Chapter 4: The value of common stocks

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EX1:

Calculate the present value of each cash flow using a discount rate of 7.25%. Which do you most prefer most?
a) Cash flow A: receive $20 today and then receive $25 every year for next five years.
b) Cash flow B: receive $15 every year, forever, starting today.
c) Cash flow C: pay $20 every year for five years, with the first payment being next year, and then subsequently receive $25 every year for 20 years.

EX2:

a) A lottery jackpot of one million is paid out $25,000 a year for 40 years. At a 10 percent required return, what is the present value of this payoff? Assume that the first payment is paid immediately.

b) You want to have $5 million in real dollars in an account when you retire in 20 years. The nominal return on your investment is 10 percent and the inflation rate is 3 percent. What is the real amount you must deposit each year to achieve your goal?

EX3:

A project will not produce any cash flows for one year. Starting in the second year, it will produce annual cash flows of $40,000 a year for two years. The project initially costs $60,000. In Year 5, the project will be closed and as a result should produce a final cash inflow of $50,000. What is the net present value of this project if the required rate of return is 7 percent?

EX4:

The company has just paid a dividend of $12 per share and has announced that it will increase the dividend by $3 per share for each of the next five years, and then never pay another dividend. If you require a return of 12 percent on the company's stock, how much will you pay for a share today?

EX5:

a) A common stock will pay a cash dividend of $4 next year. The dividends are expected to increase indefinitely at 5% per year. If the discount rate is 14%, what is the PV of the stream of dividend payments?

b) Company F paid a dividend of $4 a share yesterday. The dividends are expected to increase indefinitely at 5% per year. If the discount rate is 14%, what is the PV of the stream of dividend payments?

EX6:

a) Company G plans to pay an annual dividend of $1, $2.5, $4.2 for the next 3 years, respectively, and then the dividend will increase by 3 percent annually thereafter. The required rate of return is 12 percent. What is this stock worth per share today?

b) Company I paid its first annual dividend yesterday in the amount of $0.3 a share. The dividend will increase by 5 percent in two year, then increase 8% in the next three year. After that, it will increase 2% indefinitely. What is one share of this stock worth today if the market rate of return on similar securities is 12 percent?

EX7:

a) Company J is expected to pay dividend of $10 a share forever. If the dividend is expected to grow 4% a year, and the required rate on the stock is 7%, what is the price of the stock six years from now?

b) Company K is expected to pay dividend of $8.32 a share, indefinitely. Yesterday, the company had just paid the dividend of $8 a share. If the dividend is expected to grow 4% a year, and the required rate on the stock is 7%, what is the price of the stock ten years from now?

EX8:

Stock M is expected to pay a dividend of $5 next year. Thereafter, dividend growth is expected to be 20% a year for five years (i.e., until year 6) and 5% thereafter. If the market capitalization rate for each stock is 8%, what is the current price of the stock M?