Input

Equation

Examples from notes

Riskfree Rate

Long term, default free, currency-matched rate.
If government is default free, use long term government bond rate
If government is not AAA rated, adjust the long term government bond rate for default risk.
Riskfree rate = LT government bond rate – Default spread

For Amgen,
US T.Bond rate = 4.78%
For Hyundai Heavy,
Korean government bond rate = 5.8% but Korean government has A2 rating, with default spread of 0.80%
Won riskfree rate = 5.8% -0.8% = 5%

Equity Risk Premium (ERP) (Mature market)

Can be estimated from

• Historical data: Difference between geometric average return on stocks and geometric average return on treasuries over very long time periods.
• Current stock prices: Compute the implied expected return based upon index level now and expected cash flows (dividends and stock buybacks) in future.

Geometric average ERP for US = 3.88% (see page 23)
Implied premium = 6.43% (see page 23)
(You will not be asked to compute the implied premium but you should be able to explain what it is and why it may change over time)

Country Risk premium (CRP) (and total risk premium)

Step 1: Get default spread for country, based upon its sovereign rating.
Step 2: Adjust the default spread for the relative volatility of equity to government bond in that market.

• Country Risk Premium = Default spread*(Standard deviation of equity/ Standard deviation of bond)
• Total Risk Premium = Mature market premium + Country risk premium

For Korea
Default spread for Korea = 0.80%
Relative equity market volatility:
Standard deviation of KOSPI = 18%
Standard deviation of bond = 12%
CRP for Korea = 0.8% (18/12) = 1.2%
Total risk premium = 4% + 1.2% = 5.2%

Beta

Can be estimated from

• Regression of stock returns against market index, but that estimate will be backward-looking and have significant standard error.
• A bottom-up beta, computed by looking at the businesses that the firm operates in and the unlevered betas of other firms in the business. Beta for company =

where wj = Weight of business j
As a final step, you can lever betas:
Levered Beta= Unlevered Beta (1+(1-t) (Debt/Equity))

Amgen: Single business company (Pg 22)
Unlevered beta = 1.59
Levered beta = 1.59 (1+(1-.35)(.11)) = 1.73
Hyundai Heavy (see page 22)
Unlevered beta = 1.49
Levered beta = 1.49 (1+(1-.275)(.007))=1.50

Lambda

Measures company exposure to country risk. Easiest way to estimate it is to use revenue exposure:
Lambda = % of revenues domesticallyfirm/ % of revenues domesticallyavg firm in market

Hyundai Heavy (Page 30)
Hyundai’s revenues in Korea = 20%
Average firm’s revenues in Korea= 80%
Lambda for Hyundai, Korea = 20%/80% = 0.25

Expected Return (Cost of equity)

If enough information provided for estimating lambda
Cost of equity = Riskfree Rate+ Beta (Mature market premium) + l (CRP)
If not enough information provided for lambda
Cost of equity = Riskfree Rate + Beta (Mature market premium + CRP)

For Amgen
Cost of Equity = 4.78%+1.73 (4%) = 11.7%
Lambda approach for Hyundai Heavy:
Cost of equity = 5% + 1.5 (4%) + 0.25 (1.2%) =11.30%
If Lambda could not be estimated:
Cost of equity = 5%+1.5 (5%+1.2%)=14.3%

Pre-tax Cost of Debt

If mature market company
Riskfree Rate + Default spread for company
If emerging market company
Riskfree Rate + Default spread for country + Default spread for company

For Amgen in 2007
4.78% + 0.85% = 5.63%
For Hyundai Heavy in 2008
5% + 0.80% + 0.75% = 6.55%

Debt

For computing the cost of capital, debt should include:

• Market value of interest bearing debt, short term as well as long term.
• Present value of all lease commitments, discounted back at the current pre-tax cost of debt.

