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Advanced Corporate Finance ACFI3310 Revision Sheet
Investment Appraisal Methods
Discounted Cash flow:






Take into account time value of money, and can be used to evaluate Stocks, Bonds, Forward
contracts (derivatives), Foreign currencies (FOREX) and Real assets
...

Find the PV of expected cash flows
...

If NPV ≥ 0, we accept the project
...


Example 1
Cost of Capital, r = 12%
T (£'000)

0

1

2

3

4

5

Pr1

(2,000)

500

250

750

600

850

Pr2

(1,500)

400

400

400

400

400

Pr3

(2,000)

1,000

200

300

800

1,000

R

1

NPVPr1

(2,000)

1/(1+r) =
0
...
5

1/(1+r)2 =
0
...
3

1/(1+r)3 =
0
...
9

1/(1+r)4 =
0
...
3

1/(1+r)5 =
0
...
3

43
...
2

318
...
7

254
...
0

(58
...
9

159
...
5

508
...
4

341
...


Example 2
Source

£'000 - MV

Proportion

Cost of capital

WACC

Bank Loans

5

5/40 = 0
...
06

0
...
125

0
...
0125

Ordinary shares

30

30/40 = 0
...
15

0
...
1325

Total

Cost of Equity (Ke)
Dividend Valuation Model (DVM)
The value of the share is the PV of expected future dividends discounted at required rate of return
(Ke)
D0 = Dividend at time 0
g = Dividend growth rate (perpetuity)
0
P0 = Value of shares
e

k 

D 1  g 
g
Po

Capital Asset Pricing Model (CAPM)

Ke  rf   (rm  rf )
Rf = Risk free rate
β = Beta risk
Rm = Market Average return





Beta > 1 are aggressive shares; they have bigger movements than the market, rise more in a
bull market and fall more in a bear market
...

Beta = 1 are neutral shares; they are expected to follow market fluctuations
...




 V ( 1 – t) 
VE
βe,u=βe, g 
+βd  D


VE+VD( 1 – t) 
VE+VD( 1 – t) 
1
...

3
...

5
...
1
16%
30%

Manufacturer
Equity : debt ratio
Cost of debt
Beta Value
Average market return, rm
Corporate tax rate, T

S Plc
Waterbeds
2:1
1
...

βe,u = βe,g (VE/(VE + VD(1 + T))) + (0)

βe,u = 1
...
3))) + (0)

= 1
...

1
...
3))) + (0)

βe,g = 1
...

Ke = rf + β(rm - rf)

Ke = 0
...
51(0
...
11) =

18
...
11(1 - 0
...
7%

Step 5: Calculate WACC
Source

£'000 - MV

Proportion

Cost of capital

WACC

Equity

5

5/7 = 0
...
55%

0
...
2857

7
...
022

Total

7

0
...

Cost of Debt Kd(1-T)
The company's post tax cost of debt
...

Debt or Equity finance?
Ongoing servicing costs,
Issue costs,
Gearing,
Cash flow profile,
Risk profile,
Covenants
...
Unlevered = debt free
...








When a firm pays no tax and capital markets function well, there isn't a difference between
borrowing and equity funding
...
VU = VL
However, this is assuming that Capital structure does not affect cash flow:
- No taxes,
- No bankruptcy costs,
- No effect on management incentives
...


M and M - Proposition II (No Tax)

When debt is cheaper than WACC (i
...
Cheaper debt), there is an increase in Ke
...


k Eg

D

 k Eu   k Eu  k D 
E


VL  VU

Tax Free proposition II equation

Tax free proposition 1 equation

Example 4
Investment Alternative:
Initial Investment = £5,000
EBIT = £1,000 forever,
Keu = 10% (Required return on unlevered equity)
Financing Alternatives:
Unlevered
£5,000

£1,000

Cash Flows
EBIT
Interest
EBT
Tax (0%)
Free cash flow
Cash flows debt + equity

£4,000
£1,000

£1,000

Equity
Debt (Kd = 5%)

Levered

£1,000
(5% * 1,000) = -£50
£950

£1,000
£1,000

£950
£1,000

Proposition 1
VU= £1,000/10% =
VL = D + E

£10,000
D = £1,000

Proposition 2
Keu = 10%

Keg = 0
...
10 - 0
...
556%

Therefore, E = £10,000 - £1,000 = £9,000

Weighted Average Cost of Capital
WACC = (10
...
Therefore, Gearing should be as high as
possible with 99
...


