James Hunt’s Dream Apartment Part 1 Annual before tax income = $ 100,000 Tax rate = 25% Monthly post tax income = 100,000 x (1 - 25%) / 12 = $ 6,250 Mother's advice: Do not spend more than 1/3 of your monthly disposable take-home pay on housing costs (mortgage and all other housing-related expenses); housing related expenses = $ 500 / month disposable income available for monthly installments = 1/3 x 6,250 - 500 = $ 1,583.33 Loan period 30 years = 12 x 30 = 360 Interest rate per period = 4.75% / 12 = 0.396% per month PV (rate, period, amount) = PV (0.396%, 360, -1583.33) = $ 303,454.85 Mother's advice 2: Always keep a minimum of $50,000 available at all times in your savings account, in case of an emergency. saving in savings account = $ 150,000 Savings available for payment= 150,000 - 50,000 = $ 100,000 the maximum price that James can afford to pay for the apartment $ 303,454.85 + $ 100,000 = $ 403,454.85 Part 2 Monthly disposable income = Gross yearly disposable income / 12 x (1 - tax rate) = 125,000 / 12 x (1 - 30%) = 7,291.67 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 15 years = 12 x 15 = 180 months Interest rate per period = 3.50% / 12 = 0.292% maximum loan that he can avail PV (rate, period, amount) = PV (0.292%, 180, -1830.56) = $ 255,994.1 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). Current outstanding loan = $ 283,333 Closing costs = $ 5,000 the amount of principal he needs to pay = $ 283,333 + $ 5,000 - $ 255994.1 = $ 32,338.9 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)? PV =283,333 Interest rate per period = 4 % / 12 = 0.3333% Period to maturity = 30 - 4 = 26 years = 12 x 26 months = 312 months total interest that will be paid over the tenure of the loan = CUMIPMT (Rate, period, PV, Start period, End period, type) = CUMIPMT (0.3333%, 312, 283333, 1,312, 0) = $172834 If he replaces the old loan by a new one, PV of the loan amount = $ 255,994.1 Interest rate per period = 3.50% / 12 = 0.292% Period to maturity = 15 years = 12 x 15 months = 180 months 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, 255994.1, 1,180, 0) = $ 73,506.7 interest saved = 172834 - 73,506.7 = 99327.48 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 $ 32,338.9 upfront. Money in his savings account = $ 80,000 balance he needs to maintain = $ 50,000 money available for immediate payment = $ 80,000 - $ 50,000 = $ 30,000 < $ 32,338.9 = amount that required upfront 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. Felix’s Retirement Plan a) What will be the $ value (to the nearest cent) of the investment in bonds at maturity, i.e., 20 years from today, after the fees are paid and assuming that the bonds perform as predicted? Management fee = 5%*1000 = 50 (per month) Monthly investment = 1000-50= 950 So, 950/2 = 475 475$ will be in bond and 475$ will be in stocks Rate= 4%/12 = 0.003333% Period = 20 * 12 = 240 Pmt= 475 Fv(rate,period,pmt) = 174,210,12 b)What will be the $ value (to the nearest cent) of the investment in stocks at maturity, i.e., 20 years from today, after the fees are paid and assuming that the stocks perform as predicted? Management fee = 5%*1000 = 50 (per month) Monthly investment = 1000-50= 950 So 950/2 = 475 475$ will be in bond and 475$ will be in stocks Rate= 8%/12 = 0.006667 Period = 20 * 12 = 240 Pmt= 475 Fv(rate,period,pmt) = 281,179.55 c)What will be the true rate of return on the entire investment plan, expressed as an Effective Annual Rate (EAR), assuming that bonds and stocks perform as predicted? (the EAR should contain 4 decimals) Total return= return on bonds + return on stocks = 0.04*0.5+ 0.08*0.5 =0.06 Nominal rate of return= 0.06 Period =12 Effect annual rate(effect(nominal_rate,npery) = 6.1678%