Managerial economics guide 9

PAYBACK PERIOD

Definition: Number of periods required to recover your initial investment so the time needed to

breakeven

Suppose you have minus 100as the initial outlay, table

This is direct, not discounted payback. IF we modify the outlays slightly,

t outlay End inflows

0 -100

1 50 -50

2 10 -40

3 50 10

4 100 40

= 2 +

50

If you discount, you might not have your beginning cost.

You won’t have to discounts the initial outlays of -100 cause every other outlay are counted backward

to reach that. But you will have to discount the consequent periods in order to calculate the final

inflows of each period. If the -100 is at the end of the project (period 5) then we will have to discount

that too. You will discount the 5 periods then you will did the same analysis.

Advantages of this techniques:

Easy to apply

Why does PBP important?

Gives you an idea about the BEP, so eventually it gives us an idea about the liquidity of the project

(how long will our fund be locked in the project), what you have later on is the extra that you can use

liberally.

Drawback:

If you don’t discount, then your calculation is not valid.

The cash flows after the payback are ignored which make a major disadvantage.

You will never base your decision on the PBP, you want to get an idea for value creation or value

destruction

CONFLICTS

To understand the conflict, we need to understand another concept which is:

= ()

NPV profile is a function giving NPV as a function of k. You change k and use a continuum of k, then a

continuum of NPV, plotting using these two continuum you will get NPV profile

Corresponding to each k you will get a value of NPV.

NPV NPV profile K* k

You will get a decreasing line with an intercept.

The intercept is when the interest rate is 0, so not discounted sum of inflows and outflows, this is a

rough measure of the dimensions of the project. The amount at risk both in term of costs and in

term of value so the net sum of the project.

The intercept with the x axis is the IRR

The slope measures the sensitivity of the NPV to the discount rate k,

Where do you think you will get a steeper/flatter NPV? Steeper means your NPV is more sensitive to

the discount rate, when do u get this? When you get more inflows later. Your discount rate increase

with time which make big impact to your NPV

The different in slope signal the difference in time schedule of the project

So looking at this you will get

IRR

Net dimension of the project

The time schedule of the project (when will you get your inflows)

Looking at this, we immediately think of possible conflicts in ranking project base on NPV and IRR

Suppose there are 2 projects

NPV NPV profile k

K K *

K *

c B

A

If you want to rank this in term of preference

∗ ∗

<

Using IRR, B is preferred to A

But using NPV, this might not be so clear but depends on what kind of k you use

> ℎ ≻

< ℎ >

:

If the projects are comparable in size then you’re probably going to find a cross over rate

For the two projects cross, they cant be parallel so they have to have different slope or different

time schedule.

Also for the two projects to cross, we also have to look at their size: If the projects are too different

in size, then there might not be a cross over rate.

You get this cross over rate as a threshold rate. If the discount rate is large enough, in some sense,

you won’t have much different between NPV and IRR ranking, otherwise we might have some

conflict

Normally, if you have to choose one of the 2 projects with this ranking conflict you usually use the

NPV methodology which represent the value creation rule which is preferable on the Balance Sheet.

But you would prefer to express adjustment on basis of concordance between these two indexes.

You have to look at more than 1 indicator in order to evaluate a project and therefore you are more

confident when these indicators give the same result

FUNDING

There are 2 sources of funding: debt and equity

When we are talking about the component cost of debt, we are thinking about what we owe

creditor, which depends on market condition and firm and taxation condition. This also depends on

the debt ratio: debt/asset

Market condition (supply of funds to firm ratio)

Firm condition using the above ratio (total debt/total asset)- if this equal to 0, then all asset are

funded by equity, if it equal to 1 then all are funded by debt. The extent of this ratio gives creditor an

idea recovering their principal and getting interest, this is related to risk so creditor wants to include

in the rate of return which they receive from the firm a component of risk premium, which contains

the risk of bankruptcy or the risk of not receiving the payment on time.

