Solution to Practice
Exercise
Reebok Valuation
Notes relevant to this
case:
(1)
Notes
on ratio analysis and valuation
(2) Notes
on "What Determines P-B and P-E Ratios?"
(3) Annotated
solutions to homework in chapters 13, 14 and 15
Consider
the following balance sheet, income statement and other information from
Reebok's 1996 10-K:
|
|
1996 |
1995 |
|
Balance Sheet: |
|
|
|
Net operating assets |
|
|
|
Cash and equivalents (financing portion) |
219.8 |
70.0 |
|
Notes payable and long-term debt |
939.8 |
321.8 |
|
Equity put options |
|
39.1 |
|
Minority interest |
33.9 |
31.1 |
|
Common stockholders' equity |
$381.2 |
$895.3 |
|
Common shares outstanding |
55.8 |
74.8 |
|
|
|
|
|
Income Statement: |
|
|
|
Sales |
$3,482.9 |
|
|
Cost of sales |
2,144.4 |
|
|
Gross margin |
1,338.5 |
|
|
Operating expenses (other than CGS) |
1,069.2 |
|
|
Pretax operating income |
269.3 |
|
|
Interest expense |
42.2 |
|
|
Interest income |
10.6 |
|
|
Pretax net financing expense |
31.6 |
|
|
Income before tax and minority interest |
237.7 |
|
|
Tax expense |
84.1 |
|
|
Income before minority interest |
153.6 |
|
|
Minority interest, net of tax |
(14.6) |
|
|
Net income |
$139.0 |
|
|
Shares used to compute EPS |
69.6 |
|
|
Earnings per share (EPS) |
$2.00 |
|
Additional
information:
·
Analysts’ consensus EPS
forecast for 1997 is $2.56. In addition,
analysts draw the following conclusions from their examination of the company’s
10-K and other information:
o
Financial assets and obligations included on the balance sheet are all
recorded at their market values.
o
The increased investment in cash equivalents during 1996 occurred on
August 1.
o Analysts' expect the company's debt and investment in cash equivalents to remain stable throughout 1997. They expect the company to earn a rate of return on financial assets similar to the rate earned in 1996, and they expect the company to incur interest expense at a 5.73% before-tax interest rate on notes payable and long-term debt.
o Analysts expect Reebok's subsidiaries in which there is a minority interest to have the same income in 1997 as in 1996.
o The enterprise cost of capital is 10%.
o Analysts believe the minority interest has a market value equal to 14 times minority interest in the earnings of the company.
(1)
From the balance sheet information given above, compute the company’s net
operating assets as of 12/31/95 and 12/31/96.
Answer to part (1):
o
NOA = NFO + MI + CSE = $1,217.3 at 12/31/95 and $1,135.1 at 12/31/96.
(2)
Explain the computation of EPS,
and speculate as to why shares used to compute EPS differs from the 55.8 million shares of common stock
outstanding at 12/31/96.
Answer to part (2):
o
The bulk of the change in shares outstanding during 1996 is due to the
share repurchase, which occurred in August 1996, and the company reported
. If we assume the entire change in
shares outstanding occurred in mid-August, then an estimate of the weighted
average shares outstanding is (7.5/12)(74.8)+(4.5/12)(55.8)=67.7. In fact, the company reported that this
weighted average was 67.4. The company
computed its $2.00 EPS as its net income of 138.95 divided by 69.6, where 69.6
represents the weighted average common shares and common share equivalents
outstanding during the year. The
difference between 69.6 and 67.4 is due to outstanding employee stock
options. Apparently, the company
estimates that if the options had been exercised in 1996, the money received
(exercise price) could have been used to repurchase approximately 6.8 million
shares of the company's common stock, and the 9.0-6.8=2.2 million share
difference is added to the denominator in the EPS calculation.
(3)
Estimate the consensus analyst forecast of 1997 earnings.
Answer to part (3):
o
Assuming that shares outstanding remain stable throughout 1997 and the
effect of outstanding stock options is the same in 1997 as in 1996, the
estimated number of shares underlying analysts’ 1997 EPS forecast = 55.8
+ 2.2 = 58.0.
o
Earnings forecast = $2.56*58.0 = $148.48.
(4)
Prepare a schedule calculating your best estimate of analysts' forecasts
of Reebok's 1997 operating income and net financing expense. Also compute the
company’s financial leverage as of 12/31/96, projected 1997 after-tax net
borrowing cost, earnings per share, return on net operating assets (RNOA),
SPREAD between RNOA and NBC, return on equity (i.e., income before subtracting
minority interest share of income divided by CSE plus minority interest
equity), and return on common equity (ROCE).
