• Choice between mutually exclusive projects of unequal life
• Optimal timing decision
• Determination of economic life
• Interrelationship between investment and financing aspects
• Inflation and capital budgeting
• International capital budgeting
• Investment in capabilities
3. Choice between Mutually Exclusive Projects
of Unequal Life
For a proper comparison of the two alternatives, that have different lives,
we have to convert the present value of costs into a uniform annual
equivalent (UAE) figure – this is also called an equivalent annual cost
(EAC) figure. The UAE is a function of the present value of cost, the life
of the asset, and the discount rate. The UAE is simply:
5. Optimal Timing
In real life, an investment is rarely a “now or never” proposition.
Typically, it can be undertaken now or at some point of time in future.
Given this option, the issue of optimal timing assumes significance.
Under conditions of certainty, the optimal timing may be
determined by using the following procedure.
1. Examine alternative dates (t) when the investment can be made.
2. Estimate the net future value as of each alternative date and
convert the same to its current value.
3. Choose the timing that has the highest current value
6. Determination of Economic Life
The economic life of an asset is conceptually defined as the period
after which the asset should be replaced to minimise the sum of
operating and maintenance costs and capital costs expressed on an
annual basis. Put differently, it is the replacement cycle that
minimises the uniform annual equivalent total cost, UAE (TC) of
operating and owning the asset. The UAE (TC) is simply the sum of
the uniform annual equivalent operating and maintenance cost, UAE
(OM), and the uniform annual equivalent capital cost, UAE (CC).
UAE (TC) = UAE (OM) + UAE (CC) (13.1)
8. Interrelationship between the Investment and
• WACC is the right discount rate for a project that is a carbon copy
of the firm’s existing business.
• A project may have financing effects that differ from those of the
existing investments of the firm. It may have a different debt
capacity or be entitled to certain subsidies or have some special
financial features. In such cases the recommended method is to
calculate the adjusted NPV (or APV for short).
9. Adjusted Present Value (APV)
APV is calculated by first estimating the base-case NPV and then
adjusting it to reflect the financing side effects of the project.
The base-case NPV is the NPV of the project under the following
• The project is financed entirely by equity.
• There is no financing side effect like issue cost or subsidy
The present value of financing side effects is equal to:
• Present value of positive financing side effects like tax shield on
debt and availability of subsidies.
• Present value of negative financing side effects like issue costs and
financial distress costs associated with excessive leverage.
Investment : Rs. 5 million
Net cash inflow : Rs.1 million per year for 8
Opportunity cost of capital : 15 percent
Issue cost of equity : 5 percent
Debt available : Rs.2.4 million at 14 percent
Repayment of debt : 8 equal annual instalments.
First instalment will be paid at
the end of first year
Tax rate : 40 percent
Base – case NPV:
-5,000,000 + = -512,700
The base-case NPV has to be adjusted for two factors: (i) issue cost, and
(ii) tax-shield associated with debt.
Out of the total financing requirement of the project Rs.2,600,000
will come from the equity sources and Rs.2,400,000 will come in
the form of debt finance. As the net equity finance required by the
project is Rs.2,600,000 and the issue costs would absorb 5 per cent
of the gross proceeds of the issue, the firm will have to issue
Rs.2,736,842 (Rs.2,600,000 / 0.95) of equity stock in order to
realise a net amount of Rs.2,600,000. The difference of Rs.136,842
is the cost of underwriting, brokerage, printing, and other issue
related expenses. The APV after adjustment for issue cost is :
APV = Base-case NPV – Issue cost
= -Rs.512,700 – Rs.136,842
Now we consider the adjustment for the tax shield associated with debt
finance. The present value of tax shield associated with Rs.2,400,000 of
debt finance is calculated. From this we find that the debt finance
associated with the project brings a stream of tax shields which has a
present value of Rs.403,385. If we make adjustment for this also, we get
APV = Base case NPV – Issue cost + Present
value of tax shield
= -Rs.512,700 – Rs.136,842 + Rs.403,385
14. Year Debt outstanding Interest Tax shield Present value of
at the beginning tax shield
(at 14% discount rate)
1 2,400,000 336,000 134,400 117,869
2 2,100,000 294,000 117,600 90,552
3 1,800,000 252,000 100,800 68,040
4 1,500,000 210,000 84,000 49,728
5 1,200,000 168,000 67,200 34,877
6 900,000 126,000 50,400 22,982
7 600,000 84,000 33,600 13,440
8 300,000 42,000 16,800 5,897
Calculation of the Present Value of Tax Shield
15. The principle underlying APV is to divide and conquer. APV does not
reflect the side effects of financing in a single calculation. Instead, it
captures them in a series of calculations. This makes it more
illuminating. You not only know what the APV is but also where it is
coming from. This is helpful in reformulating the project.
Merits of APV
APV makes more sense for projects that have a capital structure
that is different from the rest of the firm or which have a capital structure
that changes significantly over time or which enjoy special concessions,
incentives, and subsidies. For example, APV is eminently suitable for
leveraged buyouts(LBOs) or infrastructure projects.
16. Adjusted Cost of Capital
rD (1- Tc) + rE (13.4)
Though conceptually sound, APV is not very popular because (i) it
requires some sophistication to assess the financing side effects, and (ii)
it involves a series of adjustments which may be cumbersome.
That is why WACC, which is the cost of capital adjusted for
financing effects, is more commonly used in practice. Recall that WACC
17. There are some other formulae also of adjusted cost of capital.
Two of them are :
Modigliani and Miller formula : r* = r (1-TL) (13.5)
Miles and Ezzell formula : r* = r – L rD T (13.6)
where r* = adjusted cost of capital
r = opportunity cost of capital assuming 100 per cent
T = tax rate applicable to the firm
L = marginal contribution of the project to the firm’s
rD = cost of debt
Adjusted Cost of Capital
18. Adjusted Cost of Capital
Example 1 A firm is considering a project for setting up a captive power
plant for which the following information has been gathered.
