FIN 331-Introductory Investments: Chapter 4 Homework

An open-end fund has a net asset value of $15.90 per share. It is sold with a front-end load of 5% What is the offering price? (Round your answer to 2 decimal places)

$15.90 * 0.05 = 0.795 $15.90 + 0.075 = $16.695 = $16.70

The offering price of an open-end fund is $20.40 per share and the fund is sold with a front-end load of 5%. What is its net asset value? (Round your answer to 2 decimal places)

$20.40 * 0.05 = 1.020 $20.40 - 1.020 = $19.380 = $19.38

The New Fund had average daily assets of $9.5 billion last year. The fund sold $550 million worth of stock and purchased $630 million during the year. What was its turnover ratio? (Round your answer to 1 decimal place)

$550,000,000 / $9,500,000,000 = 0.058 = 5.8%

Corporate Fund started the year with a net asset value of $28.80. By year-end, its NAV equaled $28.30. The fund paid year-end distributions of income and capital gains of $1.70. What was the (pretax) rate of return to an investor in the fund? (Round your answer to 2 decimal places)

($28.30 + $1.70)/$28.80 = 1.042 1.042-1 = 0.042 0.042 * 100 = 4.167 Rate of return =4.17%

City Street Fund has portfolio of $480 million and liabilities of $16 million. If there are 10 million shares outstanding, what is net asset value? (Round your answer to 2 decimal places)

($480 million - $16 million) / 10 million shares outstanding =$46.40 per share

Suppose that every time a fund manager trades stock, transaction costs such as commissions and bid-ask spreads amount to 0.5% of the value of the trade. If the portfolio turnover rate is 40%, by how much is the total return of the portfolio reduced by trading costs? (Round your answer to 2 decimal places)

0.40%

You purchased 1,000 shares of the New Fund at a price of $31 per share at the beginning of the year. You paid a front-end load of 3%. The securities in which the fund invests increase in value by 10% during the year. The fund's expense ratio is 1.1%. What is your rate of return on the fund if you sell your shares at the end of the year? (Do not round immediate calculations. Round your answer to 2 decimal places)

1,000 * $31 = $31,000 $31,000 /(1-0.03) = $31,958.763 $31,000*(1+0.10-0.011)= $33,759 ($33,759 - $31,958.763) / $31,958.763 = 5.60%

The composition of the FinGroup Fund portfolio is as follows: Stock A= 200,000 shares @ $35 Stock B= 276,000 shares @ $44 Stock C= 412,000 shares @ $32 Stock D= 560,000 shares @ $25 During the year the portfolio manager sells all of the holding of stock D and replaces it with 200,000 shares of stock E at $45 per share and 62,500 shares of stock F at $80 per share. What is the portfolio turnover rate? (Round your answer to 1 decimal place)

200,000 * $35 = $7,000,000 276,000 * $44 = $12,144,000 412,000 * $32 = $13,184,000 560,000 * $25 = $14,000,000 ________________________________________ $46,328,000 200,000 * $45 = $9,000,000 62,500 * $80 = $5,000,000 ________________________________________ $14,000,000 $14,000,000 / $46,328,000 =0.302 = 30.2%

The composition of the FinGroup Fund portfolio is as follows: Stock A= 200,000 shares @ $41 Stock B= 270,000 shares @ $53 Stock C= 415,000 shares @ $35 Stock D= 530,000 shares @ $40 The fund has not borrowed any funds, but its accrued management fee with the portfolio manager currently totals $44,000. There are 2.4 million shares outstanding. What is the net asset value of the fund? (Round your answer to 2 decimal places)

200,000 * $41 = $8,200,000 270,000 * $53 = $14,310,000 415,000 * $35 = $14,525,000 530,000 * $40 = $21,200,000 ________________________________________ $58,235,000 $58,235,000 - $44,000 =$58,191,000 $58,191,000 / 2,400,000 =$24.246 = $24.25

The Investments Fund sells Class A shares with a front-end load of 5% and Class B shares with 12b-1 fees of 1% annually as well as back-end load fees that start at 5% and fall by 1% for each full year the investor holds the portfolio (until the fifth year). Assume that you have $1,000 to invest and the portfolio rate of return net of operating expenses is 12% annuall. A-1) If you invest in each fund and sell after 4 years, how much will you receive from each sale? (Round your answers to 2 decimal places) A-2) Are Class A or Class B shares the better choice for you? B-1) If you invest in each fund and sell after 10 years, how much will you receive from each sale? (Round your answers to 2 decimal places) B-2) Are Class A or Class B shares the better choice for you?

A-1) Class A: $1000 * 0.05 = $50 $1000 - $50 = $950 $950 * (1.12)^4 = $1494.84 Class B: 12%-1% = 11% 1-0.01 = 0.99 $1000 * (1.11)^4 = $1518.07 $1518.07 * 0.99 = $1502.89 A-2) Class B B-1) Class A: $1000 * 0.05 = $50 $1000 - $50 = $950 $950 * (1.12)^10 = $2950.56 Class B: Class B: 12%-1% = 11% 1-0.01 = 0.99 $1000 * (1.11)^10 = $2839.42 B-2) Class A. At this longer horizon, Class B shares are no longer the better choice. The effect of Class B's 1.00% 12b-1 fees accumulates over time and finally overwhelms the 5% load charge to Class A investors

A closed-end fund starts the year with a net asset value of $17.00. By year-end, NAV equals $17.30. At the beginning of the year, the fund was selling at a 1.5% premium to NAV. By the end of one year, the fund is selling at a 6% discount from NAV. The fund paid year-end distributions of income and capital gains of $1.90. A.) What is the rate of return to an investor in the fund during the year? (Do not round intermediate calculations. Round your answer to 2 decimal places) B.) What would have been the rate of return to an investor who held the same securities as the fund manager during the year? (Do not round intermediate calculations. Round your answer to 2 decimal places)