Answer to part (4):
o
NFO = $939.8 – 219.8 = $720.
o
Average 1996 investment in financial assets = (7/12)*(70)+(5/12)*(219.8) =
$132.4.
o
Pretax rate of return on investment in financial assets = $10.6/132.4 =
8.0%
o
Forecasted 1997 pretax interest income = 0.08*219.8 = $17.60.
o
Forecasted 1997 pretax interest expense = 0.0573*939.8 = $53.85
o
Forecasted NBC=NFE/NFO = ($53.85-17.60)*(1-0.367)/720 = 3.2%.
(5)
Add a column to the schedule prepared in (4) above and fill in the
amounts you would expect if Reebok had not undertaken the share repurchase and
associated debt financing in 1996.
Answer to parts (4 and 5):
|
|
With Share Repurchase |
Without Share Repurchase |
|
Analysts'
1997 EPS forecast |
2.56 |
2.28 |
|
Estimated
shares underlying 1997 EPS forecast |
58.00 |
74.70 |
|
Derived
forecasts for 1997: |
|
|
|
Earnings (E) = OI – NFE + MI |
148.48 |
170.29 |
|
Interest income |
17.60 |
17.60 |
|
Interest expense |
53.85 |
19.40 |
|
Pretax net financing expense |
36.26 |
1.81 |
|
Tax on pretax NFE |
13.31 |
0.66 |
|
NFE |
22.95 |
1.14 |
|
Minority interest share of income (MI) |
(14.60) |
(14.60) |
|
Operating income (OI) = E + NFE – MI |
186.03 |
186.03 |
|
|
|
|
Estimated
borrowing to finance share repurchase
|
601.20 |
|
|
At
12/31/96: |
|
|
|
Financial assets |
219.80 |
219.80 |
|
Financial obligations |
939.80 |
338.60 |
|
NFO |
720.00 |
118.80 |
|
CSE |
381.20 |
982.40 |
|
MI |
33.90 |
33.90 |
|
FLEV |
1.73 |
0.12 |
|
NBC |
3.19% |
0.96% |
|
Forecast
for 1997: |
|
|
|
RNOA |
16.39% |
16.39% |
|
SPREAD |
13.2% |
15.43% |
|
Return on all equity |
39.29% |
18.19% |
|
ROCE |
38.95% |
17.33% |
(6)
With reference to your schedule prepared in (5) above, given that
operating income and RNOA do not change and earnings decreases with the share repurchase,
why do EPS and return on total equity increase with the share repurchase?
Answer to part (6):
Let E1=earnings before the repurchase, E2=earnings
after the repurchase, i=the after-tax interest rate on borrowing to finance the
repurchase, P=the price per share before and after the repurchase, S=the shares
outstanding before the repurchase, and n=the number of shares repurchased. Then
EPS1=E1/S, EPS2=(E1-n*i*P)/(S-n),
and EPS2>EPS1 if (E1‑n*i*P)/(S‑n)>E1/S,
which is true as long as EPS1/P>i (click
here for algebraic derivation). In
other words, as long as the earnings yield (EPS/P) before the repurchase is
greater than the interest rate, then the reduction in shares (the denominator
of EPS) more than offsets the decline in earnings (the numerator of EPS)
due to increased interest expense, and the effect of the repurchase is to
increase EPS.
Since the repurchase does not affect RNOA, and Return on total equity=RNOA+SPREAD*NFO/(CSE+MI), return on total equity increases with the share repurchase as long as the increase in leverage more than offsets any decrease in the SPREAD. The SPREAD could change due to an increase in the interest rate on debt or due to differences in interest rates on financial assets and obligations, but these effects are usually small in comparison to the increase in leverage.
(7)
If analysts expect constant 7% sales growth rate, constant net operating
asset turnover, and constant operating profit margin for 1997 and all future
periods, estimate the market price of a share of Reebok common stock as of
12/31/96 under both the stock repurchase and no stock repurchase scenarios. Be
sure to consider the option overhang, the market value of the minority interest
and unrecorded option-based compensation in your calculations. Assume there are
no other unrecorded assets or obligations to consider.
Answer to part (7):
With the share repurchase:
Use the earnings-based valuation model: V0
= B0 – (VNFO0-NFO0) – (VMI0-MI0)
+ PvReOI
o
In this case, VNFO-NFO is due entirely to the option overhang, which we
can value as the options outstanding at year end times the Black-Scholes market
value per option, adjusted for the tax benefit.
