H04 - Chun Lee PDF

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H04

1. An open-end fund has a net asset value of $11.40 per share. It is sold with a front-end load of 7%. What is the offering price? Offering price

$

12.26 ± 1%

A 7% front-end load, or sales commission, means that every dollar paid results in only $0.93 going toward the purchase of shares. Therefore: Offering price =

$ 11.4 NAV = =$ 12.26 1−load 1−0.07

2. If the offering price of an open-end fund is $12.40 per share and the fund is sold with a frontend load of 6%, what is its net asset value? 11.66 ± 1%

Net asset value $ NAV = Offering price × (1 – load) = $12.40 × 0.94 = $11.66 3. The composition of the Fingroup Fund portfolio is as follows: Stock Shares Price A 270,000 $ 30 B 370,000 35 C 470,000 10 D 670,000 15 The fund has not borrowed any funds, but its accrued management fee with the portfolio manager currently totals $50,000. There are 5 million shares outstanding. What is the net asset value of the fund? Net asset value

$

7.15 ± 1%

Stock Value Held by Fund A $ 8,100,000 B 12,950,000 C 4,700,000 D 10,050,000 Total $ 35,800,000 NAV =

MV of assets−MV of liabilities $ 35,800,000 −$ 50,000 = =$ 7.15 Shares outstanding 5,000,000

4. The composition of the Fingroup Fund portfolio is as follows: Stock Shares Price A 320,000 $ 40 B 420,000 45 C 520,000 10

D

720,000

15

If during the year the portfolio manager sells all of the holdings of stock D and replaces it with 240,000 shares of stock E at $30 per share and 240,000 shares of stock F at $15 per share, what is the portfolio turnover rate? 22.64 ± 1%

Turnover rate

%

Stock Value Held by Fund A $ 12,800,000 B 18,900,000 C 5,200,000 D 10,800,000 Total $ 47,700,000 The value of stocks sold and replaced = $10,800,000. Value of stocks sold ∨replaced $ 10,800,000 = =22.64 % Turnover rate = $ 47,700,000 Value of assets 5. The Closed Fund is a closed-end investment company with a portfolio currently worth $215 million. It has liabilities of $6 million and 4 million shares outstanding. a. What is the NAV of the fund? 52.25 ± 1%

NAV $ b. If the fund sells for $49 per share, what is its premium or discount as a percent of NAV? The fund sells at an from NAV.

6.22 ± 1%

%

MV of assets−MV of liabilities $ 215 M −$ 6 M = =$ 52.25 Shares outstanding 4M Price − NAV $ 49−$ 52.25 =−6.22% = b. Premium or discount = $ 52.25 NAV a. NAV =

6. Corporate Fund started the year with a net asset value of $13.10. By year-end, its NAV equaled $12.40. The fund paid year-end distributions of income and capital gains of $1.80. What was the rate of return to an investor in the fund? Rate of return Rate of return =

8.40 ± 1%

%

∆ NAV + Distribution −$ 0.7 + $ 1.8 =8.4 % = Starting NAV $ 13.1

7. A closed-end fund starts the year with a net asset value of $31. By year-end, NAV equals $33.00. At the beginning of the year, the fund is selling at a 3% premium to NAV. By the end of the year, the fund is selling at a 8% discount to NAV. The fund paid year-end distributions of income and capital gains of $3.40.

a. What is the rate of return to an investor in the fund during the year? 5.73 ± 1%

Rate of return % b. What would have been the rate of return based on NAV? 17.42 ± 1%

Rate of return

%

a. Start of year price = $31.00 × 1.03 = $31.93 End of year price = $33.00 × 0.92 = $30.36 Although NAV increased, the price of the fund fell by $1.57. ∆ Price+ Distribution −$ 1.57 + $ 3.40 =5.73 % = Rate of return = $ 31.93 Starting price b. Rate of return =

