Estimate the US bank JP Morgan's share price using a price earnings (PE) multiples approach with the following assumptions and figures only:
- The major US banks JP Morgan Chase (JPM), Citi Group (C) and Wells Fargo (WFC) are comparable companies;
- JP Morgan Chase's historical earnings per share (EPS) is $4.37;
- Citi Group's share price is $50.05 and historical EPS is $4.26;
- Wells Fargo's share price is $48.98 and historical EPS is $3.89.
Note: Figures sourced from Google Finance on 24 March 2014.
The average of Citi and Wells Fargo's back-looking PE ratio multiplied by JP Morgan's EPS gives a backward-looking PE multiple valuation of JP Morgan's stock price:
###\begin{aligned} P_\text{0,JPM} &= \dfrac{ \left( \dfrac{P_\text{0,C}}{EPS_\text{0,C}} + \dfrac{P_\text{0,WFC}}{EPS_\text{0,WFC}} \right) }{2}.EPS_\text{0,JPM} \\ &= \dfrac{ \left( \dfrac{50.05}{4.26} + \dfrac{48.98}{3.89} \right) }{2} \times 4.37 \\ &= \dfrac{ \left(11.74882629 + 12.59125964 \right) }{2} \times 4.37 \\ &= 12.17004297 \times 4.37 \\ &= 53.18308776 \\ \end{aligned}###JP Morgan's share price actually closed at $61.07 on 24 March 2014 so the PE ratio valuation approach gives a number in the right ball park.
Since the actual market traded price of $61.07 is higher than the estimated price of $53.18 based on similar firms, JP Morgan stock might be over-priced and therefore should be sold. Or, perhaps JP Morgan has higher expected future growth potential or lower systematic risk compared to its peers so it's fairly priced or even under-priced after taking these factors into account.
Estimate the Chinese bank ICBC's share price using a backward-looking price earnings (PE) multiples approach with the following assumptions and figures only. Note that the renminbi (RMB) is the Chinese currency, also known as the yuan (CNY).
- The 4 major Chinese banks ICBC, China Construction Bank (CCB), Bank of China (BOC) and Agricultural Bank of China (ABC) are comparable companies;
- ICBC 's historical earnings per share (EPS) is RMB 0.74;
- CCB's backward-looking PE ratio is 4.59;
- BOC 's backward-looking PE ratio is 4.78;
- ABC's backward-looking PE ratio is also 4.78;
Note: Figures sourced from Google Finance on 25 March 2014. Share prices are from the Shanghai stock exchange.
ICBC's earnings per share (EPS) multiplied by the average of the other Chinese banks' backward-looking PE ratios gives a backward-looking PE multiple valuation of ICBC's stock price:
###\begin{aligned} P_\text{0,ICBC} &= \dfrac{ \left( \dfrac{P_\text{0,CCB}}{EPS_\text{0,CCB}} + \dfrac{P_\text{0,BOC}}{EPS_\text{0,BOC}} + \dfrac{P_\text{0,ABC}}{EPS_\text{0,ABC}} \right) }{3}.EPS_\text{0,ICBC} \\ &= \dfrac{ \left( \text{PE}_\text{0,CCB} + \text{PE}_\text{0,BOC} + \text{PE}_\text{0,ABC} \right) }{3}.EPS_\text{0,ICBC} \\ &= \dfrac{ \left( 4.59 + 4.78 + 4.78 \right) }{3} \times 0.74\\ &= 4.716666667 \times 0.74 \\ &= 3.490333333 \\ \end{aligned}###ICBC's share price actually closed at RMB3.35 on 25 March 2014 so the PE ratio valuation approach gives a number that's pretty close to the market's valuation.
Since the actual market traded price RMB3.35 is lower than the estimated price of RMB4.49 based on similar firms, ICBC stock might be under-priced and therefore should be bought. Or, perhaps ICBC has lower expected future growth potential or higher systematic risk compared to its peers so it's fairly priced or even over-priced after taking these factors into account.
Estimate Microsoft's (MSFT) share price using a price earnings (PE) multiples approach with the following assumptions and figures only:
- Apple, Google and Microsoft are comparable companies,
- Apple's (AAPL) share price is $526.24 and historical EPS is $40.32.
- Google's (GOOG) share price is $1,215.65 and historical EPS is $36.23.
- Micrsoft's (MSFT) historical earnings per share (EPS) is $2.71.
Source: Google Finance 28 Feb 2014.
