SBS _MBA FM_Discussion on Time Value of Money Spring 16

8/19/2019 SBS _MBA FM_Discussion on Time Value of Money Spring 16

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Discussion

on

Time Value of Money (How to determine the value of resources)

Agenda:

-

Plotting different types of CFs,-

Calculation of PV (value) and NPV (Measure of Value Maximization)

-

Investment decision (selection of appropriate project)

The objective of financial management is to maximization VALUE of the firm.

Then the important question is, what do we mean by VALUE and maximized value?

Investors put their resources in a firm with expectation to get more than they put. This

excess return from their investment is termed as value maximization.

Now, the next question is: Or how can we define or determine the VALUE and value

maximization of the firm?

In fact, this is one of the most important questions of finance. Because: (a) investors invest

(their cash outflows) in one time and get cash inflows from the investment in future, means

time variance of cash inflows and outflows (b) investors sacrifice the benefits of the best

alternative opportunity (opportunity cost) to invest in the firm.

Finance has imported the theory of Time Value of Money from Mathematics to incorporate

these two factors in determining value of the resources invested in a firm.

As time of cash flows is very crucial, we can classify the value of resources into two

categories i.e., PRESESNT VALUE (PV) and FUTURE VALUE (FV). Then question is, which

value we would like to maximize as par finance? It is……….PRESENT VALUE.

Present value of future cash flow can be calculated by discounting technique i.e.,

PV=FV/(1+DR)^n, here DR=discount rate or rate of opportunity cost or cost of capital, and

n=time period

Let’s look at, how can we calculate the PRESENT VALUE of different cash flow streams as follows:



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Type 1: Single cash flow streamSuppose you want to purchase a flat in Dhanmondi for tk. 15,000, and expect to sale it tk. 28,000

after 5 years. If the opportunity cost (discount rate) is 9%, what is the present value of the expected

cash inflow?

now/time of taking

decisionTime line 0 1 2 3 4 5

CF stream -15000 0 0 0 0 28000

28000/(1+0.09)^5

PV (value of your

investment) 18198.08

Here, PV of your expected Cash inflow is higher than your cash outflow (investment) which is definitely

favorable to you, but question is how excess value it will create is. To know that we can calculate NPV as:

Net Present value (NPV)=PV of future cash inflow-Investment

NPV 18198.08-15000 =3198.08

Here, we get positive NPV because PV of future cash inflow is higher than investment,

means your investment is able to maximize the value of your resources by tk. 3198. So itwill be wise for you to purchase the flat by which you will be able to maximize the value of

your resources.

So, according to finance, the objective of a firm is to maximize the value of firm’s resources.

Above example tells us that:

VALUE (tk. 18198.08) means PV of future cash inflows of any project

VALUE maximization level (tk. 3198.08) means excess value of investment

Now let’s look at the above example further that you need tk.21, 500 to buy the flat, in thatcase, NPV = -3302, which indicates that your value tk. 18198.08 is lower than your

investment by 3302 means value of resources is minimized rather than maximizing.

SHOULD YOU BUY THE FLAT in this case? Definitely NOT. Because, you want to maximize

the value of your resources rather than minimize.

How many important points we have learned from the above example?

(a) To calculate value of future cash flow i.e. VALUE of any investment

(b)

Two important inputs are required to calculate VALUE i.e., cash flow stream and

discount rate(c)

Value maximization measures i.e., NPV (Positive NPV means value is maximized,

Negative NPV means value is minimized)

(d) First function of finance i.e. INVESTMENT DECISION (where should the firm invest?)

based on NPV, if select project with positive NPV, reject project with Negative NPV

as firm’s objective is maximizing the value of firm.



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Now let’s look at, if your investment produces multiple cash flows based on the

sample example:

Type 2: Multiple cash flow stream

Suppose you want to purchase a flat in Dhanmondi for tk. 15,000, and expect to get rent tk.

