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Solutions to Problems
P7-1 Authorized and available shares (LG 2; Basic)
a. Maximum shares = Authorized shares – Shares outstanding = 2,000,000 – 1,400,000 = 600,000.
P7-2 Preferred dividends (LG 2; Intermediate)
a. Annual dividend in dollars = Price of preferred stock annual dividend rate
on common stock.
c. $3.20—For cumulative preferred, all dividends in arrears must be paid before paying dividends
P7-3 Preferred dividends (LG 2; Intermediate)
Case Answer Explanation
A $16 Three quarters of passed dividends plus current quarter (4 quarters × $4 per
quarter)
B $2.20 Dividend is 2% of $110 per quarter, or $2.20 per quarter; only current quarter
must be paid because stock is noncumulative.
passed, so only current $2.10 dividend is due.
P7-4 Convertible preferred stock (LG 2; Challenge)
$100.
b. The investor should covert because value would be $100 while preferred stock price is only
$96.
c. This question is trickier than it first appears. Students might note conversion of one share of
preferred to five shares of common stock will reward an investor with $5 in common dividends
it) until the profit opportunity vanishes.] Investors might not convert for other reasons as well.
Suppose the preferred stock is worth $100, so no immediate profit is available from converting.
P7-5 Preferred stock valuation (LG 4; Basic)
a. Annual dividend = Price of preferred stock × annual dividend rate = $65 × 10% or $6.50.
b. Because the dividend stream is a perpetuity, value of preferred stock is just annual dividend
P7-6 Personal finance: Common-stock valuation—Zero growth (LG 4; Intermediate)
Using the perpetuity formula (P0 D1 r, where D1 = $2.80 and r = 9.25%), Kelsey Drums
P7-7 Preferred stock valuation (LG 4; Intermediate)
a. Preferred stock price = Expected perpetual dividend (D1) Required rate of return (r)
b. New value of preferred stock is $6.40 $60.95. The investor would lose $7.87 per
P7-8 Common stock value: Constant growth (LG 4; Basic)
Let P0 be the current price of the common stock, D1 the next expected dividend, r the required
return, and g the expected constant growth rate of dividends:
Firm P0 D1 (r g) Share Price
AP0 $1.20
(0.13
0.08)
$ 24.00
BP0 $4.00
(0.15
0.05)
$ 40.00
(0.14
P7-9 Common stock value: Constant growth (LG 4; Intermediate)
a. Let P0 be current price of common stock, D1 the next expected dividend, r the required return,
and g the expected dividend growth rate; stock price is given by P0 D1 (r g). The next
P7-10 Common stock value: Constant growth (LG 4; Intermediate)
Let P0 be current price of common stock, D1 the next expected dividend, r the required return, and g
the expected dividend growth; stock price is given by P0 D1 (r g). Historical growth in
P7-11 Personal finance: Common stock value- Constant growth (LG 4; Intermediate)
Let P0 be current price of common stock, D1 the next expected dividend, r the required return, and g
price equation and solving for expected dividend growth (g):
P7-12 Personal finance: Common stock value—Constant growth (LG 4; Challenge)
a. Let P0 be current stock price, D1 the next expected dividend, r the required return, and g the
expected dividend growth rate; stock price is given by P0 D1 (r g). Historical growth in
c. A fall in required return means future dividends are discounted at a lower rate, so stock price rises.
P7-13 Common stock value: Variable growth (LG 4; Challenge)
P0 Present value of dividends during initial growth period
Present value of stock price at end of initial growth period.
Step 1: Present value of cash dividends during initial growth period, given last dividend of $2.55,
Total = $9.05
Step 2: Present value of price of stock at end of initial growth period—given dividend at the end of
Step 3: Add present value of dividends during initial growth period to present value of stock price
P7-14 Personal finance: Common stock value—Variable growth (LG 4; Challenge)
P0 Present value of dividends during initial growth period
Present value of stock price at end of initial growth period.
