Question

Mary plans to buy a flat in Tuen Mun, and the selling price is $6,000,000. Mary is offered two mortgage loans: one from Hang Seng Bank (HSB) and another from the developer Sino Group (Sino). (i) a 25-year loan at “Prime rate (P) – 2.8%” from HSB, based on a loan-to-value ratio (LTV) of 60% (ii) a 25-year loan at “Prime rate (P) + 1%” from Sino, based on an LTV of 80%, but Mary can pay interest only in the first three years Both loans require monthly payments and are fully amortizing.

(a) Suppose the prime rate is 5% and is expected to remain constant for a long period of time, calculate the (i) down payments, (ii) monthly payments, and (iii) also the loan balances at the end of Year 3, of the two loans mentioned above.

(b) Calculate the total interest expenses of the two loans. How much do they differ?

(c) Suppose Mary takes up the loan offered by Hang Seng Bank finally. If the housing price is expected to rise by 7% per year, and Mary would like to hold the property for four full years before selling it. Calculate Mary’s expected appreciation on housing price and expected return on equity.

(d) If the housing price grows at the rate expected by Mary, what is her realized return from this investment when she sells the property at the end of Year 4?

Answer 1

(a)

Given Data

Cost of Flat         $600,000                                                                                                                                    

Loan (i)-Prime rate -2.8%                                                                                                                                     

Monthly interest rate = (5-2.8)/12 = 0.18% (Rate)                                                                                                     

Number of Months of Loan=25*12 = 300 (Nper)                                                                                                       

Loan amount =600000*LTV=600000*60% = $360,000 (Pv)                                                                                                     

Monthly Payment    = $1,561.17              

(Using PMT function of excel with Rate=0.1833%, Nper=300, Pv=-360000)                                                                                                       

Down Payment =600000-360000 = $240,000      

Loan Balance at end of three years:

Number of Payments to be made after 3 years = 22*12 = 264                                                                                               

Loan Balance = Present Value of future payments                                                                                                                                  

PV Loan Balance at end of first three years =     $326,495

(Using PV function of excel with Rate=0.1833%, Nper=264, Pmt=-1561.17)                                                                                                      

                                                                                                                                                     

(b).   

Cost of Flat         $600,000

Loan (ii)-Prime rate +1%                                                                                                                        

Rate -    Monthly interest rate =(5+1)/12= 0.50%                                                                                                                       

Nper -   Number of Months of Loan=25*12 = 300                                                                                                                      

Pv -        Loan amount =600000*LTV = 600000*80% = $480,000                                                                                                            

PMT-     Monthly Payment   = $3,092.65

(Using PMT function of excel with Rate=0.5%, Nper=300, Pv=-480000)                                                                                               

Down Payment = 600000-480000 =   $120,000   

                                                                                                        

Loan Balance at end of three years:                                                                                                                                 

Nper-   Number of Payments to be made after 3 years = 22*12 = 264                                                                                                

Loan Balance = Present Value of future payments                                                                                                                                  

Loan Balance at end of first three years = $452,754       

(Using PV function of excel with Rate= 0.5%,Nper =264, Pmt=-3092.65)                                                                                             

                                                                                                                                                     

(c) Total Interest Expense:

  Loan (i)- Prime rate -2.8%                                                                                                                                      

Loan amount (C1) =   $360,000                                                                                                                     

Total Payment (C2) = 300*1561.17 = $468,351                                                                                                           

Total Interest expense (C3) =C2-C1

                                              = $4,68,351 - $3,60,000

                                               = $108,351        

Loan (ii)-Prime rate +1%

Loan amount (C1) = $480,000                                                                                                            

Total Payment (C2) =300*3092.65 = $927,794                                                                                                            

Total Interest expense (C3) = C2 – C1

                                             = $927,794 - $480,000

                                              =$447,794                                                                                                            

Diffrence in total interest expense under (i) and (ii) = 447794-108351

                                                                                 = $339,443                                                                                                            

                                                                                                                                                     

(d)         

Expected appreciation on housing price and return on Equity                                                                                                                              

Housing Price after 4 years = 600000*(1.07^4)

                                                = $786,478                                                                                

Loan Balance at the end of 4 years = $314,827

(Using PV function of excel with Rate=0.1833%, Nper=(300-48), Pmt=-1561.17)                                                                                             

Fv- Net Cash Flow at the end of 4 years = 786478-314827

                                                                   = $471,651                                                                                                          

Pmt- Annual Cash Flow = ($1,561.17)                                                                                                            

Pv-    Initial Cash flow=Down Payment = ($240,000)                                                                                                        

Nper- Number of months    = 48                                                                                                                       

Rate-   Return on Equity (Monthly) = 0.95%        

(Using RATE function of excel with Nper= 4, Pmt= -1561.17, Pv=-240000, Fv= 471651)                                                                                                

Annualized Return on Equity = Rate*12

                                                      = 11.37%

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