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15-10. The purpose of problem 10 is to examine the effect of different interest rates and varying
lengths of time on the amount of the mortgage payment. To reduce calculations, the student is
asked to construct the mortgage schedule for only the first two years. The annual payments are
a. $100,000 = X + ... + X
b. $100,000 = X + ... + X
c. $100,000 = X + ... + X
If the term of the loan is shortened, the periodic payments are increased. (Compare a and b.)
If the rate of interest is increased, the periodic payments are increased. (Compare a and c.)
The repayment schedules:
Number Interest Principal Balance of
of the payment repayment loan
payment
a. 1 $5,000 $2,095 $97,905
15-11. While not explicitly covered in the chapter, this problem permits a discussion of several
factors that need to be considered when the investor refinances an existing mortgage.
a. The expenses associated with the loan are $2,750:
b. The homeowner needs $52,750 to retire the old mortgage. At this point the problems may be
c. If the investor pays the $2,750 ($1,000 application fee + $1,000 for points + $750 other fees)
up front from existing cash and continues to owe $50,000, The new mortgage payment is
The difference between the current payment and the new payment is $800 ($6,897 - $6,097). Net
savings implies you should refinance.
The difference between the current payment and the new payment is $363 ($6,897 - $6,534).
Even after borrowing the closing costs and the points, the net savings implies you should
refinance.
15-12. a. This problem is a straightforward mortgage problem. The expected payments are
$100,000 = X + ... + X
b. If interest rates decrease to 7 percent, the value rises:
c. Using a computer program, the amount owed after four years is $91,061.13. (You may choose
to give the students the amount owed after four years. Problem #13 uses the same mortgage; see
the answers for that problem for the mortgage schedule.) The value of the mortgage is
d. The valuations differ because in (b) the payments are assumed to be made for twenty years but
in (c) the payments are assumed to be made over four years because the homeowner refinances.
e. If the investor purchases the mortgage for $106,585.24 and the mortgage is not refinanced, the
annual return is
Thus, the return falls between 8 and 9 percent.
You did better than your expected return of 7 percent, because you receive the cash inflow over a
more extended period of time.
This problem may be used to illustrate one reason why valuing a Ginnie Mae is difficult. The
investor does not know when the mortgages will be retired or if it will be refinanced.15-13. This
The repayment schedule:
Number of Interest Principal Balance
Payment Payment Repayment on Loan
1 $9,000.00 $1,954.65 $98,045.35
2 8,824.08 2,130.57 95,914.78
3 8,632.33 2,322.32 93,592.46
4 8,423.32 2,531.33 91,061.13
5 8,195.50 2,759.15 88,301.98
b. According to the repayment schedule, $70,303.14 is owed at
c. Total payments: 20 x $10,954.65 = $219,093
d. Total interest payments: $119,093
e. In the question, the homeowner makes the required payment of $10,954.65 and an additional
f. Ten years
g. In effect the homeowner makes all the odd number interest payments, which is a total of
h. The advantages of this strategy include
3. Increased equity in home increases borrowing capacity
4. Retiring the loan generates an assured return through
The disadvantages include
1. Loss of tax deductions for interest payments
2. Loss of using the funds elsewhere.
i. This question facilitates comparing an investment in a mortgage with an investment in any
j. This part requires discounting each year's cash flow back at 7 percent to get the present value.
The individual present values are then summed; that is, the value of the payments is $110,297.43.
Number of Amount of Present Value
Payment Payment at 7 percent
1 $13,085.22 $12,229.18
2 13,485.98 11,779.18
k. In this scenario, the annual payment is $10,954 but is made for only four years at which time
the balance owed ($91,061.13) is repaid. The value of the payments is
The equation may be solved for by trial and error or a financial calculator. Using a financial
calculator, the answer is N = 4; PMT = 10954; FV = 91061; I = 7, and
PV = ? = 106575.81.).
l. The values differ because the cash inflows differ. In (i) the payments occur over twenty years,
but in (j) the homeowner retires the loan faster and in (k) refinances the loan.
These three parts illustrate how difficult it may be to value a fixed income security such as a
Ginnie Mae since the inflows are not certain and the investor must make assumptions concerning
the timing and the amounts of the cash inflows.
1. The annual interest to be earned is $14,750 (i.e., $75,000 at 4% plus $75,000 at 5% plus
2. One advantage of the laddered strategy over placing all the funds in bonds that mature after
ten years is the reduction in interest rate risk. Each year $25,000 will come due and the term of
3. In this question interest rates are increased by 100 basis points. The new structure of interest
rates is
Term Rate
(years)
1 5%
2 5
3 5
Each of the bonds has one less year to maturity, so the term, coupons, current comparable rates
of interest, price of each bond are
Term Current Coupon Price of $25,000
(years) Rate on Bond Face Value of Debt
0 - 4% $25,000
1 5% 4 24,762
2 5 4 24,535
3 5 5 25,000
(Calculation of the value of the bond with one year to maturity:
Notice that the one-year bond now matures and the old seven-year bond with the 6 percent
4. The loss in the portfolio's value is slightly less than the $5,750 increase in interest income.
5. If $250,000 were invested in the ten-year bonds, the annual interest payment would be .07 x
$250,000 = $17,500. If one year later interest rates rose to 10 percent, the value of the bonds
6. The $25,000 bond that matures at the end of the first year may be reinvested. One possibility
would be to buy another ten-year bond to maintain the ladder.
As this problem illustrates, a laddered strategy increases interest income for a modest increase in
