Question

Case Questions/Information:

The responses to the case questions must be typed. You must turn a printed copy by the beginning of class on the day that the case is due. You may work alone or in a group of up to 4 students. Only 1 copy of the case is required for any groups, but please be sure that all students’ names are included on that copy. You should use an Excel spreadsheet to show your calculations. Any text responses can be typed in the Excel spreadsheet or printed via a word processor.

Case Information:

Mary Jones is in the market for a new home. She will need a $300,000 mortgage in order to purchase her “dream house.” Mary is meeting with a loan officer at her bank to discuss some loan options. Information about these options is given below and should help you answer the 6 questions for this case. The seller of her potential new home has agreed to pay for the closing costs in order to entice buyers.

Mortgage Option #1: 30 year fixed rate mortgage:

A 30-year home mortgage is the most popular option chosen by potential homeowners. This loan would be repaid in equal monthly installments. The monthly installment payments are made up of principal payments (which reduce the principal of the loan) and interest payments (paid to the bank for the use of the money). Since Mary has an excellent credit rating, the bank has offered her 4.0 % annual loan rate.

Mortgage Option #2: 20 year fixed rate mortgage:

The bank also has a 20 year fixed rate mortgage. This loan would also be repaid in equal monthly installments and the bank is willing to offer Mary the same 4.0% annual loan rate.

Mortgage Option #3: SMART loan:

A smart loan works as follows: every two weeks, Mary will make a mortgage payment that is ½ of the amount that she would pay for her monthly 30 year mortgage. The APR for the SMART loan is the same as that of the 30 year fixed rate mortgage. This option would save interest as compared to the 30 year fixed rate mortgage option.

Mortgage Option #4: Bullet Loan:

The loan officer also mentions a bullet loan, which will provide a greater interest savings. For the first 60 months, Mary would pay the bank the same monthly payment as she would for the 30 year fixed rate mortgage. However, the “bullet” payment is due immediately after the 60^th payment is paid. The “bullet” payment occurs as Mary must pay the remaining principal on her loan at that time. The remaining principal can be shown as the ending balance in an amortization table after 60 payments are made. Alternatively, this principal balance may be calculated as a present value of this loan considering 25 years are left on the loan (note that this should be shown as months in the PV calculation).

Mortgage Option #5: Interest Only Loan:

There is a final mortgage option that the loan officer presents to Mary. An interest-only loan is typically not offered for consumer loans, but the bank has a trial that it is offering currently. For the interest only loan, Mary does not have to make any principal payments on the loan until it is due 10 years from now. In the meantime, she makes monthly interest only payments. The APR for this loan is 2.8%.

Case Questions/Information:

The responses to the case questions must be typed. You must turn a printed copy by the beginning of class on the day that the case is due. You may work alone or in a group of up to 4 students. Only 1 copy of the case is required for any groups, but please be sure that all students’ names are included on that copy. You should use an Excel spreadsheet to show your calculations. Any text responses can be typed in the Excel spreadsheet or printed via a word processor.

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Question #4:

1. How much does Mary pay for each of the 60 monthly payments for the Bullet loan? (5 points)
2. How much is the bullet? Remember that the bullet is the principal remaining on the loan after the 60 payments are made. (10 points)

Question #5:

1. How much does Mary pay for each of the 120 monthly payments for the interest only loan? (5 points)
2. How much does Mary owe the bank after she makes the 120 monthly payments? While she can make additional principal payments during the term of the loan, for this calculation consider that she does not make any additional principal payments. (10 points)

Question #6:

1. Find the E.A.R. (effective annual rates) for the 5 types of mortgages that Mary is considering. (10 points)
2. Which mortgage should Mary choose? Please include in your explanation a comparison of the EARs, interest saved between the 30 year mortgage and the other loans, and any risks she might face with the different types of loans. (10 points)

Answer 1

Q. 4  
The monthly payment for bullet loan is same as the monthly payments for 30 year fixed interest loan.   
Loan value   300,000
Tenure   30
Interest rate   4%
Monthly payment   1,432.25
   =PMT(4%/12,30*12,-300000)
PV of bullet loan after 5 years   $271,342.54
   =FV(4%/12,5*12,1432.25,-300000)

