CAPITAL BUDGETING EXTENSIONS
Equivalent Annual Costs /Benefits (Uniform Annual Equivalent)
Where mutually exclusive projects have unequal lives selecting a project on the basis of the
traditional NPV gives misleading results. This is where the equivalent annual cost benefit should
be used. This is calculated as follows.
Equivalent annual costs/benefit = PV of costs/benefits
Annuity factor
Annuity factor =
1−(1+𝑟)−𝑛
𝑟
Selection criterion
 Choose a project with the highest equivalent annual benefit
 Choose a project with the lowest equivalent annual cost
Question 1
Alpha Limited is considering two machines, A and B. Though designed differently, they serve
the same function. Machine A, a standard model costs $75 000 and lasts for 5 years. Its annual
operating costs will be $12 000. Machine B, an economy model, costs $50 000 but lasts for only
3 years. Its annual operating costs will be $20 000.
Required
How should Alpha choose between the two machines?
Question 2
The initial outlay of an internal transportation system of Great Zimbabwe University to service
its multi-campus system is estimated to be $1,500,000. The operating costs are expected to be
as follows:
Year
1
2
3
4
5
1
Operating costs
300,000
360,000
400,000
450,000
500,000
Compiled by T T Herbert (0773 038 651 / 0712 560 772)
The estimated salvage value at the end of five years is $300,000.
Required
Calculate the uniform annual equivalent (UAE) if the cost of capital is 13%
[5 marks]
Adjusted Present value (APV)
The APV method may be used when a business entity is considering an investment in a project
that will have different business risks and different financial risks from its current operations.
For example, a business entity might wish to evaluate an investment in a different industry or a
different market, and raise new capital to finance the investment.
A project is financially viable and should be undertaken if its adjusted present value (APV) is
positive. The APV of a project contains three elements, and is calculated as follows:
Adjusted NPV = Base case NPV minus PV of issue costs plus PV of tax shield
To calculate the NPV of a project, we must therefore calculate three amounts: the base case
NPV, the PV of other costs (issue costs) and the PV of tax relief on interest.
Base case NPV
The approach with the APV method is to calculate an NPV ignoring entirely the way in which
the project will be financed. The cost of capital should therefore be the cost of equity and this is
the discount rate. The base case NPV is therefore calculated assuming the project is financed
entirely by equity, so that the method of financing is ignored.
PV of other costs
Other costs are the costs arising a consequence of the project, but not directly related to the
project cash flows. Typically, these costs include the costs of raising new equity to finance the
project, or the costs of obtaining debt finance.
Present value of the tax shield (PV of the tax relief on interest costs)
When a new project is financed wholly or partly with new debt finance, there will be tax relief
on the interest. The PV of these tax benefits should be included in the APV of the project.
The PV of the tax relief on interest is calculated by:
 calculating the interest costs in each year
 calculating the savings in taxation arising as a consequence, for each year of the project
 discounting these savings in taxation to a present value, using the pre-tax (before-tax)
rate of interest on the debt as the discount rate.
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Compiled by T T Herbert (0773 038 651 / 0712 560 772)
Calculating interest payments
The amount of interest costs in each year will depend on the terms of repayment of the debt
capital.
 If the debt finance is repaid in full at the end of the term of the borrowing, the interest
cost is calculated simply as:
Amount borrowed × Interest rate on the loan or the bonds
 If the loan is an amortising loan, and the debt is repaid gradually over the term of the loan,
you will need to work out:
 the annual payment on the loan, principal repayment + interest, and
 separate this total annual payment into the principal repayment and the interest payment.
This separation of interest charges and the loan principal repayment is necessary because the
tax relief applies to the interest payments only and not to the repayment of the loan principal.
Question 3
Grey Ltd is evaluating an expansion project that is expected to cost $5 000 000 and generate an
annual after tax cash flow of $1 000 000 for the next 5 years. The corporate tax rate is 25%.
Grey Ltd has a target debt to equity ratio of 1:1. Its cost of capital is 12% and it’s before tax cost
of debt is 10%. The floatation cost of equity is 8% whilst the floatation cost of debt is 3%.
Required:
Determine the NPV of the expansion project
Question 4
Olivine Limited is considering a project requiring $5 000 000 of investment. It is expected to
generate a net cash flow of $1 000 000 per year for 8 years. The opportunity cost of capital is
15% - this reflects the return required by equity investors from the project. The cost of issuing
equity is 5%. The project enables the firm to raise $2,4 million of debt finance. The debt finance
will carry 14% interest and will be repaid in equal annual instalments over the eight year period
– the first instalment will be paid at the end of the first year. The tax rate applicable to the firm
is 60%.
(i.) What is the base case NPV?
(ii) What is the adjusted net present value?
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Compiled by T T Herbert (0773 038 651 / 0712 560 772)
Question 5
Windmill Fertilizers Ltd is considering a capital project requiring an outlay of $15 million. It is
expected to generate a net cash inflow of $3,75 million for 6 years.
The opportunity cost of capital is 18%. Windmill Fertilizers can raise a term loan of $10 million
for the project. The term loan will carry an interest rate of 16% and would be repayable in 5
equal instalments, the first instalment falling due at the end of the second year. The balance
amount required for the project can be raised by issuing equity. The issue cost is expected to be
8%. The tax rate for the company is 50%.
Required
(i.) What is the base case NPV?
(ii) What is the adjusted net present value?
[10 marks]
Question 6
Pro Electronics is evaluating an expansion project that is expected to cost $60 million and
generate an annual after-tax cash flow of $12 million for the next 10 years. The tax rate for the
company is 35%.
Pro Electronics has a target debt-equity ratio of 1:1. Its cost of capital is 15% whereas its pre-tax
cost of debt is 12%. The floatation cost of equity is 10% whereas the floatation cost of debt is
4%.
Required
What is the NPV of the expansion project?
Reasons for using the APV method
The APV method might be used in preference to adjusting the weighted average cost of capital
(WACC) of the company using the Modigliani-Miller formulas. This is for several reasons.
 The APV method does not rely on assumptions about the new WACC of the firm if the
project is undertaken.
 The APV method allows for the specific tax relief on the borrowing to finance the project,
and does not assume that the debt will be perpetual debt.
 The APV method allows for other costs, such as the costs of raising new finance (issue
costs)
It might be argued that APV is therefore the best method of estimating the effect of a new
investment on the value of the business entity, and the wealth of its
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Compiled by T T Herbert (0773 038 651 / 0712 560 772)