Normally there is a schedule of the cost of loans which depends on the debt ratio, this is stable at

the beginning but then will increase when the debt ratio starts to move toward 1

You rarely get a debt ratio greater than 1 which is a dangerous situation Debt ratio

Interest expense is deductible from income, which means that if you pay enough taxes, you can

recover some of them using payment over debt or your interest expense

For cash flows and capital budgeting, you have to express your interest payment only after taxes

t: tax rate (1

= ∗ − )

Then your interest rate on debt

If you have market rate of 10% and tax rate of 40%

Here you have = 0.1(1 − 0.4) = 0.06

The component cost of overall cost to funding project is 6% if you have enough taxes to recover your

expense

This doesn’t apply for equity; equity expenses aren’t deductible

The component cost for equity will not be adjusted in tax rate and depends on the capital

components = +

⏟

⏟

This is obviously depends on the attitude toward risk and the market then you can identify the

proper return for the equity holder

To assess this, you can use the implementation of CAPM

st

1 we have to understand the type of risk we can try running a regression

= + +

0

You look at this model in which return f your asset is a linear function to the market return with slop

beta, this measure the contribution of aggregate risk to the total return

)

( = + −

( )

The covariance of the cash flow of the project and that of the market, you can apply this to Rm: all

the inflows and outflows connected to the investment in your firm compare to the total return of

the market or the making comparison between the investment’s return and the firm overall return,

The CAPM is a one factor model, then you might come up with models of multiple factor

Simple rule of thumb like adding some decimal to the long-term investment rate. Long term debt

requires certain compensation which is compensation mixed from time value and risk premium,

when you take that you already have the risk factor, but adding 5% to your long-term bond.

You can use a different model which is the constant growth model

= +

So you are assuming that everything important to the flows is growing at a constant rate (price,

dividend, earnings). This also means that prices of the stocks will grow at the same rate. Therefore

you have

1

= +

Dividend at time 1

Stock price at time 0

g is the constant growth rate

the immediate dividend yield is forecastable while it is more difficult to calculate the constant

growth rate. The risk here is the estimation of g.

when we have the 2 components of cost of funding and investment project we can come up with a

measure of weighted average cost of capital

= ℎ

This can possibly depend on the debt ratio. You would like to fix your debt ratio to have min wacc.

By minimizing wacc, we can find the optimal capital structure of a firm

If the ratio is concave, you want to minimize your wacc

wacc

kd Debt ratio

K*

Suppose that you have this situation, so debt ratio, here we plot

Ke start from a point, move stable then increase because you want to get compensated more for

holding the equity

Kd start stable then increase because the leverage is increasing

Wacc has the same intercept as ke, but then as your leverage increase, your wacc goes down then

after k* it goes up again, remember tax also plays a big role. If you fund your investment by debt,

you will get tax saving and the wacc goes up again

Investment opportunity schedule (IOS) that is simply a graph represent the amount of fund needed

to run a project and their profitability. You run that from the most profitable to the least profitable

Example from text book

Return rate A B C WACC

D E IRR

Invest (fund needed

to run project)

3 4 8 11

IOS

The optimal capital budget is the funding level required to underwrite a value-maximizing level of

new investment. The investment opportunity schedule (IOS) shows the pattern of returns for all of

the firm’s potential investment projects. Figure 17.3(a) shows an IOS for a hypothetical firm. The

horizontal axis measures the dollar amount of investment commitments made during a given year.

The vertical axis shows both the rate of return earned on each project and the percentage cost of

capital. Each box denotes a given project. Project A, for example, calls for an outlay of $3 million and

promises a 17 percent rate of return, project B requires an outlay of $1 million and promises a 16

percent yield, and so on. The last investment, project E, simply involves buying 9 percent

government bonds.

By displaying this stepwise pattern of potential returns on a single graph, the firm’s IOS is depicted.

Figure 17.3(b) generalizes the IOS concept to show a smooth pattern of potential returns.

The curve labelled IRR shows the internal rate of return potential for each project in the portfolio of

investment projects available to the firm. It is important to remember that these projects are

arrayed from left to right in terms of declining attractiveness as measured by the IRR criterion.

Therefore, project A is more attractive than project E, and the IRR schedule is downward

sloping from left to right. Although the IOS provides important input in