Question

1. James Hunt’s Dream Apartment

Part 1

James Hunt currently earns a yearly salary of $100,000 (paid on a monthly basis at the end of each month) and his average income tax rate is 25% (taxes are withheld by the employer from the employee’s gross monthly pay). He wishes to buy an apartment in Boston. He can obtain from his bank a 30-year fixed rate mortgage loan at a nominal interest rate of 4.75% per annum, with equal monthly payments paid at the end of each month.

James also has accumulated $150,000 in savings, which he holds in a separate bank account.

He figures that all other housing-related expenses (e.g., condominium fees, utilities, insurance, and property taxes) should come up to a total of about $500/month (assume that these expenses are all paid at the end of each month).

As he is trying to figure out how much he can afford to pay for the apartment of his dreams, he suddenly remembers the advice his mother once gave him:

• Do not spend more than 1/3 of your monthly disposable take-home pay on housing costs (mortgage and all other housing-related expenses); and,

• Always keep a minimum of $50,000 available at all times in your savings account, in case of an emergency.

Given all the information above, and if he follows his mother’s advice, what is the maximum price that James can afford to pay for the apartment?

Part 2

Four years after having purchased the apartment, James learns that mortgage interest rates have substantially declined due to the recession and to the Federal Reserve Bank’s aggressive expansionary monetary policy. He currently still owes $283,333 on his loan principal.

The 30-year mortgage interest rate is now at 4% and a 15-year rate at 3.50%. In addition, his annual salary base is now $125,000, as a result of a recent promotion, and his savings account was partially replenished and now stands at $80,000.

Rather than lowering his monthly mortgage payments, James is more interested in shortening the maturity of his mortgage, so as to save a substantial amount of future interest payments. As a result, he wishes to switch from a 30-year to a 15 year mortgage at 3.50%.

Assume that his average tax rate is now 30% , that housing-related costs are now $600 instead of $500, and that the closing costs (legal and processing fees to modify the mortgage) are approximately $5,000, payable at closing (when the new loan is approved).

Assuming that James continues to strictly follow his Mom’s recommendations,

1. How much of the existing loan principal would he have to repay upfront before setting up the new loan? (Include the closing costs to the amount).
2. What is the total amount of interest that he would save over the entire duration of the loan if he were to refinance it (i.e., switch to the 15-year mortgage loan mentioned above)?
3. Can he afford to refinance his loan, all things considered? Should he do it? Explain.

Answer 1

Part (1)

Annual pre tax income = $ 100,000

Tax rate = 25%

Monthly post tax income = 100,000 x (1 - 25%) / 12 = $ 6,250

Mother's advise: Do not spend more than 1/3 of your monthly disposable take-home pay on housing costs (mortgage and all other housing-related expenses);

Other housing related expenses = $ 500 / month

Hence, disposable income available for monthly installments = 1/3 x 6,250 - 500 = $ 1,583.33

Loan period = nos. of month in 30 years = 12 x 30 = 360

Interest rate per period = 4.75% per annum / 12 = 0.396% per month

Hence, maximum loan that he can avail = PV of all future payments

Use PV function of excel.

PV(rate, period, amount) = PV(0.396%, 360, -1583.33) = $ 303,525.62

Mother's advice 2: Always keep a minimum of $50,000 available at all times in your savings account, in case of an emergency.

Accumulated saving in savings account = $ 150,000

Savings available for down payment= 150,000 - 50,000 = $ 100,000

Hence the maximum price that James can afford to pay for the apartment

= Maximum loan that he can take out + maximum down payment possible by him today = $ 303,525.62 + $ 100,000 = $ 403,525.62

Part (2)

Monthly disposable income = Gross yearly disposable income / 12 x (1 - tax rate) = 125,000 / 12 x (1 - 30%) = 7,291.67
With the revised figures, money available with him for monthly installment = 1 / 3 x monthly Disposable income - other housing related expenses = 1/3 x 7,291.67 - 600 =   1,830.56

Period = nos. of months in 15 years = 12 x 15 = 180 months

Interest rate per period = 3.50% / 12 = 0.292%

Hence, maximum loan that he can avail = PV of all future payments

Use PV function of excel.

PV(rate, period, amount) = PV(0.292%, 180, -1830.56 ) = $ 256,063.82

How much of the existing loan principal would he have to repay upfront before setting up the new loan? (Include the closing costs to the amount).

Current outstanding loan = $ 283,333

Closing costs = $ 5,000

So, the amount of principal he needs to pay down = Current outstanding loan + Closing costs - maximum loan he can sustain after shift = $ 283,333 + $ 5,000 - $ 256,063.82 = $ 32,269.18

What is the total amount of interest that he would save over the entire duration of the loan if he were to refinance it (i.e., switch to the 15-year mortgage loan mentioned above)?

We will make use of the excel function CUMIPMT that sums all the interest payments between two period of a loan.

If he continues with the existing loan then,

PV of the loan amount = Current outstanding = 283,333

Interest rate per period = 4.75% / 12 = 0.396%

Period to maturity = 30 - 4 = 26 years = 12 x 26 months = 312 months

Hence total interest that will be paid over the tenure of the loan = CUMIPMT(Rate, period, PV, Start period, End period, type) = CUMIPMT(0.396%, 312, 283333, 1, 312, 0) = $  210,581.33

If he replaces the old loan by a new one,

PV of the loan amount = $ 256,063.82

Interest rate per period = 3.50% / 12 = 0.292%

Period to maturity = 15 years = 12 x 15 months = 180 months

Hence total interest that will be paid over the tenure of the loan = CUMIPMT(Rate, period, PV, Start period, End period, type) = CUMIPMT(0.292%, 180, 256063.82, 1, 180, 0) = $ 73,436.18

Hence interest saved =  210,581.03 - 73,436.18 =  137,145.15

Can he afford to refinance his loan, all things considered? Should he do it? Explain.

In order to refinance, he needs to repay an amount of $ 32,269.18 upfront.

Money in his savings account = $ 80,000

balance he needs to maintain = $ 50,000

Hence, money available for immediate payment = $ 80,000 - $ 50,000 = $ 30,000 < $ 32,269.18 = amount that required upfront

Hence, he will not be able to refinance his loan.

Yes, he should refinance the loan as there is a significant interest cost savings for him.