Question 989 PE ratio, Multiples valuation, leverage, accounting ratio
A firm has 20 million stocks, earnings (or net income) of $100 million per annum and a 60% debt-to-equity ratio where both the debt and asset values are market values rather than book values. Similar firms have a PE ratio of 12.
Which of the below statements is NOT correct based on a PE multiples valuation?
The debt-to-assets ratio should actually be 37.5%, not 40%. To find the debt-to-assets ratio based on the debt-to-equity ratio (D/E), divide the D/E ratio by one which won't change its value :
DE=0.6=0.61So debt (D) could be 0.6 and equity (E) could be 1. Therefore the value of assets (V) could be:
V=D+E=0.6+1=1.6Now find the debt-to-assets ratio: DV=0.61.6=0.375
The more mathematically rigorous approach is to use simultaneous equations and algebra:
DE=0.6 E=D0.6Substitute this into:
V=D+E=D+D0.6=0.6D0.6+D0.6=1.6D0.6 D=0.6V1.6 DV=0.61.6=0.375To find the earnings per share (EPS):
EPS=Earnings per share=EarningsNumberOfShares=100m20m=5Since similar firms have a PE ratio of 12, we can value our firm's current market value of equity E0 based on the earnings:
E0=Earnings×PriceToEarningsRatioOfSimilarFirms=100m×12=1200 million=1.2 billionAlternatively, the valuation can be done on a per share basis to find the current share price P0:
P0=EPS×PriceToEarningsRatioOfSimilarFirms=5×12=60The debt's market value D0 can be found based on the debt-to-equity ratio D/E and the market capitalisation of equity E0 found above:
D0=E0×D0E0=1.2b×0.6=0.72bQuestion 990 Multiples valuation, EV to EBITDA ratio, enterprise value
A firm has:
2 million shares;
$200 million EBITDA expected over the next year;
$100 million in cash (not included in EV);
1/3 market debt-to-assets ratio is (market assets = EV + cash);
4% pa expected dividend yield over the next year, paid annually with the next dividend expected in one year;
2% pa expected dividend growth rate;
40% expected payout ratio over the next year;10 times EV/EBITDA ratio.
30% corporate tax rate.
The stock can be valued using the EV/EBITDA multiple, dividend discount model, Gordon growth model or PE multiple. Which of the below statements is NOT correct based on an EV/EBITDA multiple valuation?
The forward looking price-to-earnings ratio is 20, not 10. But it takes many steps to verify this since we can't find the earnings directly from the EBITDA due to not knowing the interest expense, depreciation and amortisation:
Earnings=(EBITDA−Interest−DepreciationAndAmortisation)×(1−TaxRate)Instead we have to follow a number of steps to find the enterprise value, then asset value, equity value, share price, dividend, EPS and finally PE ratio. It's a long and difficult question!
First find the Enterprise Value (EV) from the EV/EBITDA ratio:
EVToEBITDARatio=EVEBITDA 10=EV200m EV=10×200m=2000mAdd the cash to the EV to get the market value of assets:
EnterpriseValue=Assets−Cash 2000m=Assets−100m Assets=2000m+100m=2100mMultiply the asset market value by the market debt-to-assets ratio to get the debt market value:
DebtToAssetsRatio=DebtAssets 13=Debt2100m Debt=13×2100m=700mSo the (gross) debt is 700m but the net debt (net of cash) is gross debt less the 100m cash:
NetDebt=GrossDebt−Cash=700m−100m=600mThe equity market capitalisation is the asset market value less the (gross) debt market value. Using the (market value, not book value) balance sheet formula:
Assets=Debt+Equity 2100m=700m+Equity Equity=2100−700=1400mThe equity market capitalisation equals the share price multiplied by the number of shares:
Equity=SharePrice×NumberOfShares 1400m=SharePrice×2m SharePrice=1400m2m=700Now that we know the current share price, we can find next year's dividend based on the dividend yield:
rdividend=Dividend1SharePrice0 0.04=Dividend1700 Dividend1=700×0.04=28To find the forward price-to-earnings ratio, we first need the earnings per share (EPS), based on the payout ratio:
PayoutRatio1=Dividend1EPS1 0.4=28EPS1 EPS1=280.4=70For the forward price-to-earnings ratio:
ForwardPriceToEarningsRatio=SharePrice0EPS1=70070=10Use the below information to value a levered company with constant annual perpetual cash flows from assets. The next cash flow will be generated in one year from now, so a perpetuity can be used to value this firm. Both the operating and firm free cash flows are constant (but not equal to each other).
