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so can be ignored in the calculation of incremental NPV. The success bonus, however, is

an incremental cost and does need to be allowed for. It is an immediate expense and so

the discount factor for it will be 1.0. The final twist concerns tax relief on this expense. We

know that the company is a new startup and so it will not be paying tax. This means that

the tax relief on the bonus will not be available until the project itself is paying tax. An

inspection of the tax line in the project spreadsheet shows a charge of $1.3m in the first

year of operation. We also know that tax is paid in the year after it is charged. Since the

$1.3m is more than the tax relief of $4m (the tax rate is 30%), the full benefit of tax relief

will be felt in the second year of operation. The resultant project value calculation is as

follows:

Depot NPV Calculation

Sanction Build Yr 1 Build Yr 2 Year 1 Year 2 Year 3

Success Fee âˆ’4.0

Fee tax relief 1.2

Project Flows 0.0 âˆ’10.0 âˆ’6.0 0.0 4.2 4.8

591 Building block 4: Planning and control

Table (cont.)

Sanction Build Yr 1 Build Yr 2 Year 1 Year 2 Year 3

Terminal Value 42.4

Total Flows âˆ’4.0 âˆ’10.0 âˆ’6.0 0.0 5.4 47.3

Discount Factor 1.000 0.867 0.788 0.716 0.651 0.592

PV Flows âˆ’4.0 âˆ’8.7 âˆ’4.7 0.0 3.5 28.0

Cumulative PV âˆ’4.0 âˆ’12.7 âˆ’17.4 âˆ’17.4 âˆ’13.9 14.1

NPV â€“ $m 14.1

So the project shows a healthy NPV of about $14m which is quite high relative to the

combined capital and bonus cost of $20m. Note that the fact that we were only asked to

calculate NPV has simplified our task a lot. Had we been asked to compute the full set of

economic indicators we would have needed to prepare a full year-by-year analysis of the

project.

There is a further potential twist in the calculation in relation to tax. We now know

that the company will be incurring substantial overhead costs before this project even

starts. These overhead costs should mean that it will not have to pay any tax for several

years. Strictly speaking the incremental analysis of the first project should allow for this.

It would serve to increase the NPV but I have not included this effect in my suggested

answer because of the complexity involved in modelling it correctly. Tax calculations

can become horribly complex and one quite often has to simplify in order to avoid exces-

sive work in getting the tax â€˜exactlyâ€™ right because the accuracy is usually spurious.

We turn now to the plan. Things will not look as good when viewed in this way.

Each year the company will incur rental, overhead and bonus costs totalling $14m. In

its second year of operation it will start the capital spend on its first project. Its first

income will not occur until its fourth year of operation. During this year it will also

incur the year 1 and year 2 building costs and also the full $14m of corporate costs.

The company will not gain any effective tax relief for these costs until well after its fifth

year of operation.

The plan is put together using the sum of projects approach but after adjusting for the

full corporate overheads and their impact on tax and the tax element of accounts payable.

I have assumed that the additional projects which are started each year have exactly the

same cash flows as the original project. I did not include any adjustments to allow for

inflation. The numbers are as follows:

Depot Company LTP

Year 1 Year 2 Year 3 Year 4 Year 5

Sales Revenue 0.0 0.0 0.0 25.0 51.8

Variable Costs 0.0 0.0 0.0 âˆ’10.0 âˆ’20.7

Contribution 0.0 0.0 0.0 15.0 31.1

Fixed Costs âˆ’14.0 âˆ’14.0 âˆ’14.0 âˆ’24.0 âˆ’34.2

Amortisation 0.0 0.0 0.0 âˆ’0.6 âˆ’1.3

Pre-Tax Profit âˆ’14.0 âˆ’14.0 âˆ’14.0 âˆ’9.6 âˆ’4.4

592 Individual work assignments: Suggested answers

Table (cont.)

