Interest tax shield = $5 million * .06 * (1-.35) = $0.195 million PV (interest tax shield) = $0.195 / .0984 = $1.98 million Condition II  Debt of $ 7.5 million  Interest tax shield = $7.5 * .06 * (1-.35) = $0.2925 million  PV (interest tax shield) = $0.2925 / .0984 = $2.97 million So APV = Base case NPV + PV (interest tax shield) Condition I: APV = -$1.067 + $1.98 = $

1. By
Arpit amar
Corporate Finance – 2011
Georg Simon Ohm University of applied Science, Nuremberg

2. Introduction
Finance
manager
Takes two decision
Investment or capital
Financing decision
budgeting decision
Where to invest or How to raise money or
purchase of real assets sale of financial assets

3. Investment decision
Finance manager
Explores good
investment
projects
Analyse NPV (net The difference
present value) between Projects
value and its cost
Assumes all cost of
financing is equity
financed
Takes opportunity
cost of capital as And calculates
discount rate NPV

4. Financing decision
When Investment project is financed with equity capital as well as
debt capital
Then this will represent the capital structure of the firm
Equity capital requires The return should be more
return to be paid to then the opportunity cost of
shareholders or investors capital
Debt capital requires fixed Interest is tax-deductible
interest to be paid to the expense, so we calculate after
creditors tax cost of debt
The weighted average of cost of debt and cost of equity taken
together is called weighted average of capital (WACC)

5. WACC
Analyse the cost of raising the equity and debt capital
Takes the weighted
And value’s project
average of cost
WACC = Rd( 1-Tc) D/V + RE E/V
Rd = cost of debt
Re = cost of equity
D= market value of debt
E= market value of equity
Tc = corporate tax rate
The formula of WACC works for average projects, where
business risk from equity and debt ratio remains constant
The managers use WACC to discount future cash flows but
when equity and debt ratios are expected to change , then
WACC may not give exact results

6. Calculating Sangria’s WACC
Sangria is a U.S.-based company whose products aim to promote happy , low stress
lifestyles. The book value and market value are :
Book values , $million Market values , $million
Assets $1000 $500 Debt Assets $1250 $500 Debt
value value
$500 Equity $750 Equity
$1000 $1000
$1000 $1250
In market values : the value of debt
In book value : the value of debt
remains same and value of equity
and equity are equal
changes from $ 500 to $750
The given cost of debt is 6%.This The given cost of equity is 12.4%.
represent interest paid on existing This represent the expected rate of
and on new borrowing debt return demanded by investors

7. Sangria’s WACC
Taking market Debt ratio = 500/1250 = .4
values for the
calculation of debt
and equity ratios Equity ratio = 750/1250 = .6
The market share price changes from $5 to $7.5.This is the current market price and
when it is multiplied by number of its outstanding shares , then it increases the
equity capital and changes equity ratio in overall capital structure. Sangria is
constantly profitable and pays taxes at the marginal rate of 35%
Therefore:
Cost of debt (rd) = .06
Cost of equity (re)= 0.124 The company’s after- tax WACC is:
Marginal tax rate (Tc) = .35 WACC= .06*(1-.35)*.4 +.124*.6 =.090 OR 9%
Debt ratio (d/v) = .4
Equity ratio (e/v) = .6

8. Using Sangria’s WAAC for the valuation of project
Suppose there is an investment in the firm of $12.5 million in perpetual crushing machine. The machine
never depreciates and generates a cash flow of $1.731 million per year pre-tax. And overall the project is
average risk
If the risk involved in project is average then
we use WACC as a discount rate NPV= Initial investment + cash flow /
that is 9% discount rate of WACC
Pre tax cash flow = $1.731 million NPV= -12.5 + 1.125 / .09
Tax at 35% of $1.731 million = .606 NPV = 0
After tax cash flow (c) = $1.125 million
When NPV is zero then the project is barely acceptable as an investment.
This states that return from investing $12.5 million in project generates the cash flow of
$1.125 million which is equals to Sangria’s WACC OF 9%.
That is: cash flow / investment
=1.125/12.5*100
=9%
Therefore return on investment is equal to cost

