Question 1

A firm has a share price of $54.75 per share. The firm's earnings are $75 million and the firm has 20 million shares outstanding. The firm has an ROE of 15% and a plowback of 65%. What is the firm's PEG ratio?

Accepted Answer

The PEG ratio is calculated as P/E ratio divided by the earnings growth rate.

First, we need to calculate the P/E ratio:

EPS = Earnings / Shares Outstanding 
EPS = $75M / 20M 
EPS = $3.75

P/E ratio = Price per share / EPS 
P/E ratio = $54.75 / $3.75 
P/E ratio = 14.6

Next, we need to calculate the earnings growth rate:

ROE = Net Income / Equity 
15% = $75M / Equity 
Equity = $500M

Plowback ratio = 65% 
Retention ratio = 1 - Plowback ratio 
Retention ratio = 1 - 0.65 
Retention ratio = 0.35

Earnings growth rate = ROE x Retention ratio 
Earnings growth rate = 15% x 0.35 
Earnings growth rate = 5.25%

Finally, we can calculate the PEG ratio:

PEG ratio = P/E ratio / Earnings growth rate 
PEG ratio = 14.6 / 5.25% 
PEG ratio = 1.50

Therefore, the answer is A) 1.50.

Question 2

The free cash flow to the firm is $300 million in perpetuity, the cost of equity equals 14% and the WACC is 10%. If the market value of the debt is $1.0 billion, what is the value of the equity using the free cash flow valuation approach?

Accepted Answer

Using the free cash flow valuation approach, the value of the firm is calculated as follows:

Value of the firm = Free Cash Flow to the Firm / (WACC - growth rate)

Since the free cash flow to the firm is given as $300 million in perpetuity, the growth rate is zero. Therefore, the value of the firm is:

Value of the firm = $300 million / (10% - 0%)

Value of the firm = $3 billion

Now, to find the value of equity, we subtract the market value of debt from the value of the firm:

Value of equity = Value of the firm - Market value of debt

Value of equity = $3 billion - $1 billion

Value of equity = $2 billion

Therefore, the value of the equity using the free cash flow valuation approach is $2 billion. The correct answer is B).

Question 3

A firm has PVGO of 0 and a market capitalisation rate of 12%. What is the firm's P/E ratio?

Accepted Answer

PVGO (or present value of growth opportunities) is equal to zero, which means that the firm's current stock price is entirely based on its current earnings. The market capitalisation rate is 12%, which is effectively the investor's required rate of return. Therefore, the P/E ratio can be calculated as 1/MC, where MC is the market capitalisation rate. Hence, P/E ratio = 1/0.12 = 8.33. Therefore the correct option is B.

Question 4

Next year's earnings are estimated to be $5.00. The company plans to reinvest 20% of its earnings at 15%. If the cost of equity is 9%, what is the present value of growth opportunities?

Accepted Answer

The present value of growth opportunities can be calculated by using the Gordon Growth Model as follows:

PVGO = (Reinvestment Rate / Cost of Equity - Growth Rate) x EPS

Reinvestment Rate = 20% 
Return on Reinvestment (i.e. rate at which earnings are reinvested) = 15% 
Cost of Equity = 9% 
Growth Rate = Return on Reinvestment x Reinvestment Rate = 15% x 20% = 3% 
EPS = $5

Plugging these values into the equation, we get:

PVGO = (0.20 / 0.09 - 0.03) x $5 
PVGO = $11.11

Therefore, the present value of growth opportunities is $11.11, which is option C).

Question 5

Sanders Ltd, paid a $4.00 dividend per share last year and is expected to continue to pay out 60% of its earnings as dividends for the foreseeable future. If the firm is expected to generate a 13% return on equity in the future, and if you require a 15% return on the share, the value of the share is ________.

Accepted Answer

The answer of Sanders Ltd, paid a $4.00 dividend per...

Question 6

A firm has an earnings retention ratio of 40%. The shares have a market capitalisation rate of 15% and an ROE of 18%. What is the share's P/E ratio?

Accepted Answer

P/E Ratio = (Market Capitalization Rate / ROE) x (1 - Earnings Retention Ratio)
P/E Ratio = (0.15 / 0.18) x (1 - 0.4) = 0.8333 = 7.69 (approx.) 
Therefore, the answer is B.

Question 7

A share is priced at $45. The share has earnings per share of $3.00 and a market capitalisation rate of 14%. What is the share's PVGO?

Accepted Answer

PVGO = Earnings per share / Market capitalization rate= $3.00 / 14%= $21.43

Question 8

ART has come out with a new and improved product. As a result, the firm projects an ROE of 25%, and it will maintain a plowback ratio of 0.20. Its earnings this year will be $3 per share. Investors expect a 12% rate of return on the shares. At what price would you expect ART to sell?

Accepted Answer

We can use the Gordon growth model to solve for the expected price of ART's shares:

Price = (Dividend*(1+g))/r-g
where
Dividend = 0.80*Earnings = 0.80*$3 = $2.40 (plowback ratio of 0.20 means that 80% of earnings will be paid out as dividends)
r = 12%
g = ROE*plowback ratio = 25%*0.20 = 5%

Substituting the values, we get:
Price = ($2.40*(1+0.05))/0.12-0.05 = $34.29

Therefore, the expected price of ART's shares is $34.29. Option B is the correct choice.

Question 9

When Google's share price reached $475 per share Google had a P/E ratio of about 68 and an estimated market capitalisation rate of 11.5%. Google pays no dividends. What percentage of Google's share price was represented by PVGO?

