ñòð. 20 |

for, say, 80% of the cost of the land to be pretty low risk as long as it had the additional security of a

mortgage on the land.

52 The five financial building blocks

The revised model is given below.37

CALCULATIONS

Times (measured in years from today)

Plot purchase 0.00

D&A 1.00

Build 2.50

Sell 3.00

Discount factors

Plot purchase 1.000

D&A 0.926

Build 0.825

Sell 0.794

Debt repayment factor 1.158

Equity cash flows

Plot purchase (net) âˆ’290,000

D&A âˆ’100,000

Build âˆ’850,000

Sell 1,657,155

Present value cash flows

Plot puchase âˆ’290,000

D&A âˆ’92,593

Build âˆ’701,228

Sell 1,315,503

NPV of build project 231,682

With no debt the project generated a total amount of cash of $600,000 and after

we allow for the time value of money, the NPV was $137,676. So we can see that the

NPV appears to have risen by almost $100,000 as a result of including finance.

Is the project a better one? The answer appears to be â€˜yesâ€™ but we cannot answer

this question properly without thinking about risk. At present the numbers have

been calculated without changing the CoC. The equity cash flows have been dis-

counted at the same 8% rate as was used in the original calculation. Is the situation

for the investor equally risky after borrowing is included?

With no debt, the project returns the original cash that was invested as long as

the selling price for the house is at least $2,400,000.38 After debt is included this

cash break-even selling price rises to $2,582,845. There must therefore be a greater

Note that I checked the model gave the original answer when I set the assumed percentage of borrow-

37

ing to zero. A check such as this should always be carried out when models are adjusted.

The original project involved a total cash outlay of $2,400,000 and was expected to return $3,000,000.

38

After we include borrowing and its associated interest cost, the initial cash outlay to purchase the

53 Building block 2: Financial markets

chance of an investor not even getting his or her money back if the project is partly

financed via debt than if there is no debt. By contrast, if the selling price rises above

the assumed $3,000,000 the relative returns per dollar invested are much greater

after borrowing is included.

Hence we must conclude that the two situations are not equally risky. Perhaps,

therefore, the change in NPV is simply down to our having ignored this change in

risk when we assess the two ways of looking at the project.39

What this example has done is provide a practical illustration of the reason

why debt is called gearing or leverage. This is because debt serves to magnify

risk exactly as a lever or a set of gears can magnify a force. When things go

well, debt magnifies a positive return. When things go badly, debt makes the

residual equity return even worse.

The clear conclusion must be that it would be wrong to apply the same cost

of equity to the two situations, one with debt and one without. The scenario

with debt must justify a higher cost of equity than the one without. The ques-

tion, though, is how much higher? In order to do this we need to introduce

another piece of theory.

The Modigliani Miller proposition

I introduced the idea that values can be added up in the Uncle Norman

example in part 3 of the first building block. We can now see a perhaps

unanticipated spin-off from this and also meet two more famous names in

the history of corporate finance. This time the names are Modigliani and

Miller or MM for short. They started with the principle that you can slice up

the value of a project however you like but should always come back to the

same overall value provided, as one might put it, the process of slicing does

not in itself consume value.

I think of this as being like a law of conservation of value. MM realised that

this conservation of value should work for liabilities as well as assets. The liabil-

ities of a company concern how it is financed. The so-called MM proposition 1

postulates that the value of a company is independent of how it is financed.40 It

is hugely important for how we carry out economic evaluations.

land falls to just $290,000 but the total outlay after one includes the need to repay the loan and the

interest charge rises to $2,582,845.

Risk has been ignored because the same discount rate is being used and discount rates should be a

39

function of risk.

This is provided there are no tax implications and that the financing choices do not result in changes

40

in the companyâ€™s other investment decisions.

54 The five financial building blocks

If value is independent of how an activity is financed then the $100,000

increase in NPV that we described in the Grand Design project above can-

not be right. All that we had done to the project was introduce some debt.

We know that the debt must have made the residual equity cash flows risk-

ier. So now we have a means of quantifying what the impact on the cost of

equity must have been. According to MMâ€™s proposition 1, the cost of equity

must have changed by exactly the extent necessary to ensure that value is

conserved. We can use our spreadsheet model and the goal-seek function

to discover that if a discount rate of 13.4% is applied to the equity cash flows

with all other assumptions as above then the NPV becomes $137,676 and

value is maintained.

So we have an answer to our question. In this particular situation where

the appropriate CoC to apply to pre-finance cash flows was 8%, the act of bor-

rowing 80% of the cost of the land means that the appropriate discount rate

to apply to equity cash flows is 13.4%. Now since the only way of calculating

the figure of 13.4% was first to do the analysis pre finance, surely there is an

obvious lesson here? Surely we should simply evaluate all investments in a

way that ignores how they are financed.

The consequence of MMâ€™s proposition 1 is a huge simplification in how we

carry out our financial analysis. We do not need to bother with identifying

the cost of equity and the cost of debt separately. These change every time

the level of borrowing changes. We can use the CoC which should remain

unchanged. What is it that sets the CoC? It is the riskiness of the underlying

cash flows before any financing effects.

The indivisible finance pool

There is another way of thinking about how financing decisions impact on

the CoC that I find quite intuitive. This way is to consider the concept of an

indivisible finance pool. Company finance can be thought of as coming from

a single source, the indivisible finance pool. This is topped up from time to

time with debt and equity but once the money is in this pool, it is not pos-

sible to distinguish between a dollar that originated as debt and a dollar that

originated as equity.

If a company were to allow one project to benefit because it happened to

need money at exactly the same time as it borrowed money it would be unfair

ñòð. 20 |