9. Assumptions about WACC
•WACC formula uses after tax cost of debt thereby capturing the value of interest shield
•The formula works for average projects where business risk and debt ratios are expected
to be constant
•When business risk and debt ratios are not constant or expected change ,then use of
WACC is not exactly correct.
•Pre tax cash flows are converted into after tax cash flows as if the project were all equity
financed.
•The project cash flow’s are then discounted by WACC in order to capture the effect from
tax shield
•When NPV is zero then project is barely acceptable stating that the cost of capital and
return from investment are equal

10. WACC and financial crisis
Cost of capital assumes risk free rate of return but in practice its not risk free
Cost of equity capital Cost of debt capital
Return investors expects Interest to be paid by company
High cost of equity capital makes High Cost of debt capital creates
it compulsory for company to pay inflation , increase investors
risk premium rate of return which expectations to cover this inflation
has to be more than its beta rate
Need to analyse good investment
Incapacity to pay back huge debt
projects.
may lead to defaults and so credit
Zero NPV or low NPV projects may
institution will not lend more
not be able pay high returns to
money, investors loose faith and
shareholders.
may invest in government bonds,
Share price and valuation of
there will be refinancing problems
company may get affected

11. Valuing Businesses
When valuing a business as a whole is necessary:
• Mergers & Acquisition
• Selling of a business unit
• Going Public
WACC can be used to value businesses that are financed by debt & equity
Assumption: constant debt ratio
FCF1 FCF2 FCFH PVH
PV = + + ×××+ +
1+ WACC ( 1+ WACC ) 2
( 1+ WACC ) ( 1+ WACC )
H H
Present Value (free cash flow) Present value
(horizon value)

12. Valuing Businesses
Example: Valuing Rio Corporation
Input data:
• Rio Corporation is a similar corporation like Sangria
• Same line of business like Sangria (Assumption: same proportion of debt like
Sangria)
⇒ Sangria's WACC can be used – 9%
Goal: Calculating the present value of Rio Corporation
Steps to do:
1. Calculation of free cash flows (FCF)
2. Estimating horizon value
3. Calculation of present value

13. Valuing Businesses
Example: Valuing Rio Corporation
Latest year Forecast
0 1 2 3 4 5 6 7
1 Sales 83.6 89.5 95.8 102.5 106.6 110.8 115.2 118.7
2 Cost of goods sold 63.1 66.2 71.3 76.3 79.9 83.1 87 90.2
3 EBITDA (1-2) 20.5 23.3 24.4 26.1 26.6 27.7 28.2 28.5
4 Depreciation 3.3 9.9 10.6 11.3 11.8 12.3 12.7 13.1
5 Profit before tax (EBIT) (3-4) 17.2 13.4 13.8 14.8 14.9 15.4 15.5 15.4
6 Tax 6 4.7 4.8 5.2 5.2 5.4 5.4 5.4
7 Profit after tax (5-6) 11.2 8.7 9 9.6 9.7 10 10.1 10
8 Investment in fixed assets 11 14.6 15.5 16.6 15 15.6 16.2 15.9
9 Investment in working capital 1 0.5 0.8 0.9 0.5 0.6 0.6 0.4
10 Free cash flow (7+4-8-9) 2.5 3.5 3.2 3.4 5.9 6.1 6 6.8
PV Free cash flow, years 1-6 20.3 113.4 (Horizon value in year 6)
PV Horizon value 67.6
PV of company 87.9