Another (longer) method   
Loan schedule-  

Months	Principal outstanding at beginning of month	Monthly repayment	Interest component	Principal repayment	Principal outstanding at end of month
	=Principal outstanding at end of previous month		=Principal outstanding at beginning of month*4%/12	=monthly repayment- interest component	=Principal outstanding at beginning of month- Principal repayment
1	300,000.00	1,432.25	1,000.00	432.25	299,567.75
2	299,567.75	1,432.25	998.56	433.69	299,134.07
3	299,134.07	1,432.25	997.11	435.13	298,698.94
4	298,698.94	1,432.25	995.66	436.58	298,262.35
5	298,262.35	1,432.25	994.21	438.04	297,824.31
6	297,824.31	1,432.25	992.75	439.50	297,384.82
7	297,384.82	1,432.25	991.28	440.96	296,943.85
8	296,943.85	1,432.25	989.81	442.43	296,501.42
9	296,501.42	1,432.25	988.34	443.91	296,057.51
10	296,057.51	1,432.25	986.86	445.39	295,612.12
11	295,612.12	1,432.25	985.37	446.87	295,165.25
12	295,165.25	1,432.25	983.88	448.36	294,716.89
13	294,716.89	1,432.25	982.39	449.86	294,267.03
14	294,267.03	1,432.25	980.89	451.36	293,815.68
15	293,815.68	1,432.25	979.39	452.86	293,362.82
16	293,362.82	1,432.25	977.88	454.37	292,908.45
17	292,908.45	1,432.25	976.36	455.88	292,452.56
18	292,452.56	1,432.25	974.84	457.40	291,995.16
19	291,995.16	1,432.25	973.32	458.93	291,536.23
20	291,536.23	1,432.25	971.79	460.46	291,075.77
21	291,075.77	1,432.25	970.25	461.99	290,613.78
22	290,613.78	1,432.25	968.71	463.53	290,150.25
23	290,150.25	1,432.25	967.17	465.08	289,685.17
24	289,685.17	1,432.25	965.62	466.63	289,218.54
25	289,218.54	1,432.25	964.06	468.18	288,750.36
26	288,750.36	1,432.25	962.50	469.74	288,280.61
27	288,280.61	1,432.25	960.94	471.31	287,809.30
28	287,809.30	1,432.25	959.36	472.88	287,336.42
29	287,336.42	1,432.25	957.79	474.46	286,861.96
30	286,861.96	1,432.25	956.21	476.04	286,385.92
31	286,385.92	1,432.25	954.62	477.63	285,908.30
32	285,908.30	1,432.25	953.03	479.22	285,429.08
33	285,429.08	1,432.25	951.43	480.82	284,948.26
34	284,948.26	1,432.25	949.83	482.42	284,465.84
35	284,465.84	1,432.25	948.22	484.03	283,981.82
36	283,981.82	1,432.25	946.61	485.64	283,496.18
37	283,496.18	1,432.25	944.99	487.26	283,008.92
38	283,008.92	1,432.25	943.36	488.88	282,520.04
39	282,520.04	1,432.25	941.73	490.51	282,029.52
40	282,029.52	1,432.25	940.10	492.15	281,537.38
41	281,537.38	1,432.25	938.46	493.79	281,043.59
42	281,043.59	1,432.25	936.81	495.43	280,548.15
43	280,548.15	1,432.25	935.16	497.09	280,051.07
44	280,051.07	1,432.25	933.50	498.74	279,552.33
45	279,552.33	1,432.25	931.84	500.40	279,051.92
46	279,051.92	1,432.25	930.17	502.07	278,549.85
47	278,549.85	1,432.25	928.50	503.75	278,046.10
48	278,046.10	1,432.25	926.82	505.43	277,540.68
49	277,540.68	1,432.25	925.14	507.11	277,033.57
50	277,033.57	1,432.25	923.45	508.80	276,524.77
51	276,524.77	1,432.25	921.75	510.50	276,014.27
52	276,014.27	1,432.25	920.05	512.20	275,502.07
53	275,502.07	1,432.25	918.34	513.91	274,988.16
54	274,988.16	1,432.25	916.63	515.62	274,472.55
55	274,472.55	1,432.25	914.91	517.34	273,955.21
56	273,955.21	1,432.25	913.18	519.06	273,436.15
57	273,436.15	1,432.25	911.45	520.79	272,915.35
58	272,915.35	1,432.25	909.72	522.53	272,392.83
59	272,392.83	1,432.25	907.98	524.27	271,868.56
60	271,868.56	1,432.25	906.23	526.02	271,342.54

Q. 5  
Mary pays only interest at an APR of 2.8% on the total principal and does not pay any portion of the principal. Hence, this is like a simple interest problem. The monthly repayments are equal to- 300,000*2.8%/12= $700. At the end of loan tenure of 10 years, the full loan principal is outstanding. Hence, she owes the full $300,000 to the bank at any point of time during the 120 months to the bank, in addition to the interest for that month.   
  
  
Q.6  
EAR is based on compounding period per year for each of the loan. The formula for EAR is EAR= (1+nominal interest rate/ number of compounding periods in the year)^ number of compounding periods in the year-1  
  
Option #1  
APR   4%
Compounding   monthly
EAR   4.074%
   =(1+4%/12)^12-1
  
Option #2  
APR   4%
Compounding   monthly
EAR   4.074%
   =(1+4%/12)^12-1
  
Option #3  
APR   4%
Compounding   fortnightly
EAR   4.078%
   =(1+4%/24)^24-1
  
Option #4  
APR   4%
Compounding   monthly
EAR   4.074%
   =(1+4%/12)^12-1
  
Option #5  
APR   2.8%
Compounding   NA
EAR   2.800%
The EAR is same as APR since there is no compounding of the principal. The principal is not paid until the end of the period.  
  
Recommendation-  
If we have to chose a loan option based on EAR or total interest payable during the tenure of t he loan, we should propose the 5th option i.e. interest only loan. It has the loan interest rate and the lowest interest charge. However, 100% of loan amount is payable at the end of 10 years. This may not be possible for Mary. If she thinks she would sell the house before this time and close out the loan then this is the best option. The next option is the Smart loan or the 30-year loan. The interest payment under both these loans over the repayment period is almost the same (~$215,500) and they both take 30 years for repayment. Hence, they both are of equal value to the borrower, except, the smart loan has only slightly higher EAR. The monthly repayment under both these loans is small and manageable. Next preferred option could be 20-year loan. The total interest payment over the tenure is lower than the 30-year loan but the monthly repayment is slightly higher $1818 (=PMT(4%/12,20*12,-300000)). The bullet loan is not preferred as much. It requires a bullet payment of ~$271,000 at the end of 5 years which is a very small period for such large amount.