Welcome to Specific Investment Decisions!

In our previous chapters, we looked at Investment Appraisal basics—deciding if a project is worth doing using NPV and IRR. But life isn't always that simple! Sometimes we know a project is good, but we have to decide how to pay for it, or we have a limited budget and can't do everything.

In this chapter, we will master three specific "real-world" scenarios: Lease vs. Buy, Asset Replacement, and Capital Rationing. Don't worry if these sound intimidating; we'll break them down step-by-step!

1. Lease vs. Buy Decisions

Imagine you need a new delivery van for your business. You know the van will help you make money, but should you buy it (using a bank loan) or lease it (rent it) from a provider? This is a financing decision.

How to approach the calculation

To decide, we compare the Present Value (PV) of the costs of each option. The one with the lowest cost wins!

Option 1: Buying
If we buy the asset, we have several cash flows to consider:
1. Initial Outlay: The purchase price of the asset (shown as a Year 0 outflow).
2. Tax-Allowable Depreciation (Capital Allowances): Because we own the asset, the taxman gives us a "discount" on our tax bill. This is a cash inflow (tax saved).
3. Scrap Value: What we sell the asset for at the end (inflow).
4. Operating Costs: Only include these if they differ between leasing and buying (usually they are the same, so we ignore them).

Option 2: Leasing
If we lease, we don't own the asset, so the flows are simpler:
1. Lease Payments: Usually an annual outflow.
2. Tax Relief on Payments: Lease payments are a business expense, so they reduce our tax bill. This is a cash inflow (tax saved).

Crucial Point: The Discount Rate

This is where many students trip up! In Lease vs. Buy, we always use the after-tax cost of debt as our discount rate. This is because the decision to lease is effectively a decision to borrow money.
Formula: \( \text{Discount Rate} = \text{Pre-tax Borrowing Rate} \times (1 - \text{Tax Rate}) \)

Example: If the bank charges 10% interest and tax is 30%, your discount rate is \( 10\% \times (1 - 0.30) = 7\% \).

Quick Review: Lease vs. Buy
  • Goal: Find the cheapest way to finance an asset.
  • Key Flows: Capital allowances (Buy) vs. Lease payments (Lease).
  • Discount Rate: After-tax cost of debt.

2. Asset Replacement Decisions

How often should a taxi company replace its cars? Every year? Every 3 years? If they replace them every year, the cars are reliable but expensive to buy. If they wait 5 years, the cars are cheap to keep, but repair costs go through the roof!

The Equivalent Annual Cost (EAC) Method

We use the EAC to compare assets with different lifespans. It tells us the "average annual cost" of owning an asset.

Step-by-Step Process:
1. Calculate the NPV of costs for one replacement cycle (e.g., for a 2-year cycle and a 3-year cycle).
2. Divide that NPV by the Annuity Factor for the number of years in the cycle.
3. The formula is: \( \text{EAC} = \frac{\text{PV of Costs}}{\text{Annuity Factor}} \)
4. Choose the cycle with the lowest EAC.

Analogy: Imagine buying a cheap pair of shoes for \$20 that lasts 1 year, vs. a quality pair for \$50 that lasts 4 years. The EAC helps you see that the \$50 pair is actually "cheaper" per year of use!

Key Takeaway

Ignore the "income" the asset generates if it's the same regardless of when you replace it. Focus only on the costs (purchase price, maintenance, and scrap value).

3. Capital Rationing

In a perfect world, a company would do every project with a positive NPV. In the real world, companies often have a limited budget. This is called Capital Rationing.

Hard vs. Soft Rationing

Soft Rationing: Internal limits set by management (e.g., "We don't want to borrow more this year to keep our debt ratios low").
Hard Rationing: External limits (e.g., "The bank refuses to lend us any more money").

Single Period Rationing: Divisible Projects

If we can do "half a project" (like building half a housing estate), we use the Profitability Index (PI) to rank them. This ensures we get the "most bang for our buck."

Formula: \( \text{PI} = \frac{\text{NPV}}{\text{Initial Investment}} \)
(Sometimes shown as \( \text{PV of Cash Inflows} / \text{Investment} \). Both work, but NPV/Investment is more common in FM exams.)

The Process:
1. Calculate the PI for each project.
2. Rank projects from highest PI to lowest.
3. Allocate your budget down the list until the money runs out.

Single Period Rationing: Indivisible Projects

If you can't do a partial project (you can't build half a bridge!), the PI method doesn't always work. Instead, you must use trial and error to find the combination of projects that fits within the budget and gives the highest total NPV.

Common Mistake to Avoid!

Don't rank projects by their absolute NPV. A project might have a high NPV but cost a huge amount of money, "eating up" the whole budget and preventing you from doing three smaller projects that combined would have a higher NPV.

Summary & Memory Aids

Lease vs Buy: Think "Cheapest Financing." Use after-tax cost of debt.
Asset Replacement: Think "Average Yearly Cost." Use the EAC formula.
Capital Rationing: Think "Best Value for Money." Use PI for divisible projects.

Did you know? Capital rationing is very common in start-ups where founders have great ideas but very little cash in the bank!

Don't worry if this seems tricky at first! The math follows a very logical pattern. Once you practice a few "Lease vs Buy" tables and "EAC" calculations, you'll start to see the patterns. You've got this!