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ACCA P4
Advanced Financial Management (AFM)
高级财务管理
ACCA Lecturer: Lily Wang
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1
3
Introduction
The adjusted present value(APV) technique
P4 Chapter 4 Content
2
4
The risk adjusted WACC
Analysis of Comprehensive Example
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Chapter Summary
Beta revisited
• Asset beta-relfects pure systematic business risk
• Equity beta-reflects business and gearing risk
• Betas can be geard and ungeard:
Investment Appraisal
Adjusted present value model
Two-part approach:
• Find base NPV
• PV of project flows using asset
beta in the CAPM
• Find PV of financing
• PV of issue costs on equity
• PV of issue costs on debt
• PV of tax relief
Problems with the risk-adjusted WACC
• Can't cope if gearing ratio changed by
project
• Over-values tax shield where debt
not pernament
• Ignore costs of raising finance
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1.Introduction
Alternatives to the use of existing WACC as a discount rate in
project appraisal
We have now established that the existing WACC should only be
used as a discount rate for a new investment project if the
business risk and the capital structure (financial risk) are likely to
stay constant. Alternatively,
If the business riskof the new project differs from the entity's
existing business risk
A risk adjusted WACC can be calculated, by recalculating the cost
of equity to reflect the business risk of the new project. (Degearing
and regearing beta factors)
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1.Introduction
If the capital structure (financial risk) is expected to change when the new
project is undertaken
The simplest way of incorporating a change in capital structure is to
recalculate the WACC using the new capital structure weightings.
This is appropriate when the chanage in capital structure is not significant,
or if the new investment project can be effectively treated as a new
business, with its own long term gearing level.
If the capital structure is expected to change significantly ,the APV method
of project appraisal should be used. This method separates the investment
element of the decision from the financing element and appraises them
independently. APV is generally recommended when there are complex
funding arrangements.
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2.The risk adjusted WACC
Basic principle
If the business risk of the new project is different from the business risk of a
company's existing operations, the company's shareholders will expect a
different return to compensate them for this new level risk. Thus, the
discount rate for project's cf is not existIng WACC, but a risk adjusted
WACC which incorporates this new required return to the shareholders
Calculating a risk-adjusted WACC
Find the appropriate equity beta from a suitable quoted company.
Adjust the available equity beta to convert it to an asset beta-degearit.
Readjust the asset beta to reflect the project gearing levels-regear the beta
Use this beta in the CAPM equation to find Ke
Use this Ke to find the WACC
Evaluate the project
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2.The risk adjusted WACC
Example
B plc is a hot air balloon manufacturer whose equity:debt ratio is 5:2
The company is considering a waterbed-manufacturing project.B plc will finance
the project to maintain its exisitng capital structure.
S plc is a waterbed-manufacturing company. I t has an equity beta of 1.59 and
a Ve:Vd ratio of 2:1
The yield on Bplc's debt, which is assumed to be risk frr, is 11%. B plc's equity
beta is 1.10. The average return on the stock market is 16% Thecorporation tax
rate is 30%
Required:
Calculate a suitable cost of capital to apply to the project.
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2.The risk adjusted WACC
Answer
Degear the equity beta of the company in the nwe industry and find the busines
s risk asset beta of the new project/industry.
=1.59x(2/(2+1(1-0.3)))
=1.18
Calculate the equity beta of the nwe project, by regearing:
incorporate the financial risk of our company using our gearing ratio(5:2)
1.18= e X [5/(5+2(1-0.3))]
1.18=0.78 e
=1.51
Ke=22%+1.51(16%-11%)=18.55% Kd=11%(1-0.3)=7.7%
WACC=18.55%X5/7+7.70X2/7=15.45%
)1( TVV
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eequityasset
)1( TVV
V
de
eequityasset
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2.The risk adjusted WACC
Using the risk-adjusted WACC
TWO other issues also need to be considered:
The method used to gear and degear betas is based on the assum
ption that debt is perpetual. This overvalues the tax shield where d
ebt is finite.
Issue costs on equity are ignored
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3.The adjusted present value(APV) technique
Basic principle
The APV method evalueates the project and the impact of financin
g separately. Hence, it can be used if a new project has a different
financial risk (debt-equity ratio) from the company
APV consists of two different elements:
APV = Base case NPV + Financing impact
(3) Value (1)Value of an all (2)Present value of
of a geared equity financed financing side effects
project project
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3.The adjusted present value(APV) technique
The investment element (Base case NPV)
The projct is evaluated as though it were being undertaken by an
all equity company with all financing side effects ignored. The fina
ncial risk is quantified later in the second part of the APV analysis.
