Download (Problems 80 points) A fully amortizing mortgage loan is made for

(Problems 80 points)
1. A fully amortizing mortgage loan is made for 580,000 at 6 percent interest for 25 years.
Payments are to be made monthly. Calculate:
a. Monthly payments.
b. Interest and principal payments during month 1.
c. Total principal and total interest paid over 25 years.
d. The outstanding loan balance if the loan is repaid at the end of year 10.
e. Total monthly interest and principal payments through year 10.
f. What would the breakdown of interest and principal be during month 50?
2. Assume that a lender offers a 30 year, $150,000 adjustable rate mortgage with the
following terms:
 Initial interest rate =7.5 percent
 Index = 1 year treasuries
 Payments reset each year
 Margin = 2 percent
 Interest rate cap = 1 percent annually, 3 percent lifetime
 Discount points = 2 percent
 Fully amortizing: however, negative amortization allowed if interest rate caps
reached
 Based on estimated forward rates, the index to which the ARM is tied is
forecasted as follows:
 Beginning of Year(BOY) 2= 7 percent, (BOY) 3 = 8.5 percent, BOY 4= 9.5
percent: EOY 5 = 11 percent.
 Compute the payments, loan balances, and yield for the ARM for the five year
period.
11. An "interest only" mortgage is made for $80,000 at 10 percent interest for 10 years. The lender
and
borrower agree that monthly payments will be constant and will require no loan amortization.
a. What will the monthly payments be?
b. What will be the loan balance after 5 years?
c. If the loan is repaid after 5 years, what will be the yield to the lender?
d. Instead of being repaid after 5 years, what will be the yield if the loan is repaid after 10 years?
12. An investor obtained a fully amortizing mortgage 5 years ago for $95,000 at 11 % for 30
years. Mortgage rates have dropped, so that a fully amortizing 25 year loan can be
obtained at 10%. There is no prepayment penalty on the mortgage balance of the original
loan, but three points will be charged on the new loan and other closing costs will be
$2000. All payments are monthly.
a) Should the borrower refinance if he plans to own the property for the remaining loan
term? Assume that the investor borrows only an amount equal to the outstanding balance
of the loan.
b) Would you answer to part (a) change if he planned to own the property for only five more
years?
13. Compare the following mortgages and determine which has the lower cost:
Mortgage amount
Term
Discount points
Initial contract interest rate
Margin
Caps
Index value at outset
Prepayment
FRM
$100,000
30 years
2.00
9.75%
…
…
…
End of year 3
ARM
$100,000
30 years
3.25
7.75%
2.75
2% annual, 6% lifetime
7.75%
End of year 3
Assume that the ARM rate adjusts from the initial beginning rate and the index has the following
values:
BEGINNING OF THE YEAR
INDEX VALUE
1
7.75%
2
9.00
3
10.75
14. Consider a property with expected future net cash flows of $25,000 per year for the
next five years (starting one year from now). After that, the operating cash flow should
step up 20%, to $30,000, for the following five years.
a. If you expect to sell the property 10 years from now for a price 10 times the net cash flow at
that time, what is the value of the property if the required return is 12%?
b. Suppose the seller of the building wants $260,000. Should you do the deal? Why or why
not? What is the IRR if you pay $260,000? How does this compare to the required return of
12%?
What is the IRR if you could get the seller to accept $248,075 for the property? What is the
NPV at that price?
c. Suppose that the required return on the property is 11% instead of 12% (in comparison to
part b). What would the value of the property be? By what percentage has this value
changed as a result of this 100-basis-point change in the required return?
15. Jacob (from Twilight) can obtain an 85 percent loan with an 8 percent interest rate and
monthly payments. The loan is to be fully amortized over 25 years. Alternatively, he
could obtain a 95 percent loan at an 8.5 percent rate with the same loan term. The
borrower plans to own the property for the entire loan term.
a. What is the incremental cost of borrowing the additional funds? (Hint: the dollar amount
of the loan doesn’t affect the answer.)
b. How would your answer change if two points were charged on the 95 percent loan?
c. Would your answer to part (b) change if the borrower planned to own the property for
only five years
16.
Year 1
Year 2
Year 3
Year 4
Year 5
Year 6
Year 7
Year 8
Year 9
Year 10
Stock
30%
13%
14%
-5%
-2%
8%
-8%
-13%
18%
23%
House
35%
40%
17%
-25%
-11%
9%
-22%
-31%
40%
50%
REIT
11%
12%
31%
32%
12%
-10%
4%
1%
-2%
-5%
Bond
4%
5%
6%
-1%
-2%
3%
-1%
-2%
-3%
-4%
A. Given the information above, calculate the mean, the standard deviation for each asset.
B. Calculate the correlation between Stock Reit, Stock House and Stock Bond.
Comment on your results.
C. Calculate the correlation between House Reit, and House Bond.
Comment on your results.
D. Let us assume that you can allocate 25% on each asset. Calculate the Rp or rate of return
on the portfolio.
E. Let us assume that you can allocate 25% on each asset. Calculate the standard deviation
of the portfolio.
F. Calculate the Sharpe Ratio of each asset given a T-bill rate of 1.7% and comment on
your results.
G. Calculate the Sharpe Ratio the entire portfolio given a T-bill rate of 1.7% and comment
on your results.
17. The following table gives the NPI total return for a three year(12-quarter) period for
Boston and San Francisco.
YYQ
Boston
San Francisco
2003.1
0.0024
0.0141
2003.2
0.0098
0.0050
2003.3
-0.0082
0.0078
2003.4
0.0156
0.0296
2002.1
0.0325
0.0429
2002.2
0.0181
0.0248
2002.3
0.0427
0.0421
2002.4
0.0655
0.0309
2001.1
0.0301
0.0439
2001.2
0.0301
0.0393
2001.3
0.0520
0.0433
2001.4
0.0487
0.0447
Compute the following quarterly statistics for both cities to the nearest basis point, and
answer the subsequent questions.
a. The arithmetic average return and the geometric return.
b. The standard deviation of the return.
c. Now compute the quarterly Sharpe ratio for each. The Sharpe ratio is a measure of riskadjusted return performance, defined as the risk premium divided by the volatility.
Assume that the average quarterly return to Treasury Bonds during the period in question
was 1.70%. Which city had the better Sharpe ratio.
18. Historical data for the LOL and SOCUTE are as follows:
LOL Common Stock Fund
SOCUTE Real Estate Fund
Period Ending Unit value
Quarterly
Unit Value
Quarterly
Dividend
Dividend
Quarter
1
$701.00
$8.28
$70.00
$2.17
2
752.50
8.11
80.05
2.14
3
850.52
10.30
90.80
2.01
4
953.75
9.81
100.50
2.01
5
1047.57
12.05
99.14
1.87
6
1221.70
14.17
95.50
1.81
7
1443.90
17.18
93.77
1.79
8
1263.31
14.91
80.31
1.54
9
1258.56
13.84
77.34
1.49
10
1526.72
18.32
76.53
1.44
11
1616.81
19.73
78.42
1.51
12
1624.08
19.98
79.01
1.53
13
1560.25
18.88
81.75
1.55
a)
b)
c)
d)
Calculate the quarterly HPR for each investment.
Calculate the arithmetic mean HPR, the standard deviation of HPRs, for each fund.
Was there any correlation between returns on the LOL fund and SOCUTE?
Would a portfolio that contained equal amounts of LOL securities and SOCUTE have
provided any investment diversification? Why?