4QQMN504 Principles of Finance
Seminar 4s
Read Chapter 4 of Brealey et al., Principles of Corporate Finance, McGraw-Hill. After
reading Chapter 4, answer the following questions. The answers can be prepared in groups of
up to 4 students. (You can find the book in the King's College Library, online or in the
nearest Bookshop)
The submission file can be in word, excel, or power point and should be identified with
student names, k_number and tutorial class. The file name should start with the tutorial
number.
1. True or false?
T a) All stocks in an equivalent‐risk class are priced to offer the same expected rate of
return.
T b) The value of a share equals the PV of future dividends per share.
2. Dividend Discount Model
Respond briefly to the following statement: “You say stock price equals the present value
of future dividends? That’s crazy! All the investors I know are looking for capital gains.”
股票价值等于每股股息的贴现流。
3. Company X is expected to pay an end‐of‐year dividend of $5 a share. After the dividend
its stock is expected to sell at $110. If the market capitalization rate is 8%, what is the
current stock price? P0 = (5+110)/ 1.08
= $ 106.48
4. Company Y does not plow back any earnings and is expected to produce a level dividend
stream of $5 a share. If the current stock price is $40, what is the market capitalization
rate? r =D1/P0 + g P0 Dividend yield
=5/40 = 12.5%
g
5. Company Z’s earnings and dividends per share are expected to grow indefinitely by 5% a
year. If next year’s dividend is $10 and the market capitalization rate is 8%, what is the
current stock price? P0 = 10/ (0.08- 0.05) = $333.33 r
6. True or false? Explain.
a) The value of a share equals the discounted stream of future earnings per share.
b) The value of a share equals the PV of earnings per share assuming the firm does not
grow, plus the NPV of future growth opportunities.
7. Consider the following three stocks:
a) Stock A is expected to provide a dividend of $10 a share forever. perpetuity
b) Stock B is expected to pay a dividend of $5 next year. Thereafter, dividend growth is
expected to be 4% a year forever. growing p with constant r
c) Stock C 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 zero thereafter.
growing p with differential r
If the market capitalization rate for each stock is 10%, which stock is the most valuable?
What if the capitalization rate is 7%? C>A>B
C>B>A
8. DCF and free cash flow
Compost Science, Inc. (CSI), is in the business of converting Boston’s sewage sludge into
fertilizer. The business is not in itself very profitable. However, to induce CSI to remain
in business, the Metropolitan District Commission (MDC) has agreed to pay what‐ever
amount is necessary to yield CSI a 10% book return on equity. At the end of the year CSI
is expected to pay a $4 dividend. It has been reinvesting 40% of earnings and growing at
4% a year.
a) Suppose CSI continues on this growth trend. What is the expected long‐run rate of
return from purchasing the stock at $100? What part of the $100 price is attributable
to the present value of growth opportunities? g= 0.1*0.4= 0.04
4=Div/ P0= 100
b) Now the MDC announces a plan for CSI to treatr= Cambridge sewage. CSI’s plant will,
therefore, be expanded gradually over five years. This means that CSI will have to
reinvest 80% of its earnings for five years. Starting in year 6, however, it will again be
able to pay out 60% of earnings. What will be CSI’s stock price once this
announcement is made and its consequences for CSI are known?
9) Valuing free cash flow D
Mexican Motors’ market cap is 200 billion pesos. Next year’s free cash flow is 8.5 billion
pesos. Security analysts are forecasting that free cash flow will grow by 7.5% per year for
the next five years.
a) Assume that the 7.5% growth rate is expected to continue forever. What rate of return
are investors expecting? The constant growth formula P= DIV/(r-g)
b) Mexican Motors has generally earned about 12% on book equity (ROE 5 12%) and
reinvested 50% of earnings. The remaining 50% of earnings has gone to free cash
flow. Suppose the company maintains the same ROE and investment rate for the long
run. What is the implication for the growth rate of earnings and free cash flow? For
the cost of equity? Should you revise your answer to part (a) of this question?
g_a= 7.5% r_a= 11.75%
g_b= 6% r_b= 10.25%
10) Crédit Agricole SA is expected to maintain a constant 5.2% growth rate in its dividends
indefinitely. If the company has a dividend yield of 4.27%, what is the required return on
the company’s shares? Dividend yield= D/P0
r= dividend yield + g
= D/P0 + g
