Your client spends $2000 per month on living expenses, including mortgage on his property
worth $800,000, with a balance of $300,000 owing at interest rate of 6%. His current bank
deposit is $30,000 and he earns 5% APR on his deposit. He wants to buy a car costing
$20,000 with estimated residual value of $7000 at end of 36 months and he is presented
with the option of buying the car outright with cash or finance at 8% interest rate per annum for 36 months with deposit of $2000. Your client currently earns $70,000 a year, paid
monthly, and expects to earn $90,000 if he can get a master degree. Income tax is 28%. If he
studies towards a master degree now, he will be without income for two years and will have
to pay $5,000 non tax deductable course related fees per semester for two years. There are
two 6-month semesters per year. For his retirement, he wants to retire on his 75th birthday and he is looking at two investment products (correlation between two asset is 0.5)
consisting of 15% return on shares (variance of 225, or a standard deviation of
p
225/10000
if converted at the same unit as reported returns) and 10% on bonds (variance of 90, or a
standard deviation of
p
90/10000 if converted at the same unit as reported returns), and
being a conservative investor, he would like to minimize his risk using combination of these
two assets.
Your client expects he will need $6000 per month by the time he is 75 and he expects to
sell his home for 1.4 million dollars and move into an apartment cost $800,000. He will
1also put any money he has in low risk investment by that time, earning APR of 3%. He
also plans to have assisted living once he reaches 85 to 90, with cost being approximately
$10,000 per month. He would also like to have $10,000 to cover his final expenses by the
time he reaches 90. He would like to know how much money he needs to put aside into
investment fund at end of every month, beginning end of this month, so he can reach his
retirement objective. The client is also aware of investment variability for his portfolio and
would like to have some information as to the amount of money he needs to put aside per
month in case the investment over or under deliver the expected return.
To determine how much money the client needs to put aside into an investment fund at the end of every month, we'll need to calculate the following:
1. Calculate the monthly living expenses, including the mortgage payment:
Monthly living expenses = $2000
2. Determine the mortgage payment:
Mortgage balance = $300,000
Mortgage interest rate = 6%
To calculate the mortgage payment, we can use a mortgage repayment calculator. Let's assume the mortgage is amortized over 30 years. Using the calculator, we find that the monthly mortgage payment is approximately $1,798.
3. Calculate the net monthly income:
Annual income = $70,000
Income tax rate = 28%
The net monthly income can be calculated by dividing the annual income by 12 and subtracting the income tax:
Net monthly income = ($70,000 / 12) - (($70,000 / 12) * 28%)
4. Calculate the monthly savings:
Monthly savings = Net monthly income - Monthly living expenses - Mortgage payment
5. Determine the cost of buying the car outright:
Car cost = $20,000
Residual value = $7,000
The cost of buying the car outright is the difference between the car cost and the residual value:
Cost of buying the car outright = Car cost - Residual value
6. Determine the monthly savings needed for the car if financed:
Financing interest rate = 8%
Deposit = $2,000
Number of months = 36
To calculate the monthly savings needed for the car if financed, we can use a car loan calculator. Input the car cost minus the deposit, the financing interest rate, and the number of months. Let's assume there are no additional fees or charges associated with the finance option. Using the calculator, we find that the monthly savings needed for the car if financed is approximately $487.
7. Determine the additional savings needed for master's degree:
Additional annual income = $90,000 - $70,000
Additional monthly income = Additional annual income / 12
The additional savings needed for the master's degree is the additional monthly income.
8. Determine the annual retirement expenses:
Retirement monthly expenses = $6,000
Retirement annual expenses = Retirement monthly expenses * 12
9. Determine the investment returns and variances:
Share return = 15%
Share variance = 225/10,000 (converted to decimal)
Bond return = 10%
Bond variance = 90/10,000 (converted to decimal)
We can calculate the expected returns on the investment portfolio by combining the share and bond returns with their respective weights. Since the correlation between the assets is given as 0.5, we can use the formula for portfolio return.
Portfolio return = (Share return * Share weight) + (Bond return * Bond weight)
To minimize risk, we need to determine the weights for the share and bond investments. We can use the formula for minimum variance portfolio.
Minimum variance portfolio weight for shares = (Bond variance - Covariance) / (Share variance + Bond variance - 2 * Covariance)
Minimum variance portfolio weight for bonds = 1 - Minimum variance portfolio weight for shares
Once we have the portfolio weights, we can calculate the expected return using the above formula.
10. Determine the retirement savings needed:
Home selling price = $1,400,000
Apartment cost = $800,000
Assisted living cost = $10,000
Final expenses = $10,000
Additional retirement savings needed = Apartment cost - (Home selling price / (1 + Bond return)^n) + (Assisted living cost * (1 + Bond return)^(n2-n1)) + Final expenses * (1 + Bond return)^(n2-n1)
Where:
n = time from current age to retirement age (in months)
n1 = time from current age to the start of assisted living (in months)
n2 = time from current age to the end of life (in months)
11. Calculate the total monthly savings needed:
Total monthly savings needed = Monthly savings + Monthly savings for car + Additional savings for master's degree + (Additional retirement savings needed / Total months to retirement)
Finally, these calculations will provide the amount of money the client needs to put aside into an investment fund at the end of every month to reach his retirement objective.