VL  VU  D

Example 5
Unlevered
£5,000

Cash Flows
EBIT
Interest
EBT

£1,000
(5% * 1,000) = -£50
£950

£1,000

Tax (34%)
Free cash flow
Cash flows debt + equity
Proposition 1
VU= £660/10% =
VL = VU + Dt =

£4,000
£1,000

£1,000

Equity
Debt (Kd = 5%)

Levered

-£340
£660
£660

-£323
£627
£677

£6,600
Dt = £1,000 x 34% = £340
£6,600 + £340 = £6,940
Therefore, E = £6,940 - £1,000 = £5,940

Proposition 2
Keu = 10%

Keg = 0
...
34)(£1,000/£5,940)(0
...
05) = 10
...
556% x (5,940/6,940)) + (5%(1 - 0
...
51%
WACCg = WACCu (1 - (D x t)/(D + E))
WACCg = 0
...
34)/(5,940 + 1,000)) = 9
...

Value of the firm = Value if all equity financed + PV of tax shield - PV of financial distress

Example 6
H International Ltd is a shipping firm
...
50
Shares outstanding: 10 million
There are plans to lower corporate taxes by borrowing £20 million and repurchasing shares
...
50 x 10m = £55m
VL = D + E
£55m = £20m + E
E = £35m

E = £35m
Number of shares repurchased:
£20m debt/£5
...
636m shares
E / remaining shares
£35m / (10m - 3
...
50

However, is you suppose that H International Ltd pays 30% in corporate tax
...
50 x 10m = £55m
Dt = £20m x 0
...
50 = 3
...
636m) = £6
...
The share price rises to £5
...
44 (calculated share price) - £5
...
69 x 6
...
39m
£4
...

Therefore, the value of the firm is = £55m (all equity financed) + £6m (PV tax shield) - £4
...
61m
VL = D + E
E = £5
...
363m shares = £36
...
59m + £20m = £56
...

The Target debt ratios vary from firm to firm, with High tech industries favouring lower
tangibles so lower debt, whilst Tangible heavy industries favour higher debt
...
e
...

If Internally generated cash flows are less than the capital expenditure required for an
investment, due to dividend policies, fluctuations in profit or investment opportunities; then
the firm must first draw down cash balance or sell marketable securities to free up cash
...

If External finances are required, then the safest security is issued first
...


Adjusted Present Value (APV)



APV can be used to appraise projects when a firm's capital structure changes
...


Investment Decision

Financing Decision

APV =

(base case NPV) - discount
project cash flows using an
un-geared Ke

Find the PV of financing
costs and benefits
...


APV Layout
Base Case NPV
PV of issue costs
Equity
Debt
PV of the tax shield
- Normal loan
- Subsidised
PV of the subsidised loan:
Interest saved
Tax relief lost
APV

X/(X)
(X)
(X)

X
X
X
(X)
X/(X)

Investment Decision: Ignore gearing! Take a geared beta for a company in the same industry as the
project, de-gear it
...
Use the ungeared Keu to discount project cash flows
...

Typical financing costs: Issue costs on debt and/or equity,
Typical financing benefits: Tax relief on debt interest, Value of a subsidised loan for saving of interest
and loss of tax shield on interest saved
...
(3% of £80,000) = £2,400
Equity beta: 1
...
70(3/(3 + 1(1 - 0
...
38

Keu = rf + βu(rm - rf)

Keu = 0
...
38(0
...
05) = 0
...
862
0
...
641

PV (£'000)
(400)
150
...
025
112
...
95)

Step 2: Financing costs of Equity and Debt, including Tax relief gained @ Pre-tax cost of debt (3 year annuity)
PV of Issue costs and Interest rate payments above
...
30 = £4,320
£4,320 * 2
...
30 = £2,400
£2,400 * 2
...

