50353612 - Sir Ali PDF

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Sir Ali...

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1. What is the required monthly mortgage payment? [1 mark]

Assuming the mortgage is a reducing balance loan, then use the formula to calculate. The total price for the house is $1.5 million, so the loan is P=$ 1500000 ×80 %= $ 1200000 With the 3% annual interest rate and the 30 year period, the monthly mortgage is： 3/12 r /n =1.0025 =1+ 100 100 n=30× 12=360 R=1+

n

Q=

P R (R−1) 1200000 ×1.0025360 (1.0025− 1) =5 059.25 = 360 1.0025 −1 Rn −1

His monthly repayment is SG$5059.25. 2. What are the initial cash outflows of the buy decision? [1 mark]

As shown in the case, the initial cash payments included a down payment of 20% of purchase,3% stamp duty, 1% agent fee, $4000 legal transfer fee and $4000 in other closing fees. Add them up to get the sum. 1500000× ( 20 %+3 %+1 %)+ 4000+4000=368000 Although a part of down payment is paid by CPF, that’s still the Wong’s money. The initial cash outflow of the buy decision is SG$368000. 3. What is the present value of all the cash outflows of the buy decision from month 0 to month 120? [2 marks]

Month 0 is the initial cash outflow, which is calculated in question 2. Since there is a series of streams of cash flows from month 1 to 120, using the result in question 1 to get a monthly payment $5059.25. Some other monthly payment should be taken into consider: Maintenance fee of $250, property tax of $100, and maintenance fee $100. C=5059.25+ 250+100 + 100 =5509.25 In assumption 2&5 we know that the deposit mortgage rate stays constant at a 3% annual percentage rate, and the risk-free interest is also 3%. The mortgage is compounded monthly, so we need to find the 1month interest rate, using formula APR r= k Where k=12 To get 1-month interest rate r=0.0025

Then plug it into the annuity formula PV Annuity =CA ( n , r )=5509.25 × A ( 120,0.0025) =570547.59 Then add the initial cash flow PV =PV Annuity + PV Innitial =570547.59 + 368000= 938547.59 The present value of all the cash outflows of the buy decision from month 0 to month 120 is SG$938547.59.

4. Compare the relevant monthly cash outflows of the buy decision and rent decision from month 0 to month 3, assuming rent stays constant. What are the additional payments required to buy versus rent? [1 mark]

Month 0 is the initial cash flow, and for month 1 to 3 the cashflow of buy decision have been calculated above. According to the material, the monthly rent is US$4000 and consider the exchange rate. 1 =5333.33(SGD ) 4000(USD)× 0.75 Month

Buy decision (SG$)

Rent decision (SG$)

1

5509.25

5333.33

2

5509.25

5333.33

3

5509.25

5333.33

The monthly additional payment is 5509.25−5333.33 =175.92 ($ SG) C 175.92 n FV = ( ( 1+r ) −1 )= ( ( 1.0025 )3−1) =529.08 r 0.0025 5. What is the principal outstanding on the mortgage at the end of 10 years? [1 mark]

After 10 years, the loan has 20 years, or 240 months, remaining. The principal outstanding on the mortgage is the value after 10 years of the remaining payments, using the loan rate of 0.25% per month (question 3): principalafter 10 years=5059.25 ×

(

)

1 1 =$ SG 912237.99 1− 240 0.0025 1.0025

6. Compute the net gain or loss of the buy versus rent decision after 10 years under the four scenarios in the case. [3 marks] Scenario 1 The condition is the same to what mentioned above, using the result in question 3

FV buy , Annuity =5509.25 ×

1 ( (1+0.0025)120−1) =769870.41 0.0025

120

FV buy , Initial= PV buy , Initial ( 1+r ) =496562.11 And

FV rent =5333.33×

1 ( (1+0.0025)120−1 ) =745287.10 0.0025

Selling price is 1500000, with outstanding $SG912237.99, the gain is 587762.01 Consider that if the initial cash paid by CPF account can be taken out, it can be invested with a 3% risk-free interest rate. In rent case, the money can’t be taken out from the CPF account with a lower 2.5% interest, which is an extra cost.

r CPF =

2.5 % =0.002083 12

120 FV extra =225000 (1+ 0.0025 )120−225000 (1+ 0.002083 ) =14785.48

Net loss=FV buy −Gain− FV rent −FV extra=SG $ 388988.07 Scenario 2 Scenario 3 Scenario 4

7. What are some other qualitative considerations that the Wongs might want to consider (other than the ones already mentioned in the case)? [1 mark] Risk tolerance, the capacity of bearing risk. Political factors, the possibility of changing in property policies. How long the landlord is willing to let them stay. Since the unit doesn’t belong to them, the landlord may change the rate of the rent or rend it to others....