Data on a Levered Firm with Perpetual Cash Flows | ||
Item abbreviation | Value | Item full name |
OFCF | $100m | Operating free cash flow |
FFCF or CFFA | $112m | Firm free cash flow or cash flow from assets (includes interest tax shields) |
g | 0% pa | Growth rate of OFCF and FFCF |
WACCBeforeTax | 7% pa | Weighted average cost of capital before tax |
WACCAfterTax | 6.25% pa | Weighted average cost of capital after tax |
rD | 5% pa | Cost of debt |
rEL | 9% pa | Cost of levered equity |
D/VL | 50% pa | Debt to assets ratio, where the asset value includes tax shields |
tc | 30% | Corporate tax rate |
What is the value of the levered firm including interest tax shields?
The cash flows continue forever so we'll use the perpetuity formula to price the company's assets (V).
V=FreeCashFlowrWACC−g'Textbook method' of firm valuation with interest tax shields
The textbook method includes the interest tax shields in the discount rate by discounting the operating free cash flow (OFCF) by the weighted average cost of capital after tax:
VL=OFCFWACCAfterTax−g=100m0.0625−0=1600m'Harder method' of firm valuation with interest tax shields
The harder method includes the interest tax shields in the cash flow by discounting the firm free cash flow (FFCF) by the weighted average cost of capital before tax:
VL=FFCFWACCBeforeTax−g=112m0.07−0=1600mUse the below information to value a levered company with constant annual perpetual cash flows from assets. The next cash flow will be generated in one year from now, so a perpetuity can be used to value this firm. Both the operating and firm free cash flows are constant (but not equal to each other).
Data on a Levered Firm with Perpetual Cash Flows | ||
Item abbreviation | Value | Item full name |
OFCF | $48.5m | Operating free cash flow |
FFCF or CFFA | $50m | Firm free cash flow or cash flow from assets |
g | 0% pa | Growth rate of OFCF and FFCF |
WACCBeforeTax | 10% pa | Weighted average cost of capital before tax |
WACCAfterTax | 9.7% pa | Weighted average cost of capital after tax |
rD | 5% pa | Cost of debt |
rEL | 11.25% pa | Cost of levered equity |
D/VL | 20% pa | Debt to assets ratio, where the asset value includes tax shields |
tc | 30% | Corporate tax rate |
What is the value of the levered firm including interest tax shields?
The cash flows continue forever so we'll use the perpetuity formula to price the company's assets (V).
V=FreeCashFlowrWACC−g'Textbook method' of firm valuation with interest tax shields
The textbook method includes the interest tax shields in the discount rate by discounting the operating free cash flow (OFCF) by the weighted average cost of capital after tax:
VL=OFCFWACCAfterTax−g=48.5m0.097−0=500m'Harder method' of firm valuation with interest tax shields
The harder method includes the interest tax shields in the cash flow by discounting the firm free cash flow (FFCF) by the weighted average cost of capital before tax:
VL=FFCFWACCBeforeTax−g=50m0.1−0=500mUse the below information to value a levered company with annual perpetual cash flows from assets that grow. The next cash flow will be generated in one year from now. Note that ‘k’ means kilo or 1,000. So the $30k is $30,000.
Data on a Levered Firm with Perpetual Cash Flows | ||
Item abbreviation | Value | Item full name |
OFCF | $30k | Operating free cash flow |
g | 1.5% pa | Growth rate of OFCF |
rD | 4% pa | Cost of debt |
rEL | 16.3% pa | Cost of levered equity |
D/VL | 80% pa | Debt to assets ratio, where the asset value includes tax shields |
tc | 30% | Corporate tax rate |
nshares | 100k | Number of shares |
Which of the following statements is NOT correct?