You can use either the 1996 marginal tax rate or the effective tax rate
on operating income to compute the tax benefit.
In class, we used the 1996 effective tax rate, computed as the total
1996 tax expense plus the tax shield on net financing expense, all divided by
pretax operating income: [$84.1+0.367*(31.6)]/269.3 = 35.54%. So, the market value of the option overhang
is 9.9*$10.76*(1-0.3554)=$68.67.
o
VMI-MI equals the market value less the book value (on the balance sheet)
of the minority interest. Since the
facts assume the market value of the minority interest is 14 times the minority
interest in earnings, VMI-MI=14*$14.6-33.9=$170.5.
o
PvReOI is the present value of the residual operating income, adjusted
for the effect of projected after-tax compensation in the form of stock
options. Normally, you would obtain
(from the most recent 10-K) the market value of the options granted over the
last two or three years, apply the tax rate and derive a historical estimate of
the annual after-tax value of options granted as a percentage of each year's
sales. Then you would use this
percentage as a basis for projecting future after-tax compensation in the form
of stock options. In this case, we
decided to simply project that the after-tax market value of stock options to
be granted in 1997 would be the same as in 1996, and then this amount would
grow perpetually at the 7% sales growth rate starting in 1998. The after-tax market value of options granted
in 1996 is computed as $9.6*4.4*(1-0.3554)=$27.23; the projected 1997
ReOI=(RNOA97 – r)*NOA96 = (0.1639-0.1)*$1135.1 = $72.53;
and the projected 1997 adjusted ReOI = $72.53-27.23=$45.30.
V0 = B0 – (VNFO0-NFO0)
– (VMI0-MI0) + PvReOI
= $381.2
– [9.9*$10.76*(1-0.3554)] – (14*$14.6 – 33.9) +
+ [(0.1639 - 0.10)*1,135.1 -
$9.6*4.4*(1-0.3554)] / (0.10-0.07)
= $381.2
– 68.67 – (204.4 - 33.9) + (72.53 – 27.23) / (0.10-0.07)
= $381.2
– 68.67 – 170.5 + 1,510
= $1,652
Price per share = $1,652.03/55.84 = $29.59.
Without the share repurchase:
Same as above, except CSE=381.2+36*16.7=982.4, and
the number of shares outstanding is 55.84+16.7=72.54, so the valuation changes
to (1,652.03+36*16.7)/(55.84+16.7) = $31.06.
(8)
Why did the share price decrease with the share repurchase?
Answer to part (8):
Anytime a firm repurchases its own shares at a premium (discount), the stock price decreases (increases). To see this, consider a simple example where a firm has no debt, no minority interest, an enterprise value of $1,000 and 100 shares of outstanding common stock selling for $10 per share.
·
If the company borrows $500 and buys back 50 shares of stock at market
prices, the stock price does not change.
The enterprise value remains at $1,000, but the company now has $500 of
debt and the total market value of the common stockholders’ equity drops to
$500. But the shares outstanding decline
to 50 shares, so the price per share is still $10.
·
If, instead, the company borrows $500 and pays $25 per share to buy back
only 20 shares of stock, the market price per share drops to
($1,000-500)/(100-20)=$6.25.
·
Or if the company borrows $500 and pays $8 per share to buy back 62.5
shares of stock, the market price per share increases to
($1,000-500)/(100-62.5)=$13.33.
Reebok has a total enterprise value of
VNOA=NOA+PvReOI =$1,135.1+1,510=$2,645.1 before and after the share repurchase.
The minority interest has a market value of $204.4=14*14.6, so the combined
market value of the company’s net financial obligations and common
stockholders’ equity is $2,645.1-204.4=$2,440.7 before the additional borrowing
to finance the stock repurchase. The market value of the net financial
obligations before borrowing to finance the stock repurchase is $118.8 plus the
$68.67 after-tax market value of the option overhang (i.e., total VNFO before
the stock repurchase is $187.47).
·
Given 72.54 million shares of outstanding common stock before the stock
repurchase, the price per common share before borrowing to finance the stock
repurchase is ($2,440.7-187.47)/72.54=$2,253.23/72.54=$31.06.
·
What if the company borrows $601.2 and buys back shares for the $31.06
market price? Then the number of shares
repurchased is $601.2/31.06=19.36, VNFO increases by $601.2 and the new price
per share is ($2,253.23-601.2)/(72.54-19.36)=$31.06.
·
What if the company borrows $601.2 and buys back shares for a discounted
price of $10 per share? Then the number
of shares repurchased is $601.2/10=60.12, VNFO increases by $601.2 and the new
price per share is ($2,253.23-601.2)/(72.54-60.12)=$133.01.