The average of Apple and Google's back-looking PE ratio multiplied by Microsft's EPS gives a backward-looking PE multiple valuation of Microsoft's stock price:
###\begin{aligned} P_\text{0,MSFT} &= \dfrac{ \left( \dfrac{P_\text{0,AAPL}}{EPS_\text{0,AAPL}} + \dfrac{P_\text{0,GOOG}}{EPS_\text{0,GOOG}} \right) }{2}.EPS_\text{0,MSFT} \\ &= \dfrac{ \left( \dfrac{526.24}{40.32} + \dfrac{1,215.65}{36.23} \right) }{2} \times 2.71 \\ &= \dfrac{ \left(13.0515873 + 33.55368479 \right) }{2} \times 2.71 \\ &= 23.30263605 \times 2.71 \\ &= 63.15014369 \\ \end{aligned}###Microsoft's share price was actually $38.31 so the PE ratio valuation approach is not doing a good job. This is probably because Google and Apple are not similar enough to Microsoft. Microsoft is an older and more mature company with lower growth prospects than either of the other two software companies.
Which of the following investable assets are NOT suitable for valuation using PE multiples techniques?
The PE ratio is very closely related to the perpetuity formula. It's usefulness in valuation stems from this close association. The perpetuity formula and therefore the PE ratio assume that cash flows continue forever or have some probability of continuing every period indefinitely.
For this reason, the perpetuity and PE ratios are not useful for valuing fixed maturity debt since its cash flows do not go on forever. Once debt matures and the principal is paid back, the cash flows cease.
Dividends from equity and rent from real estate are expected to continue forever so the perpetuity and PE multiple valuation techniques are suitable for valuation.
To see the relationship between the PE ratio and perpetuity with growth equation, consider an all-equity firm that pays out all of its earnings (##EPS## for earnings per share) as dividends (##C## for dividend income cash flow), so ##C=EPS##. Assume that the dividend was just paid and the next dividend (##C_1##) will be paid in one period. Dividends are nominal and grow by the rate of inflation (##g##) each period. Starting with the perpetuity with growth equation, re-arranging, and substituting ##C_1=EPS_1##: ###P_0 = \dfrac{C_1}{r-g}### ###\dfrac{1}{r - g} = \dfrac{P_0}{C_1} =\dfrac{P_0}{EPS_1} = \text{forward looking PE ratio} ###
To value a firm using PE multiples, the firm's earnings are multiplied by some PE ratio, usually an average of similar firms' PE ratios in the same industry.
To value a firm using the perpetuity with growth equation, the firm's dividends or earnings are multiplied by ##1/(r-g)##.
Clearly these approaches are identical, at least for the simple firm described above. This shows the relationship between the perpetuity with growth equation and the PE ratio: the PE ratio is the inverse of the income return.
Which firms tend to have low forward-looking price-earnings (PE) ratios?
Only consider firms with positive earnings, disregard firms with negative earnings and therefore negative PE ratios.
Highly illiquid small private companies tend to have low PE ratios because their share prices trade at a discount due to their illiquidity and because they are more systematically risky compared with bigger firms.
Small companies cannot be easily liquidated if the owner needs cash, unlike large listed firms whose shares can be sold on the stock exchange. To make up for this disadvantage, small firms' required returns are higher compared with bigger firms, so their share prices are relatively cheaper and their price-to-earnings ratio is lower. Small private companies are usually sold through a business broker who charges a significant fee. There are few potential buyers of small businesses since they often require a significant level of owner involvement. Potential buyers may include competitors, firms in related industries or wealthy individuals with management expertise and spare time. Due to the small number of bidders, the price of these firms is usually very low. In the extreme case of just one bidder and many small business sellers the smaller business buyer is a 'monopsonist' and can offer very low bids.
Small companies are more vulnerable to competition from larger firms. Small companies tend to be under-capitalised which means that they do not have enough fixed assets and equipment, they tend to use labour instead of automation. They cannot reap the economies of scale that larger firms can. For example, if a large firm installs an expensive new computer system for quoting and invoicing clients, that fixed cost will be spread over its large number of customers, causing a negligible price increase per customer. If a small business did the same thing, the cost would be spread over a small number of customers causing a significant price increase and they will leave the small firm to join the larger firm which is cheaper. This makes small companies more likely to go out of business due to competition from larger firms, and therefore makes them more risky. This means that their discount rates are higher and price is lower. Therefore their PE ratio will be lower than larger firms.