Therefore:
• ignore the financial risk in the investment decision process
• use a beta that reflects ust the business risk, i.e.β
Find the project β
Calculate the base case discount rate=Keu
by putting the βasset in the CAPM formula
Calculate the base case NPV
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3.The adjusted present value(APV) technique
The financing impact
Financing cashflows consist of :
issue cost
tax reliefs
As all financing cash flows are low risk they are discounted
at either:
the Kd or
the risk free rate
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3.The adjusted present value(APV) technique
APV exam tricks
Grossing up
A firm will know how much finance is required for the investment.
Issue costs of finance will usually be quoted on top. It will therefore
be necessary to gross up the funds to be raised.
• e.g. the finance required for a planned investment is 2m (net of
issue costs), Issue costs are 3%. And the finance raised will
also have to cover the issue costs. What are the issue costs
and what sum will need to be raised altogther?
• 2m is 97% of the amount to be raised:
• therefore,2m/0.97=2,061,856 will be needed.
• Issue costs are 3% 3%x2061856=61,856
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3.The adjusted present value(APV) technique
APV exam tricks
PV of debt issue costs
Method:
issue costs at T0 (X)
tax relief at the CT rate(issue costs x CT rate) X
PV of the tax relief(RTQ for timing of tax flows) X
PV of the issue costs X
(issue costs-PV of tax relief)
Equity issue costs
Not tax deductible Are tax deductible-
RTQ for timing of tax flows
Equity issue costs
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3.The adjusted present value(APV) technique
APV exam tricks
PV of the tax relief on interest payment
The PV of the tax relief on interest payments is also known as the
PV of the tax shield .
The method adopted depends on the information given:
Simple scenario: Debentures- interest paid at a fixed amount
each year
Annual tax relief= total loan x interest rate x tax rate (X)
Annuity factor for n years X
Year one discount factor(if tax is delayed one year) X
PV of the tax shield X
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3.The adjusted present value(APV) technique
APV exam tricks
Calculation of APV( in detail)
The base case NPV is used as a starting point. The costs and benefits
of the financing are then added to find a final adjusted present value.
Base case NPV x
PV of the issue costs
Equity (x)
Debt (x)
PV of the tax shield x
Adjusted Present Value x
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3.The adjusted present value(APV) technique
Example
Rounding plc is a company currently engaged in the manufacture of
baby equipment. It wishes to diversify into the manufacture of snowboards
The investment details
The company's equity beta is 1.27 and is current debt to equity ratio is
25:75,, however the company's gearing ratio will change as a result of the
new project.
Firms involved in snowboard manufacture have an average equity
beta of 1.19 and an average debt to equity ratio of 30:70
Assume that the debt is risk frr, that the risk free rate is 10% and that
the expected return from the market porfolio is 16%
The new projct will invove the purchase of new machinery for a cost of
800,000(net of issue cost), which will produce annual cash inflows of
450,000 for 3years. At the end of this time it will have no scrap value.
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3.The adjusted present value(APV) technique
Example
Corporation tax is payable in the same year at rate of 33%. The
machine will attract writing down allowances of 25% pa on a reducing
balance basis, with a balancing allowance ata the end of the project life
when the machine is scrapped.
The financing details:
The new investment will be financed as follows:
Debentues(redeemble in three years time ) 40%
Rights issue of equity 60%
The issue costs are 4% on the gross equity issued and 2% on the
gross debt issud , Assume that the debt issue costs are tax deductible.
Calculate the APV
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3.The adjusted present value(APV) technique
Answer
The investment element
Firstly,COMPUTE the asset beta of the project. This is achieved by de
gearing the equity beta from the snow board indutry average.
βa=1.19 x (70/(70+30(1-0.33)))
βa=0.92
The next task is to determine base case discount rate for the project.
E(Rf)=Rf + (E(Rm)-Rf) βa
=10%+(16%-10%)0.92
=15.52%(round to 16%)
)1( TVV
V
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eequityasset
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3.The adjusted present value(APV) technique
Answer
(1) Base case NPV calculation($000)
Time 0 1 2 3
Receipts 450 450 450
Corporation tax (149) (149) (149)
@33%
Tax relief on capital allowance(W1) 66 50 149
Initial outlay ( 800)
Net cash flow (800) 367 351 450
Discount rate@16% 1 0.862 0.743 0.641
Present value (800) 316 261 288
Base case NPV 65
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3.The adjusted present value(APV) technique
Answer
(W1)Capital allowances computation W1
W.D.A Tax relief@33% Timing
Investment 800
Y1 WDA (200) 66 T1
600
Y1 WDA (150) 50 T2
450
Y1 WDA 0
Balancing allowance 450 149 T3
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3.The adjusted present value(APV) technique
Answer
(2) The financing impact
lay out the financing package.