For Amgen in 2007 (See page 14)
MV of interest bearing debt = $7,402
PV of leases @ 5.63% = $870
Total debt =$8,272 million

Cost of capital

Cost of equity (E/(D+E)) + Cost of Debt (1- marginal tax rate) (D/(D+E))

For Amgen,
11.7%(.9) + 5.63%(1-.35) (.1)
For Hyundai Heavy
11.3% (.993)+6.55%(1-.275)(.007)

EBIT

Start with the stated operating income, but adjust for:

• Leases: by adding back the current year’s lease expense and subtracting out depreciation on the lease asset.
• R&D: by adding back the current year’s R&D expense and subtracting out amortization on the research asset.

For Amgen, (Pge 14-15)
Stated Operating Income = $5,071
+ Current year lease exp =  $ 69
- Deprec’n on lease asset=   $ 72.5
+ Current year R&D =          $ 3,366
- Amortization of  R&D =    $ ,1150
Adjusted Operating inc =   $ 7,336

Capital Expenditures & Net Cap Ex

Should include:

• Stated Capital Expenditures (from statement of CF)
• R&D expense for the current year
• Costs of all acquisitions, whether paid for with cash or stock.
• Current year’s lease expense

Net Cap ex = Cap Ex – Depreciation
Depreciation should include depreciation on leased asset and R&D

For Amgen,
Stated capital expenditure= 1,218
Adjusted capital expenditure= 1.218 + 3366 (R&D) + 3975 (Acquisitions) + 69 (lease exp)= 8628
Net Cap Ex = 8628-2185 = 6443

Non-cash Working Capital

Non-cash Current Assets – Non-debt Current liabilities.

For Amgen in 2007
Inventory (1903)+Accounts Rec (2124)+Other current assets(1408)-Acc Pay (555)-Other current liab (4589) = 291
Change from previous year = +37

FCFF

EBIT (1- tax rate) – (Cap Ex – Depreciation) – Change in non-cash Working Capital

For Amgen in 2007
7336 (1-.28) – 6443 – 37 = -423

Return on Capital

where
BV of Equity includes the value of the research asset
BV of Debt includes the PV of lease commitments
All values in denominator are from previous year.

For Amgen in 2007

Reinvestment Rate

For Amgen in 2007

Expected Growth

Reinvestment Rate * Return on Capital
In making these estimates, you do not have to stick with current numbers but should use your best forecasts. This may require looking at the reinvestment rate over time.

For Amgen
Expected Reinvestment rate = 60% (average over last 5 years)
Expected ROC = 16% (trend downward continues)
Expected growth = .6*.16 = .096 or 9.6%
For Hyundai Heavy
Expected Reinvestment rate = 50% (close to last year’s number)
Expected ROC = 30% (below last year’s number)
Expected growth = .5*.30 = .15 or 15%

Terminal value

where gn = Growth rate forever (< Riskfree Rate)
ROCn = Return on capital forever (should move to or towards the stable period cost of capital)

For Amgen

Note that we switch to the marginal tax rate (35%), stable period cost of capital (8.08%) and stable ROC (10%)
For Hyundai Heavy

Since the ROC = Cost of capital, the value will remain the same as growth changes.

Value of Operating Assets today

For Amgen:
PV of Cash flows for next 10 years + PV of terminal value = $94,214
For Hyundai Heavy:
PV of Cash flows for next 5 years + PV of terminal value = 20,211 billion Won

Value of firm today

Value of Operating Assets
+ Cash and Marketable Securities
+ Market Value of Cross holdings in other companies

For Amgen
94,214+ 183 (Cash) =95,497
For Hyundai Heavy
20,211+ 3612 (Cash) +3,937 (Cross holdings) = 27,759

Value of equity today

Value of firm today

• Market value of debt outstanding
• Market value of minority interests (if consolidated)

For Amgen
95,497 – 8272 (Debt) = 87,226
For Hyundai Heavy
27,759 – 186 (Debt) = 27,574

Value of equity per share

Value of Equity today

• Value of Equity options granted by firm

/ Number of shares outstanding

For Amgen
(87226 – 479 (Options))/1167.11 = $74.33
For Hyundai Heavy
27574/76 = 362,200 Won/share