Question

can you please give example and explanation about opportunities cost, discount cash flow, discount rates ,prescent value, free cash flow, NPV, IRR , stock valuation in finance management.

Answer 1

Hi...have tried to explain the terminologies that you have asked in a very simple and precise way. Hope this helps.Have invested a lot of time in preparing this answer :)

1) Opportunities Cost - Resources are limited and scarce. Financial resources have to be judiciously used for wealth maximization.If a company has, let's say ,a land and it can use the land for a project which can give a return of 8% ,then this would be the opportunity cost if it doesnot use the land and it is idle. Simply put, opportunity to use any financial asset (Land, Cash,etc) to generate return would be a cost if it is not used.

2) Discounted Cash Flow-

Discounted Cash flow Technique(DCF) helps to compute the intrinsic value of an asset , which is the Present Value of the future cash flows discounted at the required Rate of Return.

IV=C1/(1+r)¹+C²/(1+r)²+C3/(1+r)³…..

Example: A project involves an initial investment of $250,000.It has a life of 5 years.The net cash flow expected to be generated from this project are shown below:

Year	1	2	3	4	5
Net cash flow	45000	80000	70000	100000	80000

The risk adjusted Nominal rate of return required from the project is 15%.

Year                            Nominal Cash Flow                Present Value @15%

1                                              45000                          45000/(1+0.15)¹=39130
2                                              80000                          80000/(1+0.15)²=60491
3                                              70000                          70000/(1+0.15)³=46026
4                                              100000                        100000/(1+0.15)⁴=57175
5                                              80000                          80000/(1+0.15)⁵=39774
Total Cash Inflow at the end of 5 year=$.242596

3)Discount Rate -

A Dollar today is more precious than a Dollar a year from now. Money that you hold today is worth more because you can invest it and earn interest. After all, you should receive some compensation for foregoing spending.

It is very important to understand the required rate of return in all investment decisions.This is called a discount rate.Primarily it has three components-

Risk Free Real Rate of Return: The rate of return required for the sacrifice of present consumption. It should be used as the discount rate if the cash flows are certain.

Inflation Premium: Purchasing power of money comes down due to rise in inflation. When people have more spending power and funds are available at cheaper rates, Inflation goes up. Hence, the lender tends to lose the value of his money for which he will charge inflation premium to compensate for the loss of purchasing power.

Risk Premium: Credit default risk , market risk, country risk(In certain cases), liquidity risk etc are some types of risk which a lender would like to cover before lending for which he will charge Risk premium as an reward for taking these additional risk.

The three components mentioned above can be combined together in an additive or multiplicative model depending on the scenario and case study.This discount rate is also called as hurdle rate, ie, the minimum you would want in return for investing your funds after factoring in the above components.

4)Present Value - Present value gives the value of an asset or Project today , discounted at a rate, for it's future earnings. SImpy put, PV is the sum of all the future earnings at present discounted at a rate.For example, the Present value of a share can be  the PV of the expected future dividends discounted at required RoR.

5)Free Cash Flow -

Free Cash Flow of a Firm (FCFF) may be defined as the cash flows available after meeting the investment requirements of the firm.

FCFF = Net Operating Profit less Adjusted Tax(NOPLAT) – Net Investment

Where NOPLAT = EBIT x (1-T)

Net Investment = Capital Spending – Depreciation + Change in Working Capital

6)NPV (Net Present Value)

When we subtract the initial investment cost ie on Year 0 from the Future cashflows ,discounted at the required rate of return, we get Net Present Value. It can be negative or Positive, depending upon the cash flow and life of the project and the discount rate used.If it is negative at a desired rate of return ,then investment should be avoided,

Continuing the example from (2)

Net Present Value(NPV)=Inflow at PV-Outflow
$242596-$250000=-$7403
Since the NPV is negative the project should not be undertaken at the current required RoR.