∆ NAV + Distribution $ 2.0 +$ 3.4 = =5.4 % $ 31 Starting NAV

8. Loaded-Up Fund charges a 12b-1 fee of 1% and maintains an expense ratio of 0.65%. Economy Fund charges a front-end load of 2%, but has no 12b-1 fee and an expense ratio of 0.35%. Assume the rate of return on both funds’ portfolios (before any fees) is 6% per year. a. How much will an investment of $100 in each fund grow to after 1 year? 104.35 ± 1% Loaded-Up Fund $ Economy Fund

103.54 ± 1%

Economy Fund

115.57 ± 1%

$ b. How much will an investment of $100 in each fund grow to after 3 years? 113.63 ± 1% Loaded-Up Fund $ $ c. How much will an investment of $100 in each fund grow to after 12 years? 166.69 ± 1% Loaded-Up Fund $ Economy Fund

$

189.52 ± 1%

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 Fund: True expense ratio = Expense ratio + (12b-1 fee) = 1% + 0.65% = 1.65% a. Year 1 = $100 × (1 + 0.06 – 0.0165) = $104.35 b. Year 3 = $100 × (1 + 0.06 – 0.0165)3 = $113.63 c. Year 12 = $100 × (1 + 0.06 – 0.0165)12 = $166.69 Economy Fund: a. Year 1 = $100 × 0.98 × (1 + 0.06 – 0.0035) = $103.54 b. Year 3 = $100 × 0.98 × (1 + 0.06 – 0.0035)3 = $115.57 c. Year 12 = $100 × 0.98 × (1 + 0.06 – 0.0035)12 = $189.52

9. City Street Fund has a portfolio of $500 million and liabilities of $20 million. a. If there are 40 million shares outstanding, what is net asset value? 12 ± 1%

Net asset value $ b-1 If a large investor redeems 3 million shares, what happens to the portfolio value? 464 ± 1%

Portfolio value to $ million. b-2 If a large investor redeems 3 million shares, what happens to shares outstanding? Shares outstanding 37 ± 1%

to million. b-3 If a large investor redeems 3 million shares, what is net asset value? Net asset value a. NAV =

$

12 ± 1%

MV of assets−MV of liabilities $ 500 M −$ 20 M =$ 12 = 40 M Shares outstanding

b. Because 3 million shares are redeemed at NAV = $12, the value of the portfolio decreases to: Portfolio value = $500 million – ($12 × 3 million) = $464 million The number of shares outstanding will be 40 million – 3 million = 37 million. Thus, net asset value after the redemption will be: MV of assets−MV of liabilities $ 464 M −$ 20 M =$ 12 = NAV = 37 M Shares outstanding 10. Consider a mutual fund with $217 million in assets at the start of the year and with 20 million shares outstanding. The fund invests in a portfolio of stocks that provides dividend income at the end of the year of $5 million. The stocks included in the fund's portfolio increase in price by 6%, but no securities are sold, and there are no capital gains distributions. The fund charges 12b-1 fees of 0.25%, which are deducted from portfolio assets at year-end. a. What is net asset value at the start and end of the year? Net Asset Value Start of the year

10.850 ± 1%

$

End of the year

11.472 ± 1%

b. What is the rate of return for an investor in the fund? Rate of return

8.04 ± 1%

%

MV of assets−MV of liabilities $ 217,000,000 =$ 10.85 = 20,000,000 Shares outstanding Ending NAV = $10.85 × 1.06 × (1 − 0.0025) = $11.472

a. Starting NAV =

b. Rate of return =

∆ NAV + Distribution = Beginning NAV

$ 5,000,000 $ 20,000,000 =$ 8.04 % $ 10.85

$ 11.472−$ 10.85 +

11. The New Fund had average daily assets of $4.0 billion in the past year. The fund sold $418 million and purchased $518 million worth of stock during the year. What was its turnover ratio? 10.45 ± 1%