Interest saved:
Tax relief lost:

£14,400 - £8,000 = £6,400
£6,400 * 2
...
30 = £4,680

Base Case NPV
PV of issue costs
Equity
Debt
PV of the tax shield
- Normal loan
- Subsidised
PV of the subsidised loan:
Interest saved
Tax relief lost
APV

(6,960)
(2,400)
(0)

10,934
6,074
16,198
(4,860)
18,996 Positive, therefore Accept
...

There is subjectivity in the cash flows
...


Efficient Market Hypothesis (EMH)



Markets are considered to be efficient, relative to a given information set, if there are no
abnormal profit opportunities for investors trading on the basis of this information
...


Determinants and Requirements of Market Efficiency






Determinants include the nature and source of information,
The time needed by the market to adjust all the share price for that information
...

New information regarding securities comes to the market in a random fashion
...


Random Walk Hypothesis
Hypothesises that changes in security prices occur randomly, there are no patterns or trends
...
" - Burton G
...

Future changes in stock prices should ideally be unpredictable
...
Therefore, if stock
prices were predictable, causing the above behaviour, price changes would equal zero
...

Weak Form Measures of market efficiency
Current stock price reflects all historic price and volume information about the company
...
Investors can't
make more than a fair return using historic information
...

Semi-strong Form Measure of market efficiency
Focused on the speed of incorporation of information into prices
...
Investors can't make abnormal return
immediately after information released as it's already incorporated into prices
...
If a market
is efficient, individual stock returns shouldn't be predicted with past returns or other public
information
...

There is strong support for semi-strong form from numerous event studies, with the exception of
IPO studies
...

Stock split studies show that splits do not result in abnormal gains after the split announcement, but
before
...
The price is adjusted
within 1 day after the offering, therefore listing of a stock on a national exchange such as the NYSE
may offer some short term profit opportunities for investors
...
g
...

Strong Form Measure of market efficiency
Stock price reflects all private and public information about a firm
...
Difficult to prove
...
The testing group of investors are:
Corporate insiders, Security analysts and professional money managers
...

What is the value of an efficient market?
It can encourage share buying, give correct signals to companies' managers regarding feedback on
their decisions, required rate of return and improving disclosure
...

There are, however, a few misconceptions to EMH
...

There are not fewer price fluctuations,
It is not the case that there is only a minority of investors that are actively trading, making efficiency
unachievable
...

2
...

4
...

6
...


Other implications for financing decisions include:





A company CAN sell large quantities of shares without changing the price,
There is no perfect time to issue equity for financing,
A merger or takeover, without associated rationalisation, should not influence the price of
shares
...


If your company's shares are overpriced, issue equity to invest in additional projects
...

If the company is caught in a bubble, it is tempting to use equity to acquire other companies and
tempting to cover up bad news/manufacture good news
...

Usually because the company may sell poorly performing stock to offset losses for tax
purposes in the 4th quarter
...


Day of the week effect




Research suggests that stocks move more on Fridays than Mondays, and that movements
tend to be more positive on Friday than Monday
...

Although movement is small, it does exist
...


Turn of the month effect


Stock prices rise on the last day of the month and first three days of the following month
...
61%
0
...
84%
0
...
29%
-0
...
20%
-0
...
60%
-5
...

These excess-returns cannot be captured by equilibrium asset pricing models such as CAPM
...

These anomalies violate weak-form efficiency and random walk hypothesis
...
Studies found that smaller firm's shares
outperformed, due to the fact that a large company needs to find billions extra to grow 10%,
whilst a small company may only need a few million to grow at the same rate
...

Investors place emphasis on short term earnings data, because unusually cheap stocks
attract investors and then encounter mean reversion
...
Can be attributed to
behavioural reactions, suggesting investors are irrational
...

Mean reversion indicates there will be a predictable positive change in the future price,
indicating stock prices are not random walk
...