14. Valuing Businesses
Example: Valuing Rio Corporation
Assumptions
Sales growth (percent) 6,7 7 7 7 4 4 4 3
75,5 74 74,5 74,5 75 75 75,5 76
13,3 13 13 13 13 13 13 13
79,2 79 79 79 79 79 79 79
5 14 14 14 14 14 14 14
Tax rate, percent 35%
WACC 9%
Long term growth forecast 3%
Fixed assets and working capital
Gross fixed assets 95 109,6 125,1 141,8 156,8 172,4 188,6 204,5
Less accumulated depreciation 29 38,9 49,5 60,8 72,6 84,9 97,6 110,7
Net fixed assets 66 70,7 75,6 80,9 84,2 87,5 91 93,8
Depreciation 3,3 9,9 10,6 11,3 11,8 12,3 12,7 13,1
Working capital 11,1 11,6 12,4 13,3 13,9 14,4 15 15,4

15. Valuing Businesses
Example: Valuing Rio Corporation
Determination of free cash flows:
FCF = profit after tax + depreciation – investment in fixed assets –
- investment in working capital
FCF1= 8,7 + 9,9 – (109,6 - 95,0) – (11,6 -11,1) = 3,5 (million $)
FCF2 = …
Calculation of PV (FCF)
3.5 3.2 3.4 5 .9 6 .1 6.0
PV(FCF) = + + + + +
1.09 (1.09) 2 (1.09 ) 3 (1.09) 4 (1.09 ) 5 (1.09 ) 6
= 20.3

16. Valuing Businesses
Example: Valuing Rio Corporation
Determination of horizon value:
•Long run growth rate: 3%
FCFH +1  6.8 
Horizon Value = PVH = =  = 113.4
wacc − g  .09 − .03 
1
PV(horizon value) = ×113.4 = $67.6
(1.09) 6
PV(business) = PV(FCF) + PV(horizon value)
= 20.3 + 67.6
= $87.9 million
Value of equity = PV(business) – value of debt = 87,9 – 36,0 = $51,9 million

17. Valuing Businesses
Tricks of the Trade
More than two sources of financing:
D  P  E 
WACC = (1 − Tc) × rD  +  × rP  +  × rE 
V  V  V 

18. Valuing Businesses
Tricks of the Trade
What about short term debt?
• Leaving short term debt out of calculation is an error
• No serious error if debt is only temporary or compensated by holdings of cash
and marketable securities
What about other current liabilities?
• Usually "netted out" (Net working capital = current assets – current liabilities)
• Net working capital is entered on the left hand side of balance sheet

19. Valuing Businesses
Tricks of the Trade
How are the costs of financing calculated?
• Interrest rate for equity can be retrieved by looking at the stock market (typical
demand by investors)
• Getting borrowing rate and D/V and E/V is not difficult
• Convertible, junk debt,

20. Valuing Businesses
Impact of the Euro Crisis on valuing businesses
• Inflation leads to increasing interest rates
• WACC is increasing with increasing interest rates
D  P  E 
WACC = (1 − Tc ) × rD  +  × rP  +  × rE 
V  V  V 
•Present value decreases with increasing WACC
FCF1 FCF2 FCFH PVH
PV = + + ×××+ +
1+ WACC ( 1+ WACC ) 2
( 1+ WACC ) ( 1+ WACC )
H H
•Key interest rate may increase  higher interest rates (like mentioned above)
•Influence of rating agencies
•Influence of currency exchange rates  Increase / decrease of FCF

21. APV -Adjusted present value
Estimating the firm or project base case value assuming it is all equity financed and
then adjust this base case value to account for the financing side effects .
APV = Base Case NPV + sum of PV Impact
 Base Case = All equity finance firm NPV
 PV Impact = all costs/benefits directly resulting from project
PV impact : Interest rate tax shields (plus)
Issuing cost of securities ( minus)
Financing packages subsidized ( plus)

22. APV- Base case
Example : Sangria Perpetual crusher project
 Cost of capital r = 9.84%
 Investment = $ 12.5 million
 Project cash flow = $ 1.125 million (perpetual).
Base –case NPV= -12.5 + 1.125 = -$1.067 million
.0984
Project is not worthwhile with all equity financing.