Equity- 60%x 800,000 480,000 issue cost 4%
Debt - 40% x 800,000 320,000 issue cost 2%
A. PV of issue cost on equity
Equity issue cost 480,000x4/96=(20,000)
B. PV of issue cost on debt
Debt issue cost: 320,000x 2/98=(6,531)
Tax relief@33% 2,155
PV of the issue cost on debt 4,376
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3.The adjusted present value(APV) technique
Answer
(2) The financing impact
C. PV of Tax shield
Total amount raised by loan- don't forget to add the issue
costs=320,000+6,531=326,531
Annual tax relief=326,531 x 0.10 x 0.33=10,776
AFfor 3 yrs 2.487
PV of the tax shield 26,800
(3) The APV calculation
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3.The adjusted present value(APV) technique
Answer
(3) The APV calculation
Base case NPV 65,000
PV of the issue costs
Equity (20,000)
Debt (4,376)
PV of the tax shield: 26,800
APV 67,424
Financially viable.
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3.The adjusted present value(APV) technique
Additional Factors regarding the APV method
Additional factors-subsidised/cheap loans
If the loan is cheap ,the interest cost is lower. However, the benefit is
reduced since the tax shield will also be lower:
PV of the cheap loan (opportunity benefit):
PV of the interest saved x
Less: PV of the tax relief lost (x)
PV of the cheap loan x
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3.The adjusted present value(APV) technique
Additional Factors regarding the APV method
Additional factors-subsidised/cheap loans
Example: A plc requires 1million in debt finance for 5years
It has borrowed 700,000 in the form of 10% debentures redeemablein
5years and the remainder under a government subsidised loan scheme
at6%. The tax rate is 30%. Assume that tax is delayed one year.
Calculate the PV of the tax shields and the PV of the cheap loan.
(a) PV of the tax shields
Although the cheap loan has a cost of 6% it has the same risk as a
normal loan ,therefore the appropriate discount rate is 10%pa
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3.The adjusted present value(APV) technique
Additional Factors regarding the APV method
Additional factors-subsidised/cheap loans
Answers: (a) PV of the tax shields
Although the cheap loan has a cost of 6% it has the same risk as a
normal loan ,therefore the appropriate discount rate is 10%pa
Normal loan Cheap loan
Annual tax relief=total loan x
interest rate x tax rate
700,000 x 0.1x 0.3 21,000
300,000 x 0.6x 0.3 54,000
Annual factor for 5 yrs@10% 3.791 3.791
Discount factor for 1 yr@10% 0.909 0.909
PV of the tax shield 72,366 18,609
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3.The adjusted present value(APV) technique
Additional Factors regarding the APV method
Additional factors-subsidised/cheap loans
Answers: (b) PV of the cheap loan
Interest saved tax relief lost
Annual amount
300,000 x (0.1-0.06) = 12,000
12,000 x 0.3= 3,600
Annual factor for 5 yrs@10% 3.791 3.791
Discount factor for 1 yr@10% 0.909
PV of the tax shield 45,492 (12,406)
0 1 2 3 4 5 6 Annuity PV of the interest saved x x x x x Deferred PV of the tax relief lost . . (x)(x)(x)(x)(x) annuity
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3.The adjusted present value(APV) technique
Additional Factors regarding the APV method
Additional factors-subsidised/cheap loans
The APV calculation is therefore amended as follows:
Base case NPV X/(X)
PV of the issue costs
Equity (X)
Debt (X)
PV of the tax shield:
Normal loan X
Cheap loan X
PV of the cheap loan:
Interest saved X
tax relief lost (X)
APV X/(X)
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3.The adjusted present value(APV) technique
Advantages and disadvantages of APV
Advantages Disadvantages
• Step-by-step approach gives Based on M&M with-tax theory.
clear understanding of the Ignores:
element of the decision * bankruptcy risk
* tax exhaustion
* agency costs
• Can evaluate any type of Based on M&M with-taxt theory
financing package Assumes:
* debt is risk free and irredeema
ble
• More straightforward than
adjusting the WACC which can
be complex
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Analysis of Example
Burung Co (6/14)
You have recently commenced working for Burung Co and are reviewing a
four-year project which the company is considering for investment. The
project is in a business activity which is very different from Burung Co's
current line of business.
The following net present value estimate has been made for the project:
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Analysis of Example
Net present value is negative $1.65 million, and therefore the
recommendation is that the project should not be accepted.
In calculating the net present value of the project, the following notes were
made:
(i) Since the real cost of capital is used to discount cash flows, neither the
sales revenue nor the direct project costs have been inflated. It is estimated
that the inflation rate applicable to sales revenue is 8% per year and to the
direct project costs is 4% per year.
(ii) The project will require an initial investment of $38 million. Of this, $16
million relates to plant and machinery, which is expected to be sold for $4
million when the project ceases, after taking any taxation and inflation
impact into account.