Investment outlay : Rs. 50 million
Annual post-tax savings : Rs. 5 million
Life of the project : Perpetual
Debt capacity of the project : Rs. 25 million
Interest rate of debt : 10 percent
Nature of debt : Perpetual
Tax rate of the firm : 40 percent
Opportunity cost of capital : 12 percent
The adjusted cost of capital as per Modigliani-Miller formula is :
r* = r (1-TL) = 0.12 (1- 0.4 x 0.5 ) = 0.096 or 9.6%
The adjusted cost of capital as per Miles and Ezzell formula is :
r* = r – L rD T = 0.12 –0.5 x 0.10 x 0.4 x = 0.100 or 10.0%
1+ rD 1.10
19. Inflation and Capital Budgeting
Inflation has been a persistent feature of the Indian economy. Hence, it
should be properly considered in capital investment appraisal. Since the
cost of capital, the discount rate, is typically expressed in nominal terms,
all the cash flows should also be expressed in nominal terms. This means
that (a) projected revenues and costs must reflect the inflation rates
expected in future and (b) salvage values, too, must be expressed in
future nominal amounts.
20. International Capital Budgeting
There are two equivalent ways of calculating the NPV of a foreign
Home Currency Approach
• Convert all the foreign currency cash flows into rupees (use fore-
casted exchange rates)
• Calculate the NPV in rupees ( use the rupee discount rate)
Foreign Currency Approach
• Calculate the NPV in foreign currency (use the foreign currency
• Convert the foreign currency NPV into rupees (use the spot ex-
21. Investment in Capabilities
Empirical evidence suggests that companies that perform well have
organisational capabilities that enable them to exploit opportunities.
What are these organisational capabilities? As Baldwin and Clark say: “
Organisational capabilities are combinations of human skills,
organisational procedures and routines, physical assets, and the systems
of information and incentives that improve performance along particular
dimensions. Such capabilities are indeed organisational assets.”
Baldwin and Clark mention five specific capabilities:
External Integration Capability The ability of the firm to link its
understanding of customers with engineering design to develop improved
Internal Integration Capability Internal integration makes a company faster
and more efficient in performing various functions like new product
development, prototyping, facilities engineering, and capacity expansion
Flexibility The ability of a firm to do a variety of things and to respond
quickly to changes.
Capacity to Experiment The capacity to experiment depends on the
investments a firm makes in developing knowledge, disseminating
knowledge, and adopting the same in practice
Capacity to Cannibalise Cannibalisation involves introducing a new
product that cuts into the sales of the existing products.
23. Characteristics of Capabilities – Building
Investments required to build capabilities have certain special
characteristics. These are:
Many of the outlays required are on things like common language
and communication, human training and skill development, and
support services. These are not ordinarily regarded as capital
expenditure in many firms.
Investments required to build a capability range widely in scale
While costs of building capabilities are visible and appear on
someone’s budget, the benefits are derived by the company as a
whole and occur only after a time lag.
24. Allocating Resources to Build Capabilities
The challenge for a company lies in developing a capital allocation
system that accommodates investment in capabilities without sacrificing
the benefits of a formal financial analysis. Towards this end, the
following actions are required.
• Identify the capabilities that the firm should develop and ensure that
there is a firm organisational commitment to them.
• Develop a capital budget for capabilities and a proper system of
authorisation and accounting for expenditures relating to
• Translate the desired capabilities into appropriate goals and rewards
that are clearly understood and used by people throughout the
• Link compensation of managers to improvements in speed, quality,
and flexibility, which are the outcomes of capabilities.
For a proper comparison of two mutually exclusive alternatives, that have
different lives, we have to convert the present value of costs into a uniform
annual equivalent (UAE) figure.
The UAE is simply:
PV (Cost)/PVIFA r,n
In real life, an investment can typically be undertaken now or at some point of
time in future. The timing that has the highest current value represents the
The economic life of an asset is conceptually defined as the period after which
the asset should be replaced to minimise the sum of operating and
maintenance costs and capital costs expressed on an annual basis.
Strictly speaking, WACC is the right discount rate for a project that is a carbon
copy of the firm’s existing business.
A project may have financing effects that differ from those of the existing
investments of the firm. It may have different debt capacity or be entitled to
certain subsidies or have some special financial features. In such cases the
recommended method is to calculate the adjusted NPV (or APV for short).
26. APV is calculated by first estimating the base-case NPV and then adjusting it
to reflect the financing impact of the project.
APV = Base-case NPV + Present value of the financing side effects of the
The base-case NPV is the NPV of the project under the following assumptions
: (a) The project is financed entirely by equity. (b) There is no financing effect
like issue cost or subsidy.
The present value of financing side effects is equal to : Present value of
positive financing side effects like tax subsidies – Present value of negative
financing side effects like issue costs.
Though conceptually sound, APV is not very popular because (i) it requires
some sophistication to assess the financing side effects, and (ii) it involves a
series of adjustments which may be cumbersome. That is why WACC, which
is the cost of capital adjusted for financing effects, is more commonly used in
WACC is equal to :
rD (1- Tc) + rE
27. There are some other formulae also for calculating the adjusted cost of capital.
Two of them are:
Modigliani and Miller formula : r* = r (1-TL)
Miles and Ezzell formula : r* = r – L rD T
The adjustment for inflation should be done properly in practice.
There are two ways of evaluating an international capital budgeting proposal:
the home currency approach and the foreign currency approach. Correctly
applied both the approaches yield the same result.
Empirical evidence suggest that companies that perform well have
organisational capabilities that enable them to exploit opportunities.