23. APV-PV (interest tax shield)
Condition I
 The project support with debt of $ 5 million
 6% borrowing rate rD =.06
 35 % tax rate ( Tc=.35)
Annual tax shield = .35 X.06 X 5 = .0105 or $ 105,000.
 Tax shields are constantly rebalanced with debt and with discount rate
r =9.84%
 PV ( interest tax shields, debt rebalanced) = $ 105, 000 = $ 1.067 million
.0984
APV = sum of base –case value and PV( interest tax shield)
APV = -1.067 million + 1.067 million = 0

24. APV-PV (interest tax shield)
Condition II
Suppose sangria plans to keep project debt fixed at $5 million
The risk of tax shield is the same of the risk o the debt and we discount at the rate of 6%
rate on debt.
PV( tax shields, debt fixed) = – 105,000 = $ 1.75 million.
.06
APV = -1.067 + 1.75 =$ .683 million
Now the project is more attractive with fixed debt , the interest tax shields are safe and
therefore worth more .( if perpetual crusher project fails , the $ 5 million of fixed debt
may end up as a burden on sangria’s other asset)

25. APV -Other financial side effects
 Suppose finance by issuing debt and equity
 $ 7.5 million equity with issue cost of 7% = $ 525.000
 $ 5 million of debt issue cost of 2% = $ 100,000
 Assume debt s fixed once is issued and tax shield worth $1.75 million
 APV = -1.067+ 1.75- 0.525 -0.100 = 0.58 million
Note : other financial side affects
Leasing ( plus) with base case NPV
subsidies loan from government ( plus)

26. APV for business
Rio corporation APV valuation
Latest year Forecast
0 1 2 3 4 5 6 7
10 Free cash flow (7+4-8-9) 2.5 3.5 3.2 3.4 5.9 6.1 6 6.8
PV Free cash flow, years 1-6 19.7
Pv Horizon value 64.6 horizon value 6 year 113.4
Base-case PV of company 84.3
Debt 51 50 49 48 47 46 45
3.06 3 2.94 2.88 2.82 2.76
1.07 1.05 1.03 1.01 0.99 0.97
PV Interest tax shields 5
APV 89.3
Tax rate, percent 35%
Opportunity cost of capital 9.84%
WACC (To discount horizon
value to year 6) 9%
Lomg term growth forecast 3%
Interest rate (years 1-6) 6%
After tax debt service 2.99 2.95 2.91 2.87 2.83 2.79

27. APV for business
Opportunity cost of capital= 9.84%
APV = base –case NPV + PV ( interest tax shields)
If the debt levels are taken as fixed and tax shield discounted by 6% borrowing rate
=$ 84.3 + 5.0 = $ 89.3 million.
There is an increase of $1.4 million from NPV , this increase is higher early debt levels.
 APV explore financial strategies with out looking the fixed debt ratio or having to calculate the
WACC for every scenario.
 APV useful when debt for a project is tied to book value or has to repaid on fixed schedule.
 Leverage buyouts( LBO) – generating cash by selling assets , shaving cost and improving profit
margins
 APV works fine for LBOs but for WACC can’t use the discount rate to evaluate an LBOs
because its debt ratio will not be constant.

28. APV for international investments
 Custom tailored project financing, special contracts with suppliers, customers and
governments.
 When debt ratio will not be constant , turn to APV
Example
1- In project ,if the competing supplier offers low interest rate project loans or lease of the
plant in their bids, then NPVs of this loans or lease should be included in project
analysis
2- A manufacture agrees a guarantee to provide in minimum price this value is also
addition to project APV –if the market price varies
3- if the government impose cost or restriction such as the investors should park their part
of incoming money in non interest bearing accounts e.g 2 years, then this period
calculate the cost of this requirement and subtract it from APV.

29. Thank you