Year 1 Year 2 Year 3 Year 4 Year 5

Tax 0.0 0.0 0.0 0.0 0.0

Profit âˆ’14.0 âˆ’14.0 âˆ’14.0 âˆ’9.6 âˆ’6.0

Balance Sheets

Fixed Assets 0.0 10.0 26.0 41.4 56.1

Accounts Receivable 0.0 0.0 0.0 3.1 6.4

Inventories 0.0 0.0 0.0 2.5 5.2

Account Payable 0.0 0.0 0.0 âˆ’0.5 âˆ’2.4

Working Capital 0.0 0.0 0.0 5.0 9.1

Capital Employed 0.0 10.0 26.0 46.4 65.2

ROACE

Funds Flow

Profit âˆ’14.0 âˆ’14.0 âˆ’14.0 âˆ’9.6 âˆ’6.0

Amortisation 0.0 0.0 0.0 0.6 1.3

Working Capital 0.0 0.0 0.0 âˆ’5.0 âˆ’4.1

Capital Investment 0.0 âˆ’10.0 âˆ’16.0 âˆ’16.0 âˆ’16.0

Funds Flow âˆ’14.0 âˆ’24.0 âˆ’30.0 âˆ’30.0 âˆ’24.8

We see a picture of a companyâ€™s reporting losses every year (this is why I did not bother

to compute ROACE) and with a very significant funding requirement in every year.

If the projects are going to perform as indicated by the assumptions then financial the-

ory suggests that the markets would fund the company. The projects all have NPVs of

$14m or more and this annual NPV is more than enough to justify the $10m of pre-tax

overheads which are incurred as part of the overall business. It is, however, what would

be called â€˜a big askâ€™. In reality a company with no track record would find it hard to con-

vince the market that its plans were viable if it was still projecting losses after five years

of operation.

In my view, the companyâ€™s problem is that it is trying to grow too fast. If it were to delay

its growth plans until the first project was operating profitably it would find it easier to

convince the markets of its viability.

This exercise should have served to illustrate how important it is to look at the LTP as

well as the project value calculations.

Finally, what might this company be worth if the market believed its plans? It is expected

to produce a steady stream of positive NPV projects. Each project has an NPV of $14m.

The present value of this is $140m if one assumes the stream will continue for ever and the

first project will be approved in one yearâ€™s time.

This analysis has excluded the office rental and overheads of $10m pa. If these never get

any tax relief their present value will be the present value of a mid-year cash flow stream

of minus $10pa which is minus $105m1. The business will eventually get the benefit of tax

relief on these costs and so their value impact will not be as bad as $105m. If tax relief was

If the costs were all incurred at the end of each year their present value would be $100m. In fact they

1

are all incurred half a year earlier and so their value impact is increased by half a yearâ€™s worth of the

time value of money.

593 Building block 4: Planning and control

immediate, the impact would be to reduce the value hit by 30%. Without a full model one

cannot calculate the exact impact. We were only asked for an estimate of value. So I will

use a tax relief factor of about 25% which suggests a value reduction owing to overheads

and rental of about $80m and hence a net after-tax value of the business of about $60m.

We will return to how the market might actually value this company later in this book.

At this stage we simply need to be able to calculate a value based on a given set of assump-

tions. In this case the value of the business before it has spent any money at all would be

$60m as long as the market believes the financial projections.

APPendix

V

Building block 5: Risk

1. What would be the fair market price for the right to play a dice rolling game where the pay-

out is the square of the number shown?

There are six possible outcomes. These are 1, 4, 9, 16, 25 and 36. The average of these is

91 Ã· 6 = 15.167. This would be the fair market price if we ignore any transaction costs.

2. A game is played that involves rolling two dice. Competitors pay $1 to play. They are paid

$5 if the combined score is seven but nothing if the score is any other amount. What is the

expected value of playing the game once?

There are 36 different ways that the two dice can come up. Six of these will add to seven.

So the player will win one sixth of the time. So if you pay $1 and have an expected payout

of one sixth of $5 the expected loss is one sixth of a dollar.

3. A casino allows players to play the game from question 2. The casino has annual overheads

of $1m and local gambling regulations limit its opening hours to just 12 hours per week while

the fire regulations limit the number of gamblers in the building to 500. What would be the

minimum number of games per hour that each gambler must play if the casino is just to

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