Turnover ratio

%

The excess of purchases over sales must be due to new inflows into the fund. Therefore, $418 million of stock previously held by the fund was replaced by new holdings. So turnover is: Turnover rate =

$ 418,000,000 Value of stocks sold ∨replaced = =10.45 % $ 4,000,000,000 Shares outstanding

12. The New Fund had average daily assets of $3.7 billion in the past year. New Fund’s expense ratio was 2.6% and the management fee was 2.2%. a. What were the total fees paid to the fund’s investment managers during the year? Total fees paid

$

81.40 ± 1%

million

b. What were the other administrative expenses? Other administrative expenses

$

14.8

million

a. Fees paid to investment managers were: 2.2% × $3.7 billion = $81.4 million. b. Since the total expense ratio was 2.6% and the management fee was 2.2%, we conclude that 0.4% must be for other expenses. Therefore, other administrative expenses were: 0.004 × $3.7 billion = $14.8 million. 13. You purchased 2,500 shares of the New Fund at a price of $20 per share at the beginning of the year. You paid a front-end load of 4%. The securities in which the fund invests increase in value by 11% during the year. The fund's expense ratio is 2.7%. What is your rate of return on the fund if you sell your shares at the end of the year? Rate of return

3.97 ± 1%

%

Because the 4% load was paid up front and reduced the actual amount invested, only 96% (1.00 − 0.04) of the contribution was invested. Given the value of the portfolio increased by 11% and the expense ratio was 2.7%, we can calculate the end value of the investment against the initial contribution: 1 + r = 0.96 × (1 + 0.11 − 0.027) = 1.0397 Rate of return = 1.0397 − 1 = 0.0397 = 3.97% 14. You are considering an investment in a mutual fund with a 3% load and an expense ratio of 0.6%. You can invest instead in a bank CD paying 5% interest. a. If you plan to invest for two years, what annual rate of return must the fund portfolio earn for you to be better off in the fund than in the CD? Assume annual compounding of returns. Annual rate of return

7.21 ± 1%

%

b. If you plan to invest for six years, what annual rate of return must the fund portfolio earn for you to be better off in the fund than in the CD? Assume annual compounding of returns. 6.13 ± 1%

Annual rate of return % c. Now suppose that instead of a front-end load the fund assesses a 12b-1 fee of 0.85% per year. What annual rate of return must the fund portfolio earn for you to be better off in the fund than in the CD? 6.45 ± 1%

Annual rate of return

%

a. After two years, each dollar invested in a fund with a 3% load and a portfolio return equal to r will grow to: $0.97 × (1 + r − 0.0060)2 Each dollar invested in the bank CD will grow to: $1 × (1.05)2 For the mutual fund to be the better investment, the portfolio return, r, must satisfy: 0.97 × (1 + r − 0.0060)2 > (1.05)2 = 1.1025 (1 + r − 0.0060)2 > 1.1366 1 + r − 0.0060 > 1.0661 1 + r > 1.0721 Therefore, r > 0.0721 = 7.21% b. If you invest for six years, then the portfolio return must satisfy: 0.97 × (1 + r − 0.0060)6 > (1.05)6 = 1.3401 (1 + r − 0.0060)6 > 1.3815 1 + r − 0.0060 > 1.0553 1 + r > 1.0613 r > 6.13% 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. c. With a 12b-1 fee instead of a front-end load, the portfolio must earn a rate of return (r) that satisfies: 1 + r − 0.0060 − 0.0085 > 1.05 In this case, r must exceed 6.45% regardless of the investment horizon. 15. Suppose that every time a fund manager trades stock, transaction costs such as commissions and bid–ask spreads amount to 2.5% of the value of the trade. If the portfolio turnover rate is 50%, by how much is the total return of the portfolio reduced by trading costs? Fall in returns

2.5 ± 1%

%

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 2.5%; the buy orders to replace those securities entail another 2.5% in trading costs. Total trading costs will reduce portfolio returns by: 2 × 0.025 × 0.5 = 0.025 or 2.5%...