(7) Internal Rate of Return (IRR)

It is the interest earned on the unrecovered investment balance.
When you are provided with a cash flow stream,the implied RoR or cost is that discount rate which equates the PV of cash flows & out flows.
ie. Outflow=Inflow technique
For computation purpose:
a)If we are provided with a cash flow stream spreading over only one year or two years, we need to use linear or quadratic equation to solve the sum.
b)If the cash flows are spread more than 2 years, we apply trial & error process using approximation technique or linear interpolation or extra polation.

Example: Consider the following cash flows:

Year	0	1	2
Net cash flow	(500)	300	350

Compute IRR & interpret.

Solution: Outflow=Inflow
ie 500=300/(1+r)+350/(1+r)²
500(1+r)²-300(1+r)-350=0
or, 10(1+r)²-6(1+r)-7=0
Let (1+r)=x
hence,10x²-6x-7=0
which is in the form:ax²+bx+c=0
Using –b+Vb²-4ac/2a
r=-158.9% or 18.9%
Hence, IRR of 18.9% is the RoR earned on the unrecovered investment balance (F₁)each year.
Thus F₀=-500
         F₁=(-500x1.189)+300=-294.5
         F₂=(-294.5x1.189)+350=0

(8) Stock Valuation

There are different approaches to stock valuation. These are -

Absolute Valuation

1. Dividend Discount Model (DDM)

This model is to be used when valuing a firm from a minority perspective and the firm has a past track record of dividends which is indicative of its earning power.

As per DDM, Intrinsic value of an equity share is the PV of the expected future dividends discounted at required RoR
ie IV=D₁/(1+Re)+D₂ /(1+Re)² According to Capital Asset Pricing Model (CAPM)
                                                    Re= R_f + (R_m- R_f) x Beta
                                               

There can be three patterns of dividend forecast:
a)No Growth DDM= D/Re Applicable to companies with 100% payout ratio ie EPS=DPS

Example: A Ltd. Has a 100% payout ratio and is a no growth company. It has an EPS of Rs.15 for the year just ended and the stock is presently trading at Rs.132. If RoR is 14% pa. Find out the intrinsic value of the share.
Solution: IV=D/Re
15/0.14=107.14 over priced.

b)Constant Growth DDM=D₁/Re-g
Forecast of sustainable growth can be done on the basis of following 2 methods:
(i) Simple average Growth Rate (SAGR)
(ii)Compounded Average Growth rate (CAGR) of past dividend

Example : DPS of X ltd for the last 5 years is as below:

Year	DPS
1	25
2	28
3	34
4	26
5	49.5

If the firm’s equity capitalization rate is 20% pa. Compute IV of the share using CAGR.

CAGR : 25 x (1+g)⁴ = 49.5
       g = 18.62%
Expected Dividend = 49.5 x 1.1862 = 58.12
Expected Dividend = 58.12/0.20 – 0.1862 = 4211.59

(iii) The earnings retention model (Gordon's growth model) Assumption
The higher the level of retentions in a business, the higher the potential growth rate.

g = br                                     where: r = post-tax accounting rate of return earned on reinvested funds
                                          b = earnings retention rate

Determining "r" One way of determining r is to use the Accounting Rate of Return on equity calculated as: r = PAT / opening shareholders' funds

Example: The RoR is 12% pa for a stock which is expected to pay Rs.17 next year as dividend. The Dividend is expected to grow @4% pa forever. Find out the IV of the share.
Solution: D₁/Re-g=106

c)Multiple Growth DDM

Example: P Ltd. Reported an EPS of Rs.12 for the year just ended and a payout ratio of 40%.The earnings are expected to grow at 30% pa for the next 4 years and beyond that at 6% pa forever.If the RoR is 18% pa, compute the IV of the share.
Solution: First 4 years
D₀₌40% of 12=4.8

Year	DPS	PV@18%
1	4.8x1.3=6.24	6.24/1.18=5.29
2	6.24x1.3=8.11	8.11/(1.18)2=5.82
3	8.11x1.3=10.55	6.42
4	10.55x1.3=13.71	7.07