Forward-looking PE ratios can be calculated on a per-share basis as the current share price divided by next year's expected earnings per share. Or by multiplying by the number of shares, the current market capitalisation of equity (E as in V=D+E) divided by next year's total expected earnings (also called net income (NI) or net profit after tax (NPAT)):
###\text{forward looking PE ratio} = \dfrac{\text{share price}_0}{\text{EPS}_1} = \dfrac{\text{market cap of equity}_0}{\text{Net Income}_1} ###PE ratios are best thought about by remembering that the current share price equals the present value of future dividend payments. For simple unlevered firms, dividends will equal earnings if there is: no debt, a 100% payout ratio, no change in net working capital and minimal accrual items such as depreciation. Therefore anything that makes the share price high, such as high levels of future earnings (high growth tech firms) or low discount rates (from low levels of systematic risk such as firms with lots of cash) will make the PE ratio high. Conversely, anything that makes next year's expected earnings low, such as temporarily low earnings, will also make the PE ratio high.
Which of the following investable assets are NOT suitable for valuation using PE multiples techniques?
The PE ratio is very closely related to the perpetuity formula. It's usefulness in valuation stems from this close association. The perpetuity formula and therefore the PE ratio assume that cash flows continue forever or have some probability of continuing every period indefinitely.
For this reason, the perpetuity formula and PE ratios are not useful for valuing firms that will cease operations and which are not 'going concerns'.
Dividends from equity and rent from real estate are expected to continue forever so the perpetuity and PE multiple valuation techniques are suitable for valuation.
To see the relationship between the PE ratio and perpetuity with growth equation, consider an all-equity firm that pays out all of its earnings (##EPS## for earnings per share) as dividends (##C## for dividend income cash flow), so ##C=EPS##. Assume that the dividend was just paid and the next dividend (##C_1##) will be paid in one period. Dividends are nominal and grow by the rate of inflation (##g##) each period. Starting with the perpetuity with growth equation, re-arranging, and substituting ##C_1=EPS_1##: ###P_0 = \dfrac{C_1}{r-g}### ###\begin{aligned} \dfrac{1}{r - g} &= \dfrac{P_0}{C_1} \\ &= \dfrac{P_0}{EPS_1} = \text{forward looking PE ratio} \\ \end{aligned}###
To value a firm using PE multiples, the firm's earnings are multiplied by some PE ratio, usually an average of similar firms' PE ratios in the same industry.
To value a firm using the perpetuity with growth equation, the firm's dividends or earnings are multiplied by ##1/(r-g)##.
Clearly these approaches are identical, at least for the simple firm described above. This shows the relationship between the perpetuity with growth equation and the PE ratio: the PE ratio is the inverse of the income return.
Which firms tend to have high forward-looking price-earnings (PE) ratios?
Forward-looking PE ratios can be calculated on a per-share basis as the current share price divided by next year's expected earnings per share. Or by multiplying by the number of shares, the current market capitalisation of equity (E as in V=D+E) divided by next year's total expected earnings (also called net income (NI) or net profit after tax (NPAT)):
###\text{forward looking PE ratio} = \dfrac{\text{share price}_0}{\text{EPS}_1} = \dfrac{\text{market cap of equity}_0}{\text{Net Income}_1} ###PE ratios are best thought about by remembering that the current share price equals the present value of future dividend payments. For simple unlevered firms, dividends will equal earnings if there is: no debt; a 100% payout ratio; no change in net working capital; and minimal accrual items such as depreciation. Simple firms like this will have low forward-looking PE ratios when next year's expected earnings are temporarily high, or when the share price is low. Factors that lead to low share prices include:
- Low levels of future earnings such as negative growth firms;
- High discount rates from high levels of systematic risk; or
- Illiquidity, such as when trying to sell a small business which has few potential buyers.
Firms with a high proportion of cash as assets will have a low level of systematic risk, and therefore a low required return, making their share price high, so the numerator of the PE ratio will be large. Next year's expected earnings will be low since a large part of their earnings are from cash which has a low interest rate, therefore the denominator of the PE ratio will be low. Therefore firms with a lot of cash tend to have high PE ratios.
Another way of looking at this is to consider again a company that pays out all of its earnings as dividends and is therefore not re-investing and is likely to have zero real growth in earnings, dividends and share price. Therefore next year's expected earnings per share (##EPS_1##) is equal to next year's expected dividends (##C_1##) and the real capital return will be zero.
For these firms the forward looking PE ratio will be the inverse of the real total expected return:
###\begin{aligned} \text{PE ratio} &= \frac{P_0}{EPS_1} = \frac{P_0}{C_1} = \frac{1}{\left( \dfrac{C_1}{P_0}\right)} = \frac{1}{\left( r_\text{income} \right)} \\ &= \frac{1}{\left( r_\text{total} - r_\text{capital} \right)} = \frac{1}{\left( r_\text{total} - 0 \right)} = \frac{1}{r_\text{total}} \\ \end{aligned}###Since cash has zero systematic risk it has a very low total return (the risk free rate) and therefore firms with a lot of cash will have low total returns and their PE ratios will be high.
