1)jan, a retired
librarian, would like to donate some money to her alma mater to endow a $5,560
annual scholarship. The first scholarship will be awarded in 6 years. The
university will manage the funds and expects to earn 3 percent per year.
How much will Jan have to donate so that the
endowment fund never runs out?
2) In 30 years, you plan to set up a fellowship fund for your university that pays out $100,000/year in perpetuity with an annually compounded discount rate of 5%. In order to set up the fund in 30 years, how much do you need to save each year (starting this year) assuming you can get a semi-annually compounded return of 10% on your savings for the next 30 years?
3)A 65-year-old man
intends to use his retirement funds to purchase an annuity from a life
insurance company. Given the amount of money the man has available to invest,
the insurance company is able to offer two alternatives. The first option is to
receive $2,942 each month for as long as he lives; the second option is to
receive $3,930 each month, but for only 20 years (payments will be made to his
estate if he should die before that time). The relevant interest rate is 6
percent per year monthly compounding.
How long must the man live so that the first
option is a better deal?
4)An investor bought a bond at par and held it for one year. If the coupon rate is 5 percent, residual maturity of the bond is 8 years, and the yield to maturity of the bond when it was sold was 6 percent, what is the holding period return of the bond?
5) Determine the market price of a $50 par value preferred share that pays annual dividends based on a 4 percent dividend rate when the market rate is 5%?
6) Assuming Carla Vista Corp. has an ROE of 14% and investors require a 13% return on shares, estimate the firm’s P/E ratio and market price given an EPS of $2.60 and a 30% payout ratio.
7) The 1.2 million preferred shares of Mighty Machines Ltd., which pay a dividend rate of 6.5 percent on a stated value of $40, are currently worth $42,000,000. What is the risk premium associated with these preferred shares if the risk-free rate is 4.25 percent?
8) Bramble Tire’s current dividend is $4.90. Dividends are expected to grow by 20 percent for years 1 to 3 and 10 percent thereafter. The required rate of return on the stock is 15 percent. What is Bramble’s current stock price?
9) Macaroni Inc. announced that it would pay the following dividends over the next five years: $0.50, $0.75, $1.50, $3, and $4. Afterwards, dividends will decline at a rate of 3 percent per year indefinitely. What is the firm’s current stock price if the required rate of return is 13%?
10) Five years ago, your dad bought 240 shares of Bonita for $5.80 each and 290 shares of Windsor for $7.30 each. He has now given you all his shares, when both stocks are trading at $7.80.What are the weights of the two stocks in your portfolio?
11)An investor owns a portfolio of $41,400 that contains $10,350 in stock A, with an expected return of 11.6 percent; $13,800 in bonds, with an expected return of 7.6 percent; and the rest in stock B, with an expected return of 19.6 percent.Calculate the expected return of the portfolio.
12) Calculate the covariance and correlation coefficient between the two securities of a portfolio that has 35 percent in stock X (with an expected return of 31 percent and a standard deviation of 11.6 percent) and 65 percent in stock Y (with an expected return of 26 percent and a standard deviation of 14.6 percent). The portfolio standard deviation is 5 percent.
13) The capital gain yield of an equity security is 9.27 percent. The security paid a quarterly dividend of $0.55 per share during the year. What is the current price of the security if the total return is 13.76 percent?
14) Stock X has a standard deviation of 25 percent and a correlation coefficient of 0.7 with market returns. The expected return of the market is 12 percent with a standard deviation of 15 percent. The risk-free rate is 5 percent. What is the required return of Stock X?
15) The expected return on stock A is 11.70 percent. The expected return on stock B is 9.40 percent. Assuming CAPM holds, if the beta of stock A is higher than the beta of stock B by 0.24, what should the risk premium be?
16) The expected return of the market portfolio is 14 percent with a standard deviation of 25 percent. The risk-free rate is 6 percent. What is the weight of the market portfolio in an efficient portfolio with a standard deviation of 30 percent?
17) The expected return of Security A is 12 percent with a standard deviation of 15 percent. The expected return of Security B is 9 percent with a standard deviation of 10 percent. Securities A and B have a correlation of 0.4. The market return is 11 percent with a standard deviation of 13 percent and the risk-free rate is 4 percent. What is the Sharpe ratio of a portfolio if 35 percent of the portfolio is in Security A and the remainder in Security B?
18) What is the NPV of an equipment purchase costing $7,000 up front, that is expected to generate $3,000 in cash flows per year for the four years following the purchase, if the discount rate used is 10%?
20) What is the IRR of the following project? After-tax initial investment = $8215; CF1 = $2140; CF2 = $3050; CF3 = $4200, CF4 = $5000. If k = 17%, should you accept the project?
21) North Pole Inc., a Canadian company, has an opportunity to invest in India. The project requires an immediate cash outlay of $2 million and is expected to provide after-tax cash flows of $600,000 in year 1, $800,000 in year 2, $1,000,000 in year 3, and $1,200,000 in year 4. The beta for a similar project in Canada is 1.2. The risk-free rate is 5 percent and the market risk premium is 7.5 percent. The risks of implementing such a project in India will require a risk premium of 4.5 percent. What will be the impact on the shareholder value of North Pole Inc. if the firm undertakes this project?
Suppose your friend Sarah came to see you with an opportunity to invest in a project that generates $5,000 in the first and the third year, and where the cash flow in the second year is $3,000. The initial investment required for the project is $10,000. If the risk-adjusted rate is 15%, she insists that the project is worth the investment. Which method is Sarah using?
| internal rate of return |
| Payback period |
| Net present value |
| Profitability index | |
22)At maturity, each of
the following zero coupon bonds (pure discount bonds) will be worth $1,000. For
each bond, fill in the missing quantity in the following table. Assume
semi-annual compounding.
Price $456, Maturity 12 years, yield to maturity = ?
Price $394, Maturity ? years , yield to maturity 6%
Price $? , Maturity 13 years , yield to maturity 11%