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Analysis of Example
(iii) Tax allowable depreciation is available on the plant and machinery at
50% in the first year, followed by 25% per year thereafter on a reducing
balance basis. A balancing adjustment is available in the year the plant and
machinery is sold. Burung Co pays 20% tax on its annual taxable profits. No
tax allowable depreciation is available on the remaining investment assets
and they will have a nil value at the end of the project.
(iv) Burung Co uses either a nominal cost of capital of 11% or a real cost of
capital of 7% to discount all projects, given that the rate of inflation has been
stable at 4% for a number of years.
(v) Interest is based on Burung Co's normal borrowing rate of 150 basis
points over the 10-year government yield rate.
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Analysis of Example
(vi) At the beginning of each year, Burung Co will need to provide working capital
of 20% of the anticipated sales revenue for the year. Any remaining working
capital will be released at the end of the project.
(vii) Working capital and depreciation have not been taken into account in the
net present value calculation above, since depreciation is not a cash flow and all
the working capital is returned at the end of the project.
It is anticipated that the project will be financed entirely by debt, 60% of which
will be obtained from a subsidised loan scheme run by the Government, which
lends money at a rate of 100 basis points below the 10-year government debt
yield rate of 2.5%. Issue costs related to raising the finance are 2% of the gross
finance required. The remaining 40% will be funded from Burung Co's normal
borrowing sources. It can be assumed that the debt capacity available to Burung
Co is equal to the actual amount of debt finance raised for the project.
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Analysis of Example
Burung Co has identified a company, Lintu Co, which operates in the same
line of business as that of the project it is considering. Lintu Co is financed
by 40 million shares trading at $3.20 each and $34 million debt trading at
$94 per $100. Lintu Co's equity beta is estimated at 1.5. The current yield on
government treasury bills is 2% and it is estimated that the market risk
premium is 8%. Lintu Co pays tax at an annual rate of 20%.
Both Burung Co and Lintu Co pay tax in the same year as when profits are
earned.
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Analysis of Example
Required
(a) Calculate the adjusted present value (APV) for the project, correcting
any errors made in the net present value estimate above, and conclude
whether the project should be accepted or not. Show all relevant
calculations. (15 marks)
(b) Comment on the corrections made to the original net present value
estimate and explain the APV approach taken in part (a), including any
assumptions made. (10 marks)
(Total = 25 marks)
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Solution of Example
Answers:
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Solution of Example
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Solution of Example
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Solution of Example
(b) Corrections made to the original net present value
(1) Cash flows are inflated and the nominal rate based on Lintu Co's
all-equity financed rate is used (see below). Where different cash flows
are subject to different rates of inflation, applying a real rate to non-
inflated amounts would not give an accurate answer because the effect of
inflation on profit margins is being ignored.
(2) Interest is not normally included in the net present value
calculations. Instead, it is normally imputed within the cost of capital or
discount rate. In this case, it is included in the financing side effects.
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Solution of Example
(b) Corrections made to the original net present value
(3) The approach taken to exclude depreciation from the net present
value computation is correct, but capital allowances need to be taken away
from profit estimates before tax is calculated, reducing the profits on which
tax is payable.
(4) The impact of the working capital requirement is included in the
estimate as, although all the working capital is recovered at the end of the
project, the flows of working capital are subject to different discount rates
when their present values are calculated
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Solution of Example
(b) Approach taken (relates to errors 5 & 6)
The value of the project is initially assessed considering only the
business risk involved in undertaking the project. The discount rate used is
based on Lintu Co's asset beta which measures only the business risk of
that company. Since Lintu Co is in the same line of business as the project,
it is deemed appropriate to use its discount rate, instead of 11% that
Burung Co uses normally.
The impact of debt financing and the subsidy benefit are then
considered. In this way, Burung Co can assess the value created from its
investment activity and then the additional value created from the manner
in which the project is financed.
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Solution of Example
(b) Assumptions made
It is assumed that all figures used are accurate and any estimates
made are reasonable. Burung Co may want to consider undertaking a
sensitivity analysis to assess this.
It is assumed that the initial working capital required will form part of the
funds borrowed but that the subsequent working capital requirements will
be available from the funds generated by the project. The validity of this
assumption needs to be assessed since the working capital requirements
at the start of years 2 and 3 are substantial.
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Solution of Example
(b) Assumptions made
It is assumed that Lintu Co's asset beta and all-equity financed
discount rate represent the business risk of the project. The validity of this
assumption also needs to be assessed. For example, Lintu Co's entire
business may not be similar to the project, and it may undertake other lines
of business. In this case, the asset beta would need to be adjusted so that
just the project's business risk is considered.
It is also assumed that there are no adverse side-effects of taking on
the extra debt eg a worsening credit rating which could impact Burung's
trading position.
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