The weighted average cost of capital (WACC) before tax is:
rWACC before tax=rD.DVL+rEL.ELVL=0.04×0.8+0.163×(1−0.8)=0.0646 rWACC after tax=rD.(1−tc).DVL+rEL.ELVL=0.04×(1−0.3)×0.8+0.163×(1−0.8)=0.055The cash flows continue forever so we'll use the perpetuity formula to price the company's assets (V).
V=FreeCashFlowrWACC−g'Textbook method' of firm valuation with interest tax shields
The textbook method includes the interest tax shields in the discount rate by discounting the operating free cash flow (OFCF) by the weighted average cost of capital after tax:
VL=OFCFWACCAfterTax−g=30k0.055−0.015=750kThe current value of debt equals the current value of assets multiplied by the debt-to-assets ratio:
D=VL×DVL=750k×0.8=600kThe benefit from interest tax shields in the first year is equal to the interest expense that year multiplied by the corporate tax rate:
BenefitFromInterestTaxShields1=InterestExpense1×tc=D0×rD×tc=600k×0.04×0.3=24k×0.3=7.2kTo find the market capitalisation of equity, use the market value balance sheet formula:
VL=D+E 750k=600k+E E=750k−600k=150kThe share price P can be found based on the market capitalisation of equity formula:
E=P×nshares P=Enshares=150k100k=1.5Use the below information to value a mature levered company with growing annual perpetual cash flows and a constant debt-to-assets ratio. The next cash flow will be generated in one year from now, so a perpetuity can be used to value this firm. The firm's debt funding comprises annual fixed coupon bonds that all have the same seniority and coupon rate. When these bonds mature, new bonds will be re-issued, and so on in perpetuity. The yield curve is flat.
Data on a Levered Firm with Perpetual Cash Flows | ||
Item abbreviation | Value | Item full name |
OFCF1 | $12.5m | Operating free cash flow at time 1 |
FFCF1 or CFFA1 | $14m | Firm free cash flow or cash flow from assets at time 1 |
EFCF1 | $11m | Equity free cash flow at time 1 |
BondCoupons1 | $1.2m | Bond coupons paid to debt holders at time 1 |
g | 2% pa | Growth rate of OFCF, FFCF, EFCF and Debt cash flow |
WACCBeforeTax | 9% pa | Weighted average cost of capital before tax |
WACCAfterTax | 8.25% pa | Weighted average cost of capital after tax |
rD | 5% pa | Bond yield |
rEL | 13% pa | Cost or required return of levered equity |
D/VL | 50% pa | Debt to assets ratio, where the asset value includes tax shields |
nshares | 1m | Number of shares |
tc | 30% | Corporate tax rate |
Which of the following statements is NOT correct?
The cash flows continue forever so we'll use the perpetuity formula to price the company's assets (V).
V0=FreeCashFlow1rWACC−g'Textbook method' of firm valuation with interest tax shields
The textbook method includes the interest tax shields in the discount rate by discounting the operating free cash flow (OFCF) which excludes the interest tax shields by the weighted average cost of capital after tax which includes interest tax shields:
V0L=OFCF1WACCAfterTax−g=12.5m0.0825−0.02=200m'Harder method' of firm valuation with interest tax shields
The harder method includes the interest tax shields in the cash flow by discounting the firm free cash flow (FFCF) which includes interest tax shields by the weighted average cost of capital before tax which excludes interest ta shields:
V0L=FFCF1WACCBeforeTax−g=14m0.09−0.02=200mThe market capitalisation of equity can be found using two different methods. We can discount the equity free cash flow by the required return on equity:
E0=EFCF1rE−g=11m0.13−0.02=100mAlternatively, the market capitalisation of equity is equal to the asset value multiplied by the equity-to-assets ratio, which is one less the debt-to-assets ratio:
E0=V0×E0V0=V0×(1−D0V0)=200m×(1−0.5)=100mThe share price is then:
E0=nshares×P0,shares 100m=1m×P0,shares P0,shares=100m1m=100The debt cash flow (DebtCF) at the end of the first year can be found in a few different ways. It should be the difference between the firm free cash flow (FFCF) including interest tax shields and the equity free cash flow (EFCF):
FFCF1=EFCF1+DebtCF1 14m=11m+DebtCF1 DebtCF1=14m−11m=3mSince the 50% debt-to-assets ratio must be constant over time, the assets, equity and debt should all grow by the same 2% pa growth rate. However, the debt will actually grow by its 5% pa yield to maturity ignoring the coupons which are a part of DebtCF. Therefore to make the debt grow by only 2% pa rather than 5% pa, the debt cash flow must be 3% pa (=5% - 2%) of the 100m current debt value which is $3m (=0.03*100m).