A.) $17 * (1 + 1.5%) = $17.255 $17.30 * (1-6%) = $16.262 $17.255 - $16.262 = $0.993 Therefore, price fell by 0.993 (-0.993 + $1.90) / $17.255 Rate of return =$5.30 B.) $17.30 - $17 = 0.30 (0.30 + $1.90) / $17 = 12.90%

A.) The Closed Fund is a closed-end investment company with a portfolio currently worth $170 million. It has liabilities of $7 million and 5 million shares outstanding. What is the NAV of the fund? (Round your answer to 2 decimal places) B.) If the fund sells for $25 per share, what is its premium or discount as a percent of net asset value? (Input the amount as a positive value. Round your answer to 2 decimal places)

A.) ($170 million - $7 million) / 5 million shares = $32.60 B.) Discount of 23.31% ($32.60 - $25) / $32.60 =0.233 *100 = $23.31

The New Fund had average daily assets of $1.6 billion in the past year. If New Fund's expense ratio was 1.00% and the management fee was 0.70%. A.) What were the total fees paid to the fund's investment managers during the year? (Enter your answer in millions. Round your answer to 1 decimal place) B.) What were the other administrative expenses? (Enter your answer in millions. Round your answer to 1 decimal place)

A.) 0.0070 * $1.6b = $11.2 mil B.) 1.00 - 0.70 = 0.30 0.30 / 100 = 0.0030 0.0030 * $1.6b = $4.8 mil

A.) You expect a tax-free municipal bond portfolio to provide a rate of return of 4.2%. Management fees of the fund are 0.62%. What fraction of portfolio income is given up to fees? (Round your answer to 1 decimal place) B.) If the management fees for an equity fund also are 0.62% , but you expect a portfolio return of 14.0%, what fraction of the portfolio income is given up to fees? (Round your answer to 1 decimal place) C.) For which fund might management fees be a bigger factor in your investment decision?

A.) 0.62% / 4.2% = 0.148 = 14.8% B.) 0.62% / 14.0% = 4.4% C.) Bond fund

You are considering an investment in a mutual fund with a 5% load and expense ratio of 0.1%. You can invest instead in a bank CD paying 2% interest. A.) If you plan to invest for 2 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. (Do not round intermediate calculations. Round your answer to 2 decimal places) B) What annual rate of return must the fund portfolio earn if you plan to invest for 9 years to be better off in the fund than in the CD? (Do not round intermediate calculations. Round your answer to 2 decimal places) C.) Now suppose that instead of a front-end load the fund assesses a 12b-1 fee of 0.80% 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? (Do not round intermediate calculations. Round your answer to 2 decimal places)

A.) After two years, each dollar invested in a fund with a 5% load and a portfolio return equal to r will grow to $0.95 * (1 + r - 0.0010)^2 Each dollar invested in the bank CD will grow to $1 * 1.02^2 If the mutual fund is to be the better investment, then the portfolio return (r) must satisfy: 0.95 * (1+r - 0.0010)^2 > 1.02^2 0.95 * (1+r-0.0010)^2 > 1.0404 (1+r-0.0010)^2 > 1.0952 1+r-0.0010 > 1.0465 1+r>1.0475 r> 0.0475 = 4.75% B) If you invest for nine years, then the portfolio return must satisfy: 0.95*(1+r-0.0010)^9>1.02^9 =1.1951 (1+r-0.0010)^9 > 1.258 1+r-0.0010 > 1.0258 r > 2.68% 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-0.0010-0.008 >1.02 In this case, r must exceed 2.90% regardless of the investment horizon

Consider a mutual fund with $220 million in assets at the start of the year and 10 million shares outstanding. The fund invests in a portfolio of stocks that provides dividend income at the end of the year of $2.3 million. The stocks included in the fund's portfolio increase in price by 5%, but no securities are sold and there are no capital gains distributions. The fund charges 12b-1 fees of 0.75%, which are deducted from portfolio assets at year-end. A.) What is the fund's net asset value at the start and end of the year? (Round "End of the year" to 3 decimal places) B.) What is the rate of return for an investor in the fund? (Round your immediate calculations to 3 decimal places and final answer to 2 decimal places.)

A.) NAV0 = $220,000,000 / 10,000,000 shares = $22 Dividends = $2,300,000/ 10,000,000 shares = $0.23 NAV1= $22 *(1.05)* (1-0.0075) = $22.927 Start of the year= $22 End of the year = $22.927 B.) Return = ($22.927 + $0.23) / $22 -1 = 0.053 * 100 = 5.259%

Loaded-Up Find charges a 12b-1 fee of 1.00% and maintains an expense ratio of 0.75%. Economy Fund charges a front-end load of 2.0%, but has no 12b-1 fee and an expense ratio of 0.25%. Assume the rate of return on both funds' portfolios (before any fees) is 9% per year. How much will an investment of $1,000 in each fund grow to after: (Round your answers to 2 decimal places) A.) 1 year B.) 3 years C.) 10 years

Loaded-Up Fund: A.) $1,000 * (1+0.09-0.0175) = $1,072.50 B.) $1,000 * (1+0.09-0.0175)^3= $1,233.65 C.) $1,000 * (1+0.09-0.0175)^10= $2,013.60 Economy Fund: A.) $1,000 * (1-0.02) * (1+0.09 -0.0025) = $1,065.75 B.) $1,000 * (1-0.02) * (1+0.09 -0.0025)^3 = $1,260.42 C.) $1,000 * (1-0.02) * (1+0.09 -0.0025)^10 = $2,267.35