Step 1: Present value of dividends during initial growth period—given last dividend (D0) of $3.40,
Step 2: Present value of price of stock at end of initial growth period—given dividend at the end of
year 4 period of $4.31, expected dividend growth of 10%, and required return of 14%:
Step 3: Add present value of dividends during initial growth period to present value of stock price
P7-15 Common stock value—Variable growth (LG 4; Challenge)
a. P0
Present value of dividends during initial growth period
Present value of stock price at end of initial growth period.
Step 1: Present value of dividends during initial growth period—given last dividend of $1.80,
Step 2: Present value of price of stock at end of initial growth period—given dividend at the
end of year 3 period of $2.27, expected dividend growth of 5%, and required return of
Step 3: Add present value of dividends during initial growth period to present value of stock
b. The present value of year 1-3 dividends is the same as in part (a). For step 2, dividend growth
rate is now zero after year 3, so D3 D4 $2.27. Moreover, now P3 may be found with the
c. Present value of year 1-3 dividends is the same as in part (a). For step 2, dividend growth is
P7-16 Personal finance: Common stock value—Free cash flow models (LG 4; Challenge)
a. Firm has no debt or preferred stock, so firm value (Vc) is present value of expected free cash
grow at a constant rate, VC can be found using the stock-valuation framework for constant
c. VC Present value of FCF in first growth period Present value of FCF after first growth
period.
Step 1: Present value of FCF during initial growth period—given FCF0 = $42,500, expected
FCF growth of 12% for two years, and required return of 18%:
n FCF0× 1.12n= FCFn1/(1.18)n = Present Value of FCFn
0 $42,500
1 $42,500 1.1200 $47,600 0.8475 $40,338.
98
Step 3: Add present value of free cash flow during initial growth period to present value of
Note: Student answers may vary by a few cents because of rounding.
P7-17 Free cash flow (FCF) valuation (LG 5; Challenge)
a. Assumes 2020 is one year in the future. Firm value (VC) may be found in three steps:
Step 1: Present value of FCF from 2025 to infinity: FCF2025 = $390,000 (1.03) = $401,700, and
present value of FCF2025 to infinity in 2024= $401,700 (0.11 0.03) $5,021,250.
0
=
b. Total value of common stock (VS) = VC – Total debt (VD)– Total value of preferred stock ((VP)
200,000 $10.76.
P7-18 Personal finance: Using the free-cash-flow valuation model to price an IPO (LG 5; Challenge)
a. The value of the firm’s common stock may be found in four steps:
Step 1: Find present value in 2023 of free cash flow (FCF) from 2024 to
infinity:
$19,800,000.
Step 3: Discount FCF from 2020 through 2024 to today to obtain total value of the firm (VC):
Year Years from
Now (n)FCFn 1/(1.08)n = Present
Value
2020 1 $ 700,000 0.92592
6 $648,148.15
2021 2 $ 800,000 0.85733
9 $685,871.06
Step 4: Find value of common stock per share:
b. IPO is overvalued by $0.73 ($12.50 $11.77), so you should not buy the stock.
c. New value of common stock may be found in four steps:
Step 1: Present value in 2023 of FCF from 2024 to infinity:
$23,760,000.
Step 3: Discount FCF from 2020 through 2024 back to today.
Year Years from
Now (n)FCFn(1.08)n= Present
Value
2020 1 $ 700,000 0.925926 $648,148.1
5
Total Firm Value (VC) = $19,552,469.14
Step 4: Find value of common stock per share:
Value per share of common stock =VS Common shares
P7-19 Book and liquidation value (LG 5; Intermediate)
a. Book value per share =
b. Liquidation value:
Assets Liquidation Value for Common Stock
Cash $40,000 Liquidation Value–Assets $722,000
Marketable Securities 60,000 Less:
Liquidation value per share = Value available for common stockholders common shares
c. Book values reflect historical prices/costs, not current market value, so it is no surprise
liquidation and book value differ for Gallinas Industries. Here, book exceeds liquidation value