4000 in first year, tk. 5000 in second year, tk. 5500 in the third, fourth and fifth year and

sale it tk. 28,000 after 5 years. If the opportunity cost (discount rate) is 9%, plot the cash

flow in the time line, calculate the value and value maximization measure.

Time

line 0 1 2 3 4

CF

stream -15000 4000 5000 5500 5500 28000+5500=335

** 4000/(1+.09)^1 5000/(1+.09)^2 5500/(1+.09)^3 5500/(1+.09)^4 33500/(1+0.09)^

PV (sum

of **

column) 37794.17

NPV 37794.17-15000=22794.17

Type 3: Multiple equal cash flow stream (Annuity cash flow)


7000 in each year for next 5 years. If the opportunity cost (discount rate) is 9%, plot the

cash flow in the time line, calculate the value and value maximization measure i.e., NPV, and

make your investment decision based NPV.

Timeline 0 1 2 3 4 5

CF

stream -15000 7000 7000 7000 7000 7000

Please look at this CF stream carefully. What is the difference between this one and prior CF stream? Both are

multiple CF stream but in this cash your cash inflows are equal in every period, and this type of CF stream is called

ANNUITY cash flow stream. Next question, can we calculate the PV of this with the same way? Why not? As we know

CF and DR, there is no problem to get PV like prior two steams. Therefore PV of the steam as follows:

7000/(1+.09)^1 7000/(1+.09)^2 7000/(1+.09)^3 7000/(1+.09)^4 7000/(1+0.09)^5

PV 27227.56

NPV 27227.56-15000=12227.56

However, we can calculate the PV of annuity CF stream with alternative way by using PVtable as well. In this case

PV=ACF x PVIFA 9%, 5years

Here our Annuity CF (ACF) is tk. 7000 (equal CF in every period), PV Interest Factor

Annuity (PVIFA) for 9% and 5 years is 3.890 (this value is available from Financial table

which is attached in your email as well)



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Therefore, PV = 7000 x 3.890=27230 which almost we calculated the value earlier.

Type 4: Perpetual Cash flow stream


2500 in each year for the unforeseeable future. If the opportunity cost (discount rate) is

9%, plot the cash flow in the time line, calculate the value and value maximization measure

i.e., NPV, and make your investment decision based NPV.

Time

line 0 1 2 3 4 ∞

CF

stream -15000 2500 2500 2500 …. …..

Here, equal CF for each year but for infinitive time. This type of CF steam is called PERPETUAL cash

flow stream, PV of Perpetual CF stream = Perpetual CF/DR

PV 2500/.09 = 27777.78

NPV 12777.78

Type 5: Growing Perpetual Cash flow streamSuppose you want to purchase a flat in Dhanmondi for tk. 15,000, and expect to get rent tk.

2500 in first year which will be growing at 4% in every year for the unforeseeable future. If

the opportunity cost (discount rate) is 9%, plot the cash flow in the time line, calculate the

value and value maximization measure i.e., NPV, and make your investment decision based

NPV.

Time

line 0 1 2 3 4CF

stream -15000 2500 2600 2812.16 …. …..

Here, CF is growing at a constant rate (g) i.e., 4% for unforeseeable future; this type of CF stream is

called growing perpetual CF stream. PV of growing perpetual CFs = CF of first period/(DR-g)

PV PV=2500/(.09-.04)=50000.00

NPV 35000.00



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Summary Note:

We have learned to calculate the PV of different CF streams which can be faced by the firm

for its different type of investment opportunity. I hope based on this discussion, you will

come up with your understanding how to calculate the value of a firm or its any project.

The key challenges are that:

(a)

What every the context, draw your time line

(b)

Plot the CF in the time line according to the incidents

(c)

Find DR

(d)

Come up with the value, and compare it with your investment

(e)

You can easily understand whether you will be able to maximize the value or not

(f)

Finally, you can take the investment decision by selecting the project which is able

to maximize the value

I will highly appreciate your any questions about the above discussion for furtherclarification.

Documents

SBS _MBA FM_Discussion on Time Value of Money Spring 16