Consider a mutual fund with $203 million in assets at the start of the year and with 10 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 7%, 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.

Consider a mutual fund with $203 million in assets at the start of the year and with 10 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 7%, 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 net asset value at the start and end of the year? (Enter your answers in dollars rounded to 3 decimal places.)

 

	Net Asset Value
Start of the year	$
End of the year

   

b.	What is the rate of return for an investor in the fund? (Use rounded "Net Asset Value". Round your answer to 2 decimal places.)

 

Rate of return

%

Explanation:

a.

Start of year NAV =	Market value of assets − Market value of liabilities
	Shares outstanding

=	$203,000,000	= $20.300
	10,000,000

End of year NAV is based on the 7% price gain, less the 0.75% 12b-1 fee:

End of year NAV = $20.300 × 1.07 × (1 − 0.0075) = $21.558

b.

Given the dividends per share is $0.50, we can calculate the rate of return using the following equation:

Rate of return =	Δ(NAV) + Distributions
	Start of year NAV

=	($21.558 − $20.300) + $0.50	= 0.0866 = 8.66%
	$20.300

The investment opportunities have these characteristics:

The investment opportunities have these characteristics:

	Mean Return	Standard Deviation
Stocks	18.40%	13.40%
Bonds	12.00%	4.29%
Portfolio	16.48%	8.09%

The best choice depends on the degree of your aversion to risk. Nevertheless, we suspect most people would choose the portfolio over stocks since the portfolio has almost the same return with much lower volatility. This is the advantage of diversification.

A stock will provide a rate of return of either −27% or +35%.

a.	If both possibilities are equally likely, calculate the expected return and standard deviation. (Do not round intermediate calculations. Round your answers to 1 decimal place.)

Expected return	%
Standard deviation	%

b.	If Treasury bills yield 4% and investors believe that the stock offers a satisfactory expected return, what must the market risk of the stock be?

Market risk

$

Explanation:

a.

The expected rate of return on the stock is 4.0%. The standard deviation is 31.0%.

b.

Because the stock offers a risk premium of zero (its expected return is the same as the expected return for Treasury bills), it must have no market risk. All the risk must be diversifiable, and therefore of no concern to investors.

You purchase 100 shares of stock for $50 a share. The stock pays a $4 per share dividend at year-end. What is the rate of return on your investment for the end-of-year stock prices listed below? What is your real (inflation-adjusted) rate of return? Assume an inflation rate of 6%.

You purchase 100 shares of stock for $50 a share. The stock pays a $4 per share dividend at year-end. What is the rate of return on your investment for the end-of-year stock prices listed below? What is your real (inflation-adjusted) rate of return? Assume an inflation rate of 6%. (Leave no cells blank - be certain to enter "0" wherever required. Negative values should be indicated by a minus sign. Do not round intermediate calculations. Round your "Real Rate of Return" answers to 2 decimal places.)

	Rate of Return	Real Rate of Return
a. $46	%	%
b. $50	%	%
c. $55	%	%

Explanation:

a.

Rate of return =	capital gain + dividend	=	($46 − $50) + $4	= 0%
	initial share price		$50

Real rate of return =	1+ nominal rate of return	−1 =	1 + 0	−1 = −0.0566 = −5.66%
	1+ inflation rate		1 + 0.06

b.

Rate of return =	capital gain + dividend	=	($50 − $50) + $4	= 0.08 = 8%
	initial share price		$50

Real rate of return =	1+ nominal rate of return	−1 =	1.08	−1 = 0.0189 = 1.89%
	1+ inflation rate		1.06

  
c.

Rate of return =	capital gain + dividend	=	($55 − $50) + $4	= 0.18 = 18%
	initial share price		$50

Real rate of return =

1+ nominal rate of return

−1 =

1.18

−1 = 0.1132 = 11.32%

A stock is selling today for $20 per share. At the end of the year, it pays a dividend of $2 per share and sells for $23.

A stock is selling today for $20 per share. At the end of the year, it pays a dividend of $2 per share and sells for $23.

a.	What is the total rate of return on the stock?

Rate of return

%

b.	What are the dividend yield and percentage capital gain?

Dividend yield	%
Capital gains yield	%

Explanation:

 a.

Rate of return =	capital gain + dividend	=	($23 − $20) + $2	= 0.25 = 25%
	initial share price		$20

b.

Dividend yield = dividend/initial share price = $2/$20 = 0.10 = 10%

Capital gains yield = capital gain/initial share price = $3/$20 = 0.15 = 15%