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Capital Budgeting

Net Present Value – computing the difference between the present value of the net cash flows from an investment and the initial investment outlay. Accept project if NPV>0, reject if NPV <0

- Recommended for investment evaluation.

- Consistent with maximization of shareholders wealth.

Incremental cash flows – cash flows earned by the firm if the project is undertaken minus cash flow earned by the firm if the project is not undertaken.

Internal rate of return is the rate of return that is earned by the project over its economic life. Accept project if r > k, reject if r < k. - Multiple IRRs and undefined IRRs.

Independent projects - can be evaluated on their own (invest in all positive NPV projects) - The decision to accept a project does not affect the decision to accept or reject other projects.

- Assumes there are enough funds for all potential independent projects being considered.

Mutually Exclusive projects – the acceptance of one project rules out the acceptance of other (competing projects). (invest in the highest NPV project).

- Assuming the projects being considered are worth undertaking (are positive NPV projects).

Accounting rate of return- the average earnings generated by the project after deducting depreciation and taxes, expressed as a percentage of the investment outlay.

- Acceptable if its ARR exceeds a pre-specified minimum rate of return.

- Earnings are not net cash flows.

- Time value of money ignored.

- Tends to favour projects with shorter lives. (A smaller N would increase the numerator).

Payback Period – The time it takes for the initial cash outlays on a project to be recovered from the net cash flows. Acceptable if its payback period is less than a pre-specified maximum payback period.

- Fails to account for the cash flows that occur after the payback period cutoff date.

- Biased against projects that have longer development periods.

- Ignores the time value of money.

Issues in Cash Flow Estimation 1) Timing of cash flows

- exact timing of project cash flows can affect the valuation of a project)

- simplifying assumption used is that the net cash flows are received at the end of period.

2) Financing charges

- Cash outflows relating to how the project is to be financed are not included in the analysis.

- Value of the project is independent of how it will be financed.

- Financing costs are not used in the cash flow because that results in their being double counted.

3) Incremental Cash Flows

- Only cash flows that change if the project is accepted are relevant in evaluating a project.

4) Sunk Costs

- These costs are not included as they have been incurred in the past and will not be affected by the project’s acceptance or rejection.

5) Allocated Costs (overhead costs allocated by management to firm’s divisions)

- Do not vary with the decision and are usually ignored.

6) Taxes and tax effects

- Taxes need to be included where they have an effect on the net cash flows generated by a project (Corporate income tax (tc.

7) Depreciation tax savings/ depreciation tax shield

- Depreciation is excluded from the net cash flows but it affects net cash flows as it decreases the taxes payable due to the depreciation tax shield.

8) Disposal or salvage value of assets

Book value = Acquisition cost – Accumulated depreciation Gain (or loss) = Disposal Value – Book Value

Taxes payable of gain = 𝑡_𝑐 × gain on sale Tax saving on loss = 𝑡_𝑐 × loss on sale

American option – can be exercised at any time up to and including the expiration due.

European option – can be exercised only at expiration.

- American options are more common for individual stocks, while European options are more common for indices.

An option gives the holder the right to buy or sell the underlying asset at, or before, a specified expiration date, at a pre-specified exercise (or strike) price.

To the buyer/ holder the contract is an option and not an obligation (unlike forward/future) - A call option gives the right to purchase the underlying security.

- A put option gives the right to sell the underlying security.

To the option writer (or seller) the contract is an obligation.

- The writer of a call option has the obligation to sell the underlying security.

- The writer of a put option has the obligation to purchase the underlying security.

𝐼𝑓 𝑆_𝑇− 𝑋 > 0, 𝑡ℎ𝑒𝑛 𝑀𝑎𝑥(𝑆_𝑇− 𝑋, 0) = 𝑆_𝑇− 𝑋.

𝐼𝑓 𝑆_𝑇− 𝑋 ≤ 0, 𝑡ℎ𝑒𝑛 𝑀𝑎𝑥(𝑆_𝑇− 𝑋, 0) = 0 The payoff from a call option cannot be negative.

All-the-money option: Current spot price 𝑺_𝒕= Exercise Price (X)

In-the-money option: If profitable to exercise at the spot price (For a call option this is when Current spot price 𝑆_𝑡 > Exercise Price (X)).

Out-of-the-money option: If unprofitable to exercise at the spot price. (For a call option this is when Current spot price 𝑆_𝑡 < Exercise Price (X)).

The breakeven price is where the profit to the buyer is zero. (For a call option this is when Exercise Price (X) + Option premium (or price, C)).

𝐼𝑓 𝑆_𝑇− 𝑋 > 0, 𝑡ℎ𝑒𝑛 𝑀𝑎𝑥(𝑆_𝑇− 𝑋, 0) = 𝑆_𝑇− 𝑋.

𝐼𝑓 𝑆_𝑇− 𝑋 ≤ 0, 𝑡ℎ𝑒𝑛 𝑀𝑎𝑥(𝑆_𝑇− 𝑋, 0) = 0 The payoff from a put option cannot be negative.

All-the-money option: Current spot price 𝑺_𝒕= Exercise Price (X)

In-the-money option: If profitable to exercise at the spot price (For a call option this is when Current spot price 𝑆_𝑡 < Exercise Price (X)).

Out-of-the-money option: If unprofitable to exercise at the spot price. (For a call option this is when Current spot price 𝑆_𝑡 > Exercise Price (X)).