 10% pa.
End of year
Cash flow ($mil)
1
1.8
2
3.0
3
6.5
4
8.4
5
12.3
(i) Based on your required rate of return would you purchase this investment? Present all calculations to support your answer. (2.5 marks)
(ii) Would you change your opinion from (i) if the expected rate of return rose to 15%? Present all calculations to support your answer. (2.5 marks)
Solutions to 1 b i)
In order to find whether we should purchase the Investment or not, Net present value (NPV) of the cash flows has to be found out.
Net Present Value (NPV): - NPV is the difference between the present value of cash inflows and Initial Investments. Present value of a series of cash flows is the current value/worth of future cash flows as of today based on a discount rate used. Projects with positive cashflows should be accepted. If any project has negative NPV, then the project should be rejected.
Now, let’s solve the above problem using the present value equation: -
PV = present value of a cash flow stream
CF = Cash flow at the end of period t
r = discount rate
n = number of periods
Since the project has positive NPV of $373,894, this project can be accepted.
Solutions to 2 b ii)
Now, let solve this problem using excel
Where the formulas in the cell looks like: -
Explanations: -
· Input each cash flows in column B against each year.
·
Find the present value by using the discounting factor . Detailed working is shown in the second excel table.
· Multiple each cash flow with their respective discounting factors.
· Sum all the present value using the “Sum” Function
Net Present Value (NPV) of this investment @15% is (2,974,495). Since NPV @15% is negative, then this project should not be accepted
(c) You have commenced work as a certified Financial Planner. Your supervisor has provided the following financial data for a new client Brant Jerome. The client turned 34 years old today and plans to retire when she turns 67. The client owns a diversified share portfolio which is valued today at $47,000. It is expected that this portfolio will earn (on average) 7% per annum indefinitely. Brant also has a superannuation account with a balance of $78,000 to which he currently contributes $1,000 per month. The superannuation account is expected to continue to earn 8% per annum. At his retirement your client plans to consolidate his financial holdings and purchase a monthly annuity as a pension to fund his planned lifestyle.
Brant believes he will need to self-fund his retirement until he reaches the age of 85 at which time, he would like to have $120,000 remaining to fund any costs not covered by the age pension. During the pension phase of his retirement Brant will adopt a Balanced investment strategy which will return 5% pa (compounded monthly) on his annuity investment.
(i) What will be the value of Brant’s financial assets when he retires at age 67? Present all calculations to support your answer. (5 marks)
(ii) What will be the monthly pension amount that Brant will receive on his retirement? Present all calculations to support your answer. (5 marks)
Solution to c i) The value of Brant’s Financial assets when he retires at age 67 has to be found out by finding value of the share portfolio & his superannuation account.
Part A: - Value of diversified share portfolio at age 67
Part B: - His superannuation balance at the age of 67
Part A: -
The relationship between future value and present value at ‘r’ rate of interest for ‘n’ period is given below: -
where;
FV = future Value (amount of money to be paid or received in future)
PV = present Value (amount of money today)
r = rate of interest paid by the investment
n = number of periods the investment will be held
If three or more values are known; value for any one variable can easily be calculated. Here; in this question three components i.e. present value, no. of years and rate of interest is already given, so Future value can easily be calculated.
To find future value (Value of diversified share portfolio), substitute following values PV = $47,000, n = 33 years, r = 7%, in the above equation: -
Now, Let’s Calculate FV Using Excel
Explanation: -
· Input all the data (PV, rate, nper) which is already given in the problem
· Click on B4 and enter all the inputs according to syntax given i.e.
FV (B3, B2, 0, -B1).
· FV = $438,291
Part B: - His superannuation balance at the age of 67
Now, Let’s Calculate this value Using Excel
To find future value (His superannuation balance at the age of 67), substitute following values PV = $78,000, n = 33*12 years, r = 8%/12, pmt = $1000*12 in the FV syntax
Explanation: -
· Input all the data (PV, rate, nper) which is already given in the problem
· Click on B5 and enter all the inputs according to syntax given i.e.
=FV (B3/12, B2*12, -B4*12, B1)
· FV = $22,120,249
Brant’s financial assets when he retires at age 67 is $438,291 + $22,120,249 = 22,558,540
Solutions to c ii)
In this question, we have to find the annuity amount to be received by Brant.
For this, we can use the pmt function in excel
Therefore, the monthly pension amount that Brant will receive on his retirement is $158,251
Assessment 2 – Question 2
a) James is applying for a new home loan. He wishes to borrow $250,000 and make his repayments monthly. The interest rates the bank has quoted him is 4% per annum.
1. Is this the real rate of interest or the notional rate of interest?
2. Explain the difference between the real rate of interest and the notional rate of interest.
3. Calculate the real rate of interest and the notional rate of interest for James.
4. Is it possible for the real rate of interest to equal the notional rate of interest? Explain. (8 marks)
Solutions to 2a)
1. Is this the real rate of interest or the notional rate of interest?
The annual interest rate quoted by the bank is often called the nominal rate (nominal means in name only).
2. Explain the difference between the real rate of interest and the notional rate of interest.
A real rate of interest refers to an interest rate after removing the effects of inflation. Real interest rates reflect real cost of funds to the borrower and the real...