Beyond 4 years:
Horizon value at the end of 4^th year P₄=D₅/Re-g=13.71x1.06/0.18-0.06=>121.11
PV of P₄=121.1/(1.18)⁴=62.46
Therefore, IV of the share=24.60+62.46=87.06

2.Free Cash Flow Approach

1. FCFF approach is based on the NPV concept ie NPV of a project =
   PV of future cash flows –    Initial      Investment
2. If we apply this approach to firm valuation, we acknowledge that investments in a firm take place each year so we deduct the investment of each year from the cash flow of that year to arrive at FCFF.Discounting these free cashflows at Cost of capital (kc) gives the value of the firm.
3. FCFF may be defined as the cash flows available after meeting the investment requirements of the firm.
4. FCFF = Net Operating Profit less adjusted tax – Net investment

                                 Where Net Operating Profit less adjusted tax = EBIT (1-t)

                                 Net investment = capital spending – depreciation – change in working capital

                OR, FCFF = Cash from operating activities (After tax) – capital expenditure

                               

5. Value of firm = PV of FCFF discounted at Kc (Kc= WdKd + WeKe)
6. Value of Equity = Value of firm – Market value of debt + Market value of non-trade investment
7. For constant growth FCFF, all components of FCFF are expected to grow at a constant growth rate forever, therefore, value of a firm = FCFF₁
                                                                                                                                           Kc – g
8. For multiple growths, there will be an explicit forecast period where we compute the FCFF for each year and discount at Kc. Then there will be a horizon period where we apply the constant growth formula to compute horizon value.

So value of firm = PV of the FCFF for the explicit forecast period + PV of the horizon period

Example: X Ltd furnishes the following financials for the year just ended.

EBIT Rs.1200 crore, capital spending Rs.250 crore, Depreciation Rs.150 crore, change in woring capital Rs.50 crore
All the components of FCFF are projected to grow at 6% pa forever. The firm’s capital structure comprises of – 20 crore shares trading at Rs.200 per share , 14% Long Term Debt of book value Rs.600 crore (MV Rs.540 crore). The firm has a tax rate of 30% and beta of 1.8. Rf = 6%, Rm- Rf = 5.5%. Should the shares be purchased, validate using FCFF approach

Solution: Computation of Kc

MV of Equity = 20 x 200         = 4000 cr

MV of Debt                                                = 540 cr
                                                           4540 cr

Wd = 540/4540 = 0.118

We = 0.882

Kd = 14 x (1-0.3) = 9.8%

Ke = 6 + (5.5) x 1.8 = 15.9%

Kc= 0.118 x 9.8 + 0.88 x 15.9 = 15.1802%

Computation of FCFF

NOPLAT = EBIT x (1 - t) = 1200 x (1 – 0.3) = 840

Net Investment = Capital Spending – depreciation + change in working capital

                               = 250 – 150 + 50 = 150

FCFF₀ = NOPLAT – Net Investment

           = 840 – 150 = 690

FCFF₁ 690 x 1.06 = 731.4

Value of the firm = FCFF ₁/ ke –g = 731.4/0.1518 – 0.06 = Rs.7967.32 crore

Value of equity = Value of Firm – MV of debt + value of non trade investment

                              = 7967.32 – 540 – nil = 7427.32 crore

IV per share = 7427.32/20 = 371.37

Hence at current market price of Rs.200, the stock is undervalued and should be bought

In continuation of the above example consider the following inputs:

1. EBIT of the firm is expected to grow at 30% pa for the next to years after which growth rate will start falling in a linear fashion so as to become 6% from the 5^th year onwards and stay at that level for ever.
2. Capital expenditure and depreciation are expected to grow at 40% for the next 2 years and then the growth rate will start falling such that the growth rate is 25% for the 3^rd year,15% for the 4^th year and 5% for the 5^th year.Beyond 5^th year,the firm will enter into a steady state wherein capital spending will be offset by depreciation such that net capital spending = nil
3. The change in working capital will follow same pattern as EBIT. Find out the IV of share s per FCFF.

