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b. Open-end mutual funds offer higher levels of service to investors. The investors do
10. Open-end funds must honor redemptions and receive deposits from investors. This
flow of money necessitates retaining cash. Close-end funds no longer take and
receive money from investors. As such, they are free to be fully invested at all times.
Open-end funds must honor redemptions and receive deposits from investors. This
flow of money necessitates retaining cash. Close-end funds no longer take and
receive money from investors. As such, they are free to be fully invested at all times.
11. The offering price includes a 6% front-end load, or sales commission, meaning that
every dollar paid results in only $0.94 going toward the purchase of shares.
Therefore:
70.10$
NAV
12. NAV = Offering price (1 – load) = $12.30 .95 = $11.69
13. Given that net asset value equals assets minus liabilitiesexpressed on a per-share basis,
we first add up the value of the shares to get the market value of the portfolio:
Stock
Value Held by
Fund
A
$ 7,000,000
B
12,000,000
C
8,000,000
D
15,000,000
Total
$42,000,000
Knowing that the accrued management fee, which adjusts the value of the portfolio, totals
$30,000, and the number of the shares outstanding is 4,000,000, we can use the NAV
equation:
Market value of assets－Market value of liabilities
000,000,4
14. The value of stocks sold and replaced = $15,000,000.
Turnover rate =Value of stocks sold or replaced
Value of assets
=
000,000,42$
000,000,15$
= 0.3571 = 35.71%
15.
a. NAV =Market value of assets－Market value of liabilities
Shares outstanding
= $200,000,000－ $3,000,000
5,000,000 = $39.40
b. Premium (or discount) =
NAV
NAVicePr −
=
40.39$
40.39$36$−
= –0.0863 = –8.63%
The fund sells at an 8.63% discount from NAV.
16. Given the NAV at the beginning and the end of the period, and the distributions
during the period, we can use the equation below to solve for the rate of return of the
Corporate Fund:
Rate of return =
Δ(NAV)＋ Distributions
50.1$40.0$ +−
= 0.0880 = 8.80%
17. As the price of a close-end fund may deviate from its NAV, we instead use the price
of the net asset value when we calculate the rate of return:
a. Start of year price = $12.00 1.02 = $12.24
End of year price = $12.10 0.93 = $11.253
Although NAV increased, the price of the fund fell by $0.987.
Rate of return =Δ(Price) ＋ Distributions
50.1$987.0$ +−
= 0.0419 = 4.19%
b. An investor holding the same portfolio as the fund manager would have earned
a rate of return based on the increase in the NAV of the portfolio:
Rate of return =Δ(NAV) ＋ Distributions
50.1$10.0$ +
= 0.1333 = 13.33%
18. Assume a hypothetical investment of $100. The end value of the investment will be
equal to I × (1– front-end load) × (1 + r– true expense ratio)T
Loaded-Up
We add the 12b-1 fee to the operating expenses to obtain the true expense
ratio:Expense ratio + (12b-1 fee) = 1% + 0.75% = 1.75%
19.
a. NAV =Market value of assets－Market value of liabilities
Shares outstanding
= $450,000,000－$10,000,000
44,000,000 = $10
b. Because 1 million shares are redeemed at NAV = $10, the value of the portfolio
decreases to:
Portfolio value = $450million –($10×1million) = $440million
43,000,000 = $10
20.
a. Empirical research indicates that past performance of mutual funds is not highly
predictive of future performance, especially for better-performing funds. While
there may be some tendency for the fund to be an above average performer next
year, it is unlikely to once again be a top 10% performer.
b. On the other hand, the evidence is more suggestive of a tendency for poor
performance to persist. This tendency is probably related to fund costs and
turnover rates. Thus if the fund is among the poorest performers, investors
would be concerned that the poor performance will persist.
21. Start of year NAV =Market value of assets－Market value of liabilities
Shares outstanding
= $200,000,000
10,000,000 = $20
End of year NAV is based on the 8% price gain, less the 1% 12b-1 fee:
End of year NAV = $201.08(1 – 0.01) = $21.384
Given the dividends per share is $0.20, we can calculate the rate of return using the
following equation:
Rate of return =Δ(NAV) ＋ Distributions
Or otherwise, you can calculate the rate of return by the actual amount invested and
value changes:
To purchase the shares, you would have had to invest: $20,000/(1 − 0.04) = $20,833
25. Suppose you have $1000 to invest. The initial investment in Class A shares is $940
net of the front-end load. After 4 years, your portfolio will be worth:
$940 (1.10)4 = $1,376.25
Class B shares allow you to invest the full $1,000, but your investment performance net
of 12b-1 fees will be only 9.5%, and you will pay a 1% back-end load fee if you sell
after 4 years. Your portfolio value after 4 years will be:
$1,000 (1.095)4 = $1,437.66
After paying the back-end load fee, your portfolio value will be:
$1,437.66 .99 = $1,423.28
Class B shares are the better choice if your horizon is 4 years.