Which firms tend to have low forward-looking price-earnings (PE) ratios? Only consider firms with positive PE ratios.
Firms in a declining industry with very low or negative earnings growth will have low stock prices, and therefore low forward looking price-to-earnings ratios.
Forward-looking PE ratios can be calculated on a per-share basis as the current share price divided by next year's expected earnings per share. Or by multiplying by the number of shares, the current market capitalisation of equity (E as in V=D+E) divided by next year's total expected earnings (also called net income (NI) or net profit after tax (NPAT)):
###\text{forward looking PE ratio} = \dfrac{\text{share price}_0}{\text{EPS}_1} = \dfrac{\text{market cap of equity}_0}{\text{Net Income}_1} ###PE ratios are best thought about by remembering that the current share price equals the present value of future dividend payments. For simple unlevered firms, dividends will equal earnings if there is: no debt; a 100% payout ratio; no change in net working capital; and minimal accrual items such as depreciation.
Simple firms like this will have high forward-looking PE ratios when next year's expected earnings are temporarily low, or when the share price is high. Factors that lead to high share prices include:
- High levels of future earnings such as high growth tech firms;
- Low discount rates from low levels of systematic risk; or
- High liquidity, such as when trying to sell big listed companies' shares which have lots of potential buyers.
Private equity firms are known to buy medium sized private companies operating in the same industry, merge them together into a larger company, and then sell it off in a public float (initial public offering, IPO).
If medium-sized private companies trade at PE ratios of 5 and larger listed companies trade at PE ratios of 15, what return can be achieved from this strategy?
Assume that:
- The medium-sized companies can be bought, merged and sold in an IPO instantaneously.
- There are no costs of finding, valuing, merging and restructuring the medium sized companies. Also, there is no competition to buy the medium-sized companies from other private equity firms.
- The large merged firm's earnings are the sum of the medium firms' earnings.
- The only reason for the difference in medium and large firm's PE ratios is due to the illiquidity of the medium firms' shares.
- Return is defined as: ##r_{0→1} = (p_1-p_0+c_1)/p_0## , where time zero is just before the merger and time one is just after.
Say a medium-sized firm makes $1m of earnings (also called profit or net income), then it will trade at a price of $5m since its price-to-earnings ratio is 5.
If lots of these firms are bought, merged and sold off as a large listed company then for each $1m of earnings, the larger firm will trade at a price of $15m since its price-to-earnings ratio is 15.
Therefore each medium-sized firm bought for $5m can be sold sold for $15m once it's merged, making a return of 200%.
###\begin{aligned} r_{0→1} &= \dfrac{p_1-p_0+c_1}{p_0} \\ &= \dfrac{15-5+0}{5} \\ &= 2 = 200\% \\ \end{aligned}###Itau Unibanco is a major listed bank in Brazil with a market capitalisation of equity equal to BRL 85.744 billion, EPS of BRL 3.96 and 2.97 billion shares on issue.
Banco Bradesco is another major bank with total earnings of BRL 8.77 billion and 2.52 billion shares on issue.
Estimate Banco Bradesco's current share price using a price-earnings multiples approach assuming that Itau Unibanco is a comparable firm.
Note that BRL is the Brazilian Real, their currency. Figures sourced from Google Finance on the market close of the BVMF on 24 July 2015.
Let Banco Bradesco be called BB, Itau Unibanco's is IU, price-to-earnings ratio is PE, share price is P, earnings per share is EPS, the total number of shares is N, and b is billions. The share price of BB based on IU's PE ratio is:
###\begin{aligned} \text{P}_\text{BB} &= \text{PE}_\text{IU} \times \text{EPS}_\text{BB} \\ &= \dfrac{\text{P}_\text{IU}}{\text{EPS}_\text{IU}} \times \text{EPS}_\text{BB} \\ &= \dfrac{ \left( \dfrac{\text{MktCapEquity}_\text{IU} }{\text{N}_\text{IU}} \right) }{\text{EPS}_\text{IU}} \times \dfrac{ \text{TotalEarnings}_\text{BB} }{\text{N}_\text{BB}} \\ &= \dfrac{ \left( \dfrac{85.744b}{2.97b} \right) }{3.96} \times \dfrac{8.77b}{2.52b} \\ &= \dfrac{ 28.87003367}{3.96} \times 3.48015873 \\ &= 7.290412543 \times 3.48015873 \\ &= 25.37179286 \end{aligned}###