Companies sometimes
repurchase shares because they believe the market price of their stock is too
low. In those cases, if the market realizes that
the company is correct, the price will increase to the true value of the
original shares plus an additional amount due to the effect of the company’s
repurchase at a discount. For example, consider again the firm with no debt, no minority
interest, a true enterprise value of $1,000 and 100 shares of outstanding
common stock. But assume the market is underpricing the company and the stock
is only selling for $7 per share. The company decides that since it believes
its stock is underpriced, it will borrow $400 and buy back 50 shares at $8 (a
premium over the current market price, but a bargain according to the company’s
own estimation of the true enterprise value).
·
If the market figures out that the stock is underpriced and adjusts to
the true value, the price will change to ($1,000-400)/(100-50)=$12. Notice that the price increases to an amount
above the $10 per share true price of the original shares, asssuming the market
adjusts its estimation to what the company believes is the true enterprise value.
·
Of course this is a gamble by the company, because if the market does
not figure out that the stock was underpriced at $7 per share or if the company
was wrong in its estimation of the enterprise’s true value, the price will
actually decrease to ($700-400)/(100-50)=$6 per share.
·
If the company was able to repurchase its shares at the current market
price of $7 per share, then it would eliminate the risk associated with the
market failing to adjust to the company’s assessment of the true enterprise value. In that case, if market assessments did not
adjust, then the price would simply stay at $7=($700-7*50)/(100-50).
(9)
Reassess the effects of the share repurchase beginning with CSE=982.4,
NFO=118.8, MI=33.9, NOA=1,135.1 and P=$31.06 [as in the case without the share
repurchase in (7) above]. Now reevaluate
the effects of the share repurchase, but assume the 16.7 million shares are
repurchased for the market price of $31.06.
Check your answer using both the residual operating income and
discounted free cash flow valuation models.
Answer to part (9):
V0 = B0 – (VNFO0-NFO0)
– (VMI0-MI0) + PvReOI
=
[$982.4 - (16.7*31.06)] – 68.67 – 170.5 + 1,510
= $463.7
– 68.67 – 170.5 + 1,510
=
$1,734.53
Price per share = $1,734.53/55.84 = $31.06.
To check the above with the discounted free cash
flow model:
V0 = PvFCF – VNFO0 – VMI0
where:
o
VNFO0 is the market value of the net financial obligations at
12/31/96. As noted above, NFO0
without the share repurchase would have been $118.8, so with the repurchase of
16.7 million shares at $31.06, NFO0 becomes $637.5, and with the
option overhang computed in (7) above as $68.67, VNFO0 = $637.5 +
68.67 = $706.17,
o
VMI0 = 14*$14.6 = $204.4, as computed in (7) above, and
o
PvFCF is the discounted present value of projected free cash flows
(projected annual operating income less projected annual changes in net
operating assets), adjusted for projected after-tax option compensation.
In this case, RNOA and sales growth are projected to
be constant for all years beginning with 1997 (year 1). This suggests constant ATO and PM (the
components of RNOA) for all future years, in which case the change in net
operating assets for year 1 is simply the sales growth rate (7%) times NOA0.
Furthermore, projected year 1 free cash flows (adjusted for the after-tax
market value of projected year 1 stock option grants) can be discounted as a
perpetuity with constant 7% growth.
V0 = PvFCF – VNFO0 – VMI0
=
[OI1 – g(NOA0) – OC1]/(r-g) – VNFO0
– VMI0
=
[186.03 – 0.07(1135.1) – 27.23]/(0.10-0.03) – 706.17 – 204.4
=
$2,644.77 – 706.17 – 204.4
= $1,734.2 (small difference
relative to $1,734.5 in residual operating income valuation above, due to
rounding RNOA=186.03/1135.1 to 16.39%).
P0 =
$1,734.2/55.84 = $31.06
(10) Describe how SF1, SF2 and
SF3 valuations differ from your valuations in (7) and (9) above.
Answer to part (10):
·
As described in the Penman text, SF1, SF2 and SF3 valuations rely only on
historical accounting information to value the firm and they assume all
financial assets and obligations are captured on the balance sheet at their
market values.
·
An SF1 valuation assumes zero residual operating income for all future
periods, and the minority interest and all financial assets and obligations are
included on the balance sheet at their market values.
·
In that case, the accounting is perfect in the sense that the book value
of the common stockholders’ equity on the balance sheet equals the market value
of the common stockholders’ equity (i.e., the price-to-book ratio, P/B, equals
one), and no forecasting is needed to value the firm’s common stock.
