Week 6-Capital Investment Appraisal

Capital Budgeting (definition)

The process of planning significant long-term outlays on projects such as purchasing new equipment or introducing new products.

Screening Decision (capital budgeting)

A decision about whether a proposed project meets a preset minimum standard of acceptance (e.g. minimum required rate of return).

Preference Decision (capital budgeting)

Selecting from among several competing projects that have already passed the screening stage.

Typical capital budgeting decisions (5 types)

Plant expansion, equipment selection, lease or buy, equipment replacement, and cost reduction projects.

Time Value of Money — core principle

A pound received today is worth more than a pound received in the future, because money received now can be invested to earn a return.

Present Value (definition)

The value today of a future cash flow, discounted at the appropriate rate of return.

Present Value of a single sum — formula

PV = Future Value × PV factor (from tables), where PV factor = 1 ÷ (1 + r)^n. E.g. £100 in 2 years at 12% → £100 × 0.797 = £79.70.

Annuity (definition)

A series of identical cash flows occurring at the end of each period for a set number of periods.

Present Value of an Annuity — how to calculate

Multiply the annual cash flow by the annuity PV factor from the annuity table for the relevant periods and discount rate. E.g. £60,000 × 3.605 (5 years, 12%) = £216,300.

Net Present Value (NPV) — definition

The difference between the present value of cash inflows and the present value of cash outflows for a project.

NPV — three steps to calculate

1. Calculate PV of all cash inflows; 2. Calculate PV of all cash outflows (initial investment + future costs); 3. NPV = PV inflows − PV outflows.

NPV decision rule

If NPV ≥ 0 → accept the project (it meets or exceeds the required rate of return). If NPV < 0 → reject the project.

NPV = 0 — what does it mean?

The project earns exactly the required rate of return (discount rate). It is on the borderline of acceptability.

Why is depreciation excluded from NPV analysis?

Depreciation is not a cash flow. Discounted cash flow methods automatically provide for the return of the original investment through the cash flows themselves.

Discount Rate — what to use

Typically the firm's cost of capital: the average rate of return the company must pay to its long-term creditors and shareholders for the use of their funds.

Internal Rate of Return (IRR) — definition

The discount rate at which the NPV of a project equals exactly zero. It is the interest yield promised by the project over its useful life.

IRR — how to calculate (annuity case)

PV factor = Investment required ÷ Net annual cash inflow. Find this factor in the annuity PV table for the correct number of periods — the column heading gives the IRR.

Decker Company IRR example

PV factor = £104,320 ÷ £20,000 = 5.216. Looking across the 10-period row → 14%. The IRR is 14%.

IRR decision rule

If IRR ≥ required rate of return → accept. If IRR < required rate of return → reject.

IRR (non-annuity) — how to estimate

Use trial and error with two discount rates close to NPV = 0, then apply linear interpolation to approximate the IRR.

NPV vs IRR — key advantage of NPV

NPV is easier to use and assumes reinvestment of cash inflows at the discount rate, which is more realistic than IRR's implicit assumption of reinvestment at the IRR.

Total-Cost Approach (comparing projects)

Calculate the full NPV of ALL cash flows for each alternative separately. Choose the alternative with the higher (or least negative) NPV.

Incremental-Cost Approach (comparing projects)

Consider ONLY the cash flows that DIFFER between the two alternatives. Gives the same answer as the total-cost approach but is more concise.

White Co. total-cost approach — result

New washer NPV = £83,202; Remodel NPV = £56,405. Difference = £26,797 in favour of new washer. Both have positive NPV but new washer is preferred.

Least-Cost Decision

When revenues are the same (or not directly involved), choose the alternative with the LOWEST total present value of costs. No need to compare NPV of revenues.

Home Furniture — least-cost decision

Compare the PV of total costs of overhauling the old truck vs buying a new truck. Choose whichever has the lower present value of total costs.

Profitability Index (PI) — purpose

Used to rank competing investment projects when capital is limited. Higher PI = more desirable. PI = NPV ÷ Investment required (or PV of inflows ÷ PV of outflows).

Payback Period — definition

The length of time required for a project to recover its initial investment from the net cash inflows it generates.

Payback Period — formula (equal annual flows)

Payback Period = Investment Required ÷ Net Annual Cash Inflow.

Daily Grind payback example

£140,000 ÷ £35,000 = 4.0 years. Acceptable because it is less than the 5-year maximum required.

Payback Period — two key shortcomings

1. Ignores the time value of money; 2. Ignores all cash flows that occur AFTER the payback period (ignores total profitability).

Simple Rate of Return (SRR) — definition

An accounting-based measure of return. Does NOT use cash flows — uses accounting (accrual) income instead.

Simple Rate of Return — formula

SRR = (Incremental revenues − Incremental expenses including depreciation) ÷ Initial investment.

Daily Grind SRR example

(£100,000 − £65,000) ÷ £140,000 = £35,000 ÷ £140,000 = 25%.

Simple Rate of Return — main weakness

Ignores the time value of money. Not recommended as a primary appraisal method.

Summary: four capital budgeting methods

1. NPV (preferred — accounts for time value, uses cash flows); 2. IRR (discount rate where NPV = 0); 3. Payback Period (quick screen — ignores time value and post-payback flows); 4. Simple Rate of Return (accounting income based — ignores time value).