26.
a. After two years, each dollar invested in a fund with a 4% load and a portfolio
return equal to r will grow to:$0.96 (1 + r – 0.005)2
Each dollar invested in the bank CD will grow to:$1 (1.06)2
If the mutual fund is to be the better investment, then the portfolio return, r,
must satisfy:
0.96 (1 + r – 0.005)2> (1.06)2
0.96 (1 + r – 0.005)2> 1.1236
(1 + r – 0.005)2> 1.1704
1 + r – 0.005 > 1.0819
1 + r> 1.0869
Therefore, r> 0.0869 = 8.69%
b. If you invest for six years, then the portfolio return must satisfy:
0.96 (1 + r – 0.005)6> (1.06)6 = 1.4185
(1 + r – 0.005)6> 1.4776
1 + r – 0.005 > 1.0672
1 + r> 1.0722
r> 7.22%
The cutoff rate of return is lower for the six year investment because the "fixed
cost" (i.e., the one-time front-end load) is spread out over a greater number of
years.
1 + r – 0.005 – 0.0075 > 1.06
In this case, r must exceed 7.25% regardless of the investment horizon.
27. The turnover rate is 50%. This means that, on average, 50% of the portfolio is sold
and replaced with other securities each year. Trading costs on the sell orders are
0.4%; the buy orders to replace those securities entail another 0.4% in trading costs.
Total trading costs will reduce portfolio returns by: 2 0.004 0.50 = 0.004 or 0.4%
28. For the bond fund, the fraction of portfolio income given up to fees is:
%0.4
%6.0
= 0.150 = 15.0%
For the equity fund, the fraction of investment earnings given up to fees is:
%6.0
b. Open-end mutual funds offer higher levels of service to investors. The investors do
10. Open-end funds must honor redemptions and receive deposits from investors. This
flow of money necessitates retaining cash. Close-end funds no longer take and
receive money from investors. As such, they are free to be fully invested at all times.
Open-end funds must honor redemptions and receive deposits from investors. This
flow of money necessitates retaining cash. Close-end funds no longer take and
receive money from investors. As such, they are free to be fully invested at all times.
11. The offering price includes a 6% front-end load, or sales commission, meaning that
every dollar paid results in only $0.94 going toward the purchase of shares.
Therefore:
70.10$
NAV
12. NAV = Offering price (1 – load) = $12.30 .95 = $11.69
13. Given that net asset value equals assets minus liabilitiesexpressed on a per-share basis,
we first add up the value of the shares to get the market value of the portfolio:
Stock
Value Held by
Fund
A
$ 7,000,000
B
12,000,000
C
8,000,000
D
15,000,000
Total
$42,000,000
Knowing that the accrued management fee, which adjusts the value of the portfolio, totals
$30,000, and the number of the shares outstanding is 4,000,000, we can use the NAV
equation:
Market value of assets－Market value of liabilities
000,000,4
14. The value of stocks sold and replaced = $15,000,000.
Turnover rate =Value of stocks sold or replaced
Value of assets
=
000,000,42$
000,000,15$
= 0.3571 = 35.71%
15.
a. NAV =Market value of assets－Market value of liabilities
Shares outstanding
= $200,000,000－ $3,000,000
5,000,000 = $39.40
b. Premium (or discount) =
NAV
NAVicePr −
=
40.39$
40.39$36$−
= –0.0863 = –8.63%
The fund sells at an 8.63% discount from NAV.
16. Given the NAV at the beginning and the end of the period, and the distributions
during the period, we can use the equation below to solve for the rate of return of the
Corporate Fund:
Rate of return =
Δ(NAV)＋ Distributions
50.1$40.0$ +−
= 0.0880 = 8.80%
17. As the price of a close-end fund may deviate from its NAV, we instead use the price
of the net asset value when we calculate the rate of return:
a. Start of year price = $12.00 1.02 = $12.24
End of year price = $12.10 0.93 = $11.253
Although NAV increased, the price of the fund fell by $0.987.