·
In Reebok’s case, an SF1 valuation would suggest V=CSE=$381.2, and
P=381.2/55.84 = $6.83.
·
The estimated market value in (7) above is $29.59, and the estimated P/B
ratio is 4.3=29.59/6.83. An SF1
valuation is clearly not appropriate, since the option overhang is not recorded
on the balance sheet, the balance sheet does not record the minority interest at
market value and analysts’ earnings forecasts suggest non-zero (positive)
future residual operating income.
·
Note the significant effect of leverage on the P/B ratio. Before the stock repurchase, CSE=$982.4 and
there are 72.54 shares outstanding (all in millions), which combine into a book
value per share of $13.54. Thus, before
the share repurchase, the P/B ratio is $31.06/13.54=2.29, and it increases to
4.3 as a result of the repurchase.
o
An SF2 valuation assumes no projected hidden (dirty surplus) effects on
common stockholders’ equity, VNFO=NFO, future RNOA equal to current RNOA, and
constant residual operating income for all future periods.
·
In that case, the forward P/E ratio equals 1/re, where re=the
equity cost of capital.
·
In Reebok’s case, we might use historical information to prepare an SF2
valuation as follows:
o
1996 tax shield on net financing expense = 0.367*(42.2-10.6)=11.6
o
1996 after-tax operating income (OI) = $269.3-(84.1+11.6)=173.6
o
1996 RNOA = OI/avgNOA = 173.6/[0.5*(1135.1+1217.3)] = 14.76%
o
SF2 forecast of 1997 ReOI = (0.1476-0.1)*1135.1 = 54.03
o
SF2 stock price = [CSE - (VMI-MI) + ReOI/r] / SHS
=
(381.2-170.5+54.03/0.1)/55.84
= 751/55.84 = $13.45
o
To check whether the forward P/E equals the reciprocal of the cost of
equity capital, first derive the cost of equity capital as follows:
§
expected 1997 NFE + expected MIis = 22.95+14.6 = 37.55
§
VNFO+VMI at 12/31/96 = 720+204.4 = 924.4
§
re=r+[(VNFO+VMI)/V]*[r-(NFE+MIis)/(VNFO+VMI)]
= 0.1 + [924.4/751]*(0.1-37.55/924.4)
= 17.3%
§
Then forecast 1997 earnings as 0.1476*1135.1-37.55=129.99, and compare
the reciprocal of re= 1/0.173 = 5.78, to the forward P/E
ratio=751/129.99=5.78.
·
An SF2 valuation is not appropriate in Reebok’s case, because analysts
forecast higher RNOA in 1997 than 1996, analysts forecast residual operating
income to grow at 7% perpetually, the forecast should include expense related
to future stock option grants that are not expected to be included on the
company’s income statement (i.e., hidden dirty surplus) and Reebok has an
option overhang causing VNFO≠NFO.
o
Like the SF2 valuation, the SF3 valuation assumes constant RNOA, but the
SF3 valuation allows constant perpetual sales growth, which causes constant
perpetual growth in NOA and ReOI.
Reebok’s NOA and sales actually declined in 1996, and therefore do not
compare well with the 7% growth rate forecast by analysts. Again ignoring the effects of the option
overhang and future compensation in the form of option grants, we can conduct
SF3 valuations as follows:
§
Assuming a perpetual growth rate equal to the percentage decline in NOA
for 1996:
·
Assume g = percentage decline in 1996 NOA = 1135.1/1217.3-1 = -6.75%
o
V = 381.2-170.5+54.03/(0.1+0.0675) = 533.2
(P=$9.56)
o
forward P/E = 533.2/129.99 = 4.1
o
re = implied cost of equity capital = 20.29%
o
reciprocal of re = 1/0.2029 = 4.93
o
negative growth causes forward P/E<1/re
·
Assume g = 7%:
o
V = 381.2-170.5+54.03/(0.1-0.07) = $2,011.6
(P=$36.05)
o
forward P/E = 2011.6/129.99 = 15.48
o
re = implied cost of equity capital = 12.73%
o
reciprocal of re = 1/0.1273 = 7.86
o
positive growth
and RNOA>r causes forward P/E>1/re
(11) Create a spreadsheet with a more
comprehensive valuation that allows detailed forecasts of ATO and PM over a
20-year forecast horizon. Incorporate
into your spreadsheet a valuation grid as a basis for reverse engineering the
company’s stock price.
Answer to part (11):