"The anomalies that had been discovered might be considered at worst small departues from the
fundamental truth of market efficiency, but if most of the volatility in the stock market was
unexplained, it would call into question the basic underpinnings of the entire efficient markets
theory
...

Provides the link between behavioural psychology and financial economics
...

Places an emphasis on investor behaviour, and how this creates the various market
anomalies
...
Concepts
from Psychology, Sociology and other social sciences are applied to the behaviour of security
prices
...
" (Carlson, 2006)
Other behaviour analysis points to investor overconfidence as perpetuating stock price
bubbles
...

Focuses too much on upwards or downwards price trends and extrapolates too far into the
future, linked to feedback theory
...


"It's a little bit like religion, you know
...
But
maybe there's some wisdom about living that comes out of all of them
...

"The market efficiency hypothesis offers a simple answer to this question - chance
...
(Fama, 1998)
Anomalies reflect inefficiency within markets
...
History is no predictor of future performance, so you should not expect every

Monday to be disastrous and every January to be great, but there will be days where this is proved
to be true
...

Record Date: When a firm pays a dividend, only shareholders on record on this date receive it
...

Payable Date/Distribution Date: Date, generally within a month after the record date, on which the
firm mails dividend payments to its registered shareholders
...

Payout policy: The way a firm chooses to distribute surplus cash to equity holders, either by paying
dividends or repurchasing shares
...
usually represents about 95% of all repurchase transactions
...

If shareholders do not tender enough shares, they may cancel the offer and hence no
buybacks occur
...
Shareholders indicate how many shares they are willing to sell
at each price, the firm then pays the lowest price at which it can buy back its desired number
of shares
...

Greenmail is when a firm avoids a threat of takeover and removal of management by a
major shareholder by buying out the shareholder, often at a large premium over the current
MV
...
Only case where differences arise is we
take into account frictional factors such as issue costs, taxation etc
...
0 Debt
Fixed assets and net working
10
...
0

0
...
0
11
...
0 Debt
Fixed assets and net working
10
...
0

0
...
0
10
...

- Shareholder wealth stays at $11 ($10 share price, plus $1 dividend)
$1m is used to repurchase shares:
- $1m/$11 = 90,909 shares repurchased
- 1m - 90,909 shares = 909,091 shares remaining
- $10m/909,091 = $11 per share
- i
...
shareholder wealth stays at $11
Repurchase at 10% premium:
- $1m/$12
...
1) = 82,645 shares repurchased
- 1m - 82,645 shares = 917,355 shares remaining
- $10m/917,355 = $10
...
e shareholder wealth falls (for those who didn't sell
...
It is un-geared and has a cost of capital of 12%
...
$2 per share can be paid immediately
...
80 per share)
...

Alternative 3 - Pay higher dividend, by making an equity issue (need to raise further £28m)
Alternative 1
Cum-dividend MV of a share, P0 is the PV of future free cash flows:
PCUM = £2 + £4
...
12 = £42
Ex-dividend price would reduce by dividend just paid:
PEX = £40

Cash
Other assets
Total market value
Shares
Share price

Cum Dividend
£20m
£400m
£420m
10m
£42

Ex dividend
£400m
£400m
10m
£40

Alternative 2
Total MV same as previous example @ £42 per share
...
04
Ex-dividend price will be
£5
...
12 = £42
The repurchase has no impact on stock price
...

Total shares = 10m + 666,667 = 10
...
67m = £4
...
50 + £4
...
12 = £42





Repurchasing gives the ability to reduce further dividend payments in the future, and a
better future EPS figure
...

Doing neither is seen as hoarding cash without purpose
...

- Currently 25% or 36
...

Capital gains tax is at a lower rate
- Currently 18% or 28% (higher rate)
- Higher rate starts at around £32,010 currently
...

- If shares lose value, no tax to pay
...


Example 10
Share prices at time of purchase were $10, fallen to $8 over the last 5 years
...
Tax rates are: Dividends: 39%, Capital Gains: 20%
...
95)
20% x $3
($0
...
05

$12

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