Rate of return =Δ(Price) ＋ Distributions
50.1$987.0$ +−
= 0.0419 = 4.19%
b. An investor holding the same portfolio as the fund manager would have earned
a rate of return based on the increase in the NAV of the portfolio:
Rate of return =Δ(NAV) ＋ Distributions
50.1$10.0$ +
= 0.1333 = 13.33%
18. Assume a hypothetical investment of $100. The end value of the investment will be
equal to I × (1– front-end load) × (1 + r– true expense ratio)T
Loaded-Up
We add the 12b-1 fee to the operating expenses to obtain the true expense
ratio:Expense ratio + (12b-1 fee) = 1% + 0.75% = 1.75%
19.
a. NAV =Market value of assets－Market value of liabilities
Shares outstanding
= $450,000,000－$10,000,000
44,000,000 = $10
b. Because 1 million shares are redeemed at NAV = $10, the value of the portfolio
decreases to:
Portfolio value = $450million –($10×1million) = $440million
43,000,000 = $10
20.
a. Empirical research indicates that past performance of mutual funds is not highly
predictive of future performance, especially for better-performing funds. While
there may be some tendency for the fund to be an above average performer next
year, it is unlikely to once again be a top 10% performer.
b. On the other hand, the evidence is more suggestive of a tendency for poor
performance to persist. This tendency is probably related to fund costs and
turnover rates. Thus if the fund is among the poorest performers, investors
would be concerned that the poor performance will persist.
21. Start of year NAV =Market value of assets－Market value of liabilities
Shares outstanding
= $200,000,000
10,000,000 = $20
End of year NAV is based on the 8% price gain, less the 1% 12b-1 fee:
End of year NAV = $201.08(1 – 0.01) = $21.384
Given the dividends per share is $0.20, we can calculate the rate of return using the
following equation:
Rate of return =Δ(NAV) ＋ Distributions
Or otherwise, you can calculate the rate of return by the actual amount invested and
value changes:
To purchase the shares, you would have had to invest: $20,000/(1 − 0.04) = $20,833
25. Suppose you have $1000 to invest. The initial investment in Class A shares is $940
net of the front-end load. After 4 years, your portfolio will be worth:
$940 (1.10)4 = $1,376.25
Class B shares allow you to invest the full $1,000, but your investment performance net
of 12b-1 fees will be only 9.5%, and you will pay a 1% back-end load fee if you sell
after 4 years. Your portfolio value after 4 years will be:
$1,000 (1.095)4 = $1,437.66
After paying the back-end load fee, your portfolio value will be:
$1,437.66 .99 = $1,423.28
Class B shares are the better choice if your horizon is 4 years.
26.
a. After two years, each dollar invested in a fund with a 4% load and a portfolio
return equal to r will grow to:$0.96 (1 + r – 0.005)2
Each dollar invested in the bank CD will grow to:$1 (1.06)2
If the mutual fund is to be the better investment, then the portfolio return, r,
must satisfy:
0.96 (1 + r – 0.005)2> (1.06)2
0.96 (1 + r – 0.005)2> 1.1236
(1 + r – 0.005)2> 1.1704
1 + r – 0.005 > 1.0819
1 + r> 1.0869
Therefore, r> 0.0869 = 8.69%
b. If you invest for six years, then the portfolio return must satisfy:
0.96 (1 + r – 0.005)6> (1.06)6 = 1.4185
(1 + r – 0.005)6> 1.4776
1 + r – 0.005 > 1.0672
1 + r> 1.0722
r> 7.22%
The cutoff rate of return is lower for the six year investment because the "fixed
cost" (i.e., the one-time front-end load) is spread out over a greater number of
years.
1 + r – 0.005 – 0.0075 > 1.06
In this case, r must exceed 7.25% regardless of the investment horizon.
27. The turnover rate is 50%. This means that, on average, 50% of the portfolio is sold
and replaced with other securities each year. Trading costs on the sell orders are
0.4%; the buy orders to replace those securities entail another 0.4% in trading costs.
Total trading costs will reduce portfolio returns by: 2 0.004 0.50 = 0.004 or 0.4%
28. For the bond fund, the fraction of portfolio income given up to fees is:
%0.4
%6.0
= 0.150 = 15.0%
For the equity fund, the fraction of investment earnings given up to fees is:
%6.0
