Solutions to Problems: Chapter 14
1. Rate of return calculation.
ASSUMPTIONS:
End of
Investment/
Qtr
Withdrawal
0
$1,000,000
1
$250,000
2
($350,000)
3
$145,000
4
($450,000)
a.)
Calculating the effective annual rate
Interest
$20,000
$17,000
$12,000
$29,000
Beginning
Ending
Value
Value
$1,000,000 $1,020,000
$1,270,000 $1,287,000
$937,000
$949,000
$1,094,000 $1,123,000
1+r
1.0200
1.0134
1.0128
1.0265
1.0746
7.46%
b.)
Rate of return based only on ending value and beginning value
12.30%
ignoring the terminal withdrawal.
2. Reaching for Yield Decision.
ASSUMPTIONS:
The question posed here is the desirability of investing short-term funds in an ultra-short bond fund. Many
investors have used these vehicles to gain extra yield while taking on a small amount of price risk.
Background Information:
Portfolio
Index
Strong Advantage Ultra
Beg. Value
11/25/1988
End. Value
2/28/1997
Short Bond
Fund
$10,000
$18,331
Index
$10,000
$16,842
Average
$10,000
$16,084
Salomon 1-Year Treasury
Lipper Ultra Short Obligation
Note: the average effective maturity takes into account the possibility of the bond
8.25833
being called before its maturity, depending upon market conditions.
Avg effective maturity of Strong Fund = 0.74 years
0.74 years
Asset composition of Strong Fund
Percent of
Net Assets
63.80%
Asset Type
Corporate Debt Securities
Non-Agency Mortgage &
Asset-Backed Securities
Short-Term Investments
Preferred Stocks
U.S. Government & Agency Issues
Total
a.)
26.40%
7.50%
1.40%
0.90%
100.00%
Calculating the annualized rates of returns
Strong Advantage
Salomon Index
Lipper Index
Beg Value
$10,000
$10,000
$10,000
End Value
$18,331
$16,842
$16,084
b.)
Risks taken by the bond fund
c.)
Diversification in the bond fund’s portfolio composition
d.)
Interest rate risk
ASSUMPTIONS:
The typical money market fund has an average effective maturity of
Interest rates immediately increase by
Investment in each fund =
Using the first approach, assume that both the MMMF and Strong Adv. have a
yield. After the rate increase (which occurs today), the discount rate is now
The solution below uses the Excel PV function.
Annual
Return
7.61%
6.52%
5.92%
1.5 Months
1.0%
$35,000
5.00%
6.00%
Maturity
(Years)
Beg Price
0.125 $35,000.00
0.74 $35,000.00
MMMF
Strong Adv.
e.)
3.
After 1%
increase in
rates:
End Price % Chg. in Price
$34,958.56
-0.118%
$34,755.36
-0.699%
Time for incremental interest to recoup price change
This solution uses the price change estimate from the first method in part d to estimate the length of time before the
additional interest offsets the greater price reduction.
incremental yield
In dollars, a
1.2%
provides
$420.00 per year
The incremental price reduction is
0.581%
which, in dollars, is a capital loss of:
$203.20
In years, it would take
0.48380 years
(or six months) to recoup the differential price reduction.
Security selection and tax considerations.
ASSUMPTIONS:
Security
CD
Muni
Term (Yr.)
1
1
Yield
6%
4.25%
Tax Rate
39%
0%
After-tax rate on CD =
After-tax return on municipal =
3.66%
4.25%
Reggie should select the municipal security, assuming equal default risk.
4.
Tax Equivalent Yields
a.)
FV
$35,214.11
$36,286.75
Comparing taxable and non-taxable securities
b.)
Calculating tax equivalent yields
Muni yield
Tax rate
5%
35%
tax-equivalent yield =
5.
7.69%
Dividend (capture) yield vs. commercial paper yield.
Dividend yield
Tax rate
a.)
8%
35%
Calculating the dividend capture yield
Assume Heather holds the stock at least 46 days and 70% of the dividend is tax
exempt.
89.50%
effective yield =
b.)
6.
7.16%
Equivalent taxable yield
r = 7.16/(1 - 0.35) =
c.)
retained
11.02%
Types of risk and return possibilities
T-bill yield calculations.
ASSUMPTIONS:
At Treasury bill auction, price was 97.569 % of par on $10,000 T-bills with maturity
of 91 days.
a.)
Discount yield on T-bills
T-bill discount yield =
9.62%
b.)
Coupon-equivalent yield on T-bills
9.99%
c.)
Calculating annual effective yields
effective yield =
d.)
7.
10.37%
Relationship between effective yield, coupon-equivalent yield, and
discount yield.
E.Y. > C.-E. Y. > D.Y.
Commercial paper nominal yield calculation.
CPNY = (Dollar discount / Purchase price) x (365 / Days to maturity)
where Dollar discount = Face value - Purchase price
a.)
Finding the nominal yields on commercial paper
ASSUMPTIONS:
A commercial paper issue has these characteristics:
Maturity
Face value
Selling
price
45
$100,000
$98,950
First, note that the selling price is equivalent to the purchase price. Substituting,
b.)
CPNY =
8.61%
Finding the nominal yields on commercial paper
A commercial paper issue with these characteristics:
Maturity
30 days
Face value $1,000,000
Selling
$990,450
price
days
First, note that selling price is equivalent to purchase price. Substituting,
CPNY =
8.
11.73%
Implied forward rates and investing strategy.
ASSUMPTIONS:
The 1-year T-bill coupon-equivalent yield = 5.25%, and the 2-year T-bill is yielding
5.95%.
a.)
Calculating the implied one-year forward rate
Using Equation 14-8 (in Term
Structure Theories section of
chapter):
tR2 is 5.95%, tR1 is 5.25%, and t+1r1, t is the
unknown we are after.
1-year spot
5.25%
2-year spot
5.95%
6.65%
t+1r1, t =
b.)
To roll or not to roll