To find the net amount of debt that needs to be repaid or bought back:
DebtCF=DebtCoupons+DebtFaceValueRepayments−DebtRaisings=DebtCoupons+NetDebtRepaymentsExcludingCoupons 3m=1.2m+NetDebtRepaymentsExcludingCoupons1 NetDebtRepaymentsExcludingCoupons1=3m−1.2m=1.8mThere are many ways to calculate a firm's free cash flow (FFCF), also called cash flow from assets (CFFA). Some include the annual interest tax shield in the cash flow and some do not.
Which of the below FFCF formulas include the interest tax shield in the cash flow?
(1) \quad FFCF=NI + Depr - CapEx -ΔNWC + IntExp (2) \quad FFCF=NI + Depr - CapEx -ΔNWC + IntExp.(1-t_c) (3) \quad FFCF=EBIT.(1-t_c )+ Depr- CapEx -ΔNWC+IntExp.t_c (4) \quad FFCF=EBIT.(1-t_c) + Depr- CapEx -ΔNWC (5) \quad FFCF=EBITDA.(1-t_c )+Depr.t_c- CapEx -ΔNWC+IntExp.t_c (6) \quad FFCF=EBITDA.(1-t_c )+Depr.t_c- CapEx -ΔNWC (7) \quad FFCF=EBIT-Tax + Depr - CapEx -ΔNWC (8) \quad FFCF=EBIT-Tax + Depr - CapEx -ΔNWC-IntExp.t_c (9) \quad FFCF=EBITDA-Tax - CapEx -ΔNWC (10) \quad FFCF=EBITDA-Tax - CapEx -ΔNWC-IntExp.t_cThe formulas for net income (NI also called earnings), EBIT and EBITDA are given below. Assume that depreciation and amortisation are both represented by 'Depr' and that 'FC' represents fixed costs such as rent.
NI=(Rev - COGS - Depr - FC - IntExp).(1-t_c ) EBIT=Rev - COGS - FC-Depr EBITDA=Rev - COGS - FC Tax =(Rev - COGS - Depr - FC - IntExp).t_c= \dfrac{NI.t_c}{1-t_c}The interest tax shield per year is IntExp.t_c, and the odd numbered equations include it. Let the firm free cash flow with the interest tax shield be FFCF_\text{wITS} and the cash flow excluding the interest tax shield be FFCF_\text{xITS}. Then:
\begin{aligned} FFCF_\text{wITS}&=NI + Depr - CapEx -ΔNWC + IntExp \\ &=EBIT.(1-t_c )+ Depr- CapEx -ΔNWC+IntExp.t_c \\ &=EBITDA.(1-t_c )+Depr.t_c- CapEx -ΔNWC+IntExp.t_c \\ &=EBIT-Tax + Depr - CapEx -ΔNWC \\ &=EBITDA-Tax - CapEx -ΔNWC \\ \end{aligned} \begin{aligned} FFCF_\text{xITS}&=NI + Depr - CapEx -ΔNWC + IntExp.(1-t_c) \\ &=EBIT.(1-t_c) + Depr- CapEx -ΔNWC \\ &=EBITDA.(1-t_c )+Depr.t_c- CapEx -ΔNWC \\ &=EBIT-Tax + Depr - CapEx -ΔNWC-IntExp.t_c \\ &=EBITDA-Tax - CapEx -ΔNWC-IntExp.t_c \\ \end{aligned}