Accepted Answer

The answer of When Google's share price reached $475 per...

Question 10

Firm A has a share price of $35 and 60% of the value of the shares is in the form of PVGO. Firm B also has a share price of $35 but only 20% of the value of Share B is in the form of PVGO. We know that ________.
I. Share A will give us a higher return than Share B
II. an investment in Share A is probably riskier than an investment in Share B
III. Share A has higher forecast earnings growth than Share B

Accepted Answer

An investment in Share A is probably riskier because a larger portion of its value is based on future growth (PVGO), which is uncertain. Share A also likely has higher forecast earnings growth due to its higher PVGO component.

Question 11

The EBIT of a firm is $300, the tax rate is 35%, the depreciation is $20, capital expenditures are $60 and the increase in net working capital is $30. What is the free cash flow to the firm?

Accepted Answer

Free Cash Flow to the Firm (FCFF) = EBIT - Taxes + Depreciation - Capital Expenditures - Increase in Net Working Capital
= 300 - (0.35*300) + 20 - 60 - 30
= $125. Hence the answer is B.

Question 12

The free cash flow to the firm is reported as $205 million. The interest expense to the firm is $22 million. If the tax rate is 35% and the net debt of the firm increased by $25, what is the market value of the firm if the FCFE grows at 2% and the cost of equity is 11%?

Accepted Answer

First, we need to calculate the Free Cash Flow to Equity (FCFE) using the Free Cash Flow to the Firm (FCFF):

FCFE = FCFF - Interest Expense (1 - Tax Rate) + Net Borrowing
FCFE = $205M - $22M(1 - 0.35) + $25M
FCFE = $149.75M

Next, we can use the Gordon Growth Model to calculate the market value of the firm:

Market Value = FCFE / (Cost of Equity - Growth Rate)
Market Value = $149.75M / (0.11 - 0.02)
Market Value = $1.4975B / 0.09
Market Value = $16.6389B

Finally, we need to add the net debt to get the enterprise value:

Enterprise Value = Market Value + Net Debt
Enterprise Value = $16.6389B + $25M
Enterprise Value = $2.397B

Therefore, the best choice is B, $2.397 billion.

Question 13

The greatest value to an analyst from calculating a share's intrinsic value is ________.

Accepted Answer

Calculating a share's intrinsic value forces analysts to understand the critical variables that have the greatest impact on value. This understanding can help in making better investment decisions. While precision is important, it's not the greatest value, and it's not always easy to come up with accurate model inputs. It's also not necessarily expected that all different models will yield identical value results.

Question 14

Transportation shares currently provide an expected rate of return of 15%. TTT, a large transportation company, will pay a year-end dividend of $3 per share. If the shares are selling at $60 per share, what must be the market's expectation of the constant growth rate of TTT dividends?

Accepted Answer

We can use the Gordon Growth Model to solve this problem:

Expected Return on TTT = Dividend Yield + Expected Dividend Growth Rate

15% = ($3/$60) + Expected Dividend Growth Rate

Expected Dividend Growth Rate = 10%

Therefore, the market's expectation of the constant growth rate of TTT dividends is 10%.

Question 15

A firm increases its dividend plowback ratio. All else equal you know that ________.

Accepted Answer

A higher dividend plowback ratio means that the firm is retaining more of its earnings for investment, which will lead to higher earnings growth. However, the P/E ratio may or may not increase, depending on how the market values the firm's future earnings growth potential.

Question 16

A company with an expected earnings growth rate which is greater than that of the typical company in the same industry, most likely has ________.

Accepted Answer

A company with an expected earnings growth rate higher than the industry average typically reinvests more of its earnings back into the company for growth, rather than distributing it as dividends. This results in a lower dividend yield compared to the typical company in the same industry.

Question 17

A firm reports EBIT of $100 million. The income statement shows depreciation of $20 million. If the tax rate is 35% and total capital expenditures and increases in working capital total $10 million, what is the free cash flow to the firm?

Accepted Answer

Free cash flow (FCF) = EBIT - taxes + depreciation - capital expenditures - increases in working capital
FCF = $100 million - ($100 million x 35%) + $20 million - $10 million = $75 million. 
Therefore, the answer is (C) $75.

Question 18

A common share pays an annual dividend per share of $1.80. The risk-free rate is 5 per cent and the risk premium for this share is 4 per cent. If the annual dividend is expected to remain at $1.80 per share, what is the value of the share?

Accepted Answer

The value of a share can be determined by the dividend discount model:

Value of share = Dividend per share / (discount rate - growth rate)

The discount rate in this case is the risk-free rate plus the risk premium: 5% + 4% = 9%.

Since the annual dividend is expected to remain at $1.80, the growth rate is 0.

Therefore, the value of the share is:

Value of share = $1.80 / (0.09 - 0) = $20.00

So, the best choice is B.

Question 19

ART has come out with a new and improved product. As a result, the firm projects an ROE of 25%, and it will maintain a plowback ratio of 0.20. Its earnings this year will be $3 per share. Investors expect a 12% rate of return on the shares. At what P/E ratio would you expect ART to sell?

Accepted Answer

The answer of ART has come out with a new...

Question 20

A firm has a share price of $55 per share and a P/E ratio of 75. If you buy the shares at this P/E and earnings fail to grow at all, how long should you expect it to take to just recover the cost of your investment?

Accepted Answer

The P/E ratio of 75 means that it would take 75 years to recover the cost of the investment if earnings do not grow at all, as the P/E ratio represents the number of years it would take to earn back the price paid for the stock at the current earnings level.

Quiz 11: Equity Valuation