Solution:

Kc = 15.18%

Explicit Forecast Period (First 5 years)

Stable growth(horizon period) beyond 5 years

FCFF₆ = 2086.36

Horizon value at (V₅) = FCFF₆/ kc – g = 2086.36/0.1518 – 0.06 = 22727.23

PV of V₅ = 272727.23/(1.1518)⁵ = 1121.43

Value of the firm = 4254.33 + 1121.43 = 15465.76 crore

Value of equity = 15465.76 – 540 = 14925.76

IV per share = 14925.76/20 = 746.29

Relative Valuation

Relative valuation involves valuing a firm on the basis of how similar firms are valued – similar in terms of nature and scale of operations.

This method involves the use of price multiples –

1. Price to Earning ratio (P/E)
2. Price to sales ratio (P/S)
3. Price to BV ratio (P/B)

IV of the share = Justified P/E Ratio x Earnings

                                Justified P/S Ratio x Sales

                                Justified P/B Ratio x BV

Justified Price multiples are very subjective. Any positive/negative factor in a firm should result in a higher/lower price multiple.

Example: The following details are available with regards to Excel Enterprises Ltd.(EEL):

                                                (Rs.Lakh)

Sales                                      600

Corporate Tax                   27

ESC                                         80

R&S                                        40

Effective tax rate             36%

The companies Ace Industries Ltd(AIL) Modern Industries Ltd.(MIL), Rover Enterprises Ltd (REL) are considered to be similar to EEL in terms of nature and size of operation.

The following details are available with regards to these companies :

                                                                AIL(Rs.Lakh)                       MIL(Rs.Lakh)                      REL(Rs.Lakh)

Sales                                                      540                                         580                                         640

Corporate Tax                                   19.6                                        22.4                                        32.4

ESC                                                         60                                           80                                           90

R&S                                                        40                                           30                                           60

Market value of the firm              648                                         725                                         896                        

Effective tax rate                             35%                                        35%                                        36%

The value of EEL has to be determined using comparable firms approach. It is felft that in the valuation of EEL ,the weightage of sales,earnings and book value should be in the ratio of 1:2:1.

Solution:

Let us first of all compute the justified price multiples as an average of the industry:

Particulars                           AIL                          MIL                        REL                         Justified Price Multiple

Sales                                      540                         580                         640

Net Income                        19.6/35 x 65        41.6                        57.6

                                                =36.4                                                    

Net worth                           100                         110                         150

MV                                         648                         725                         896

a)P/S                                     648/540                1.25                        1.4                          (1.2+1.25+1.4)/3=1.28

                                                =1.2

b)P/E                                     648/36.4               17.43                     15.56                     16.93

                                                =17.8

c)P/B                                     648/100                6.59                        5.97                        6.35

                                                =6.48

Value of EEL is given by:

a)On basis of sales :

Value = P/S x Sales = 1.28 x 600 = 768

b)on the basis of Earnings:

Value = P/E x Earnings = 16.93 x 48 = 812.64

c)On the basis of book value:

Value = P/B x Net worth =6.35 x 120 = 762

IV of EEL = (1/4 x 768) + (2/4 x 812.64) + (1/4 x 762) = 788.82 Lakh

Residual valuation

A firm should invest in a project only if NPV is positive ie return on project is greater than the RoR. This extra income generated by the firm is called residual Income or Economic Value Added (EVA). The PV of all future EVA is known as Market Value Added (MVA)

Thus, Value of equity is given by –

Networth + MVA, where MVA is PV of EVA_s

EVA can be computed by the following two methods:

1) EVA = NOPLAT – Kc x Invested capital

2) EVA = PAT – Ke x Net worth

Example: Consider a firm with the following capital structure – Networth =200, 15% Long term debt = 100,Ke=18%,t=40%. The firm is expected to generate EBIT of 80 in the next year, find EVA.

Solution: We = 2/3 ; Wd = 1/3

Kd = 15 % x (1-0.4) = 9%

Ke = 18%

Kc = 2/3 x 18 + 1/3 x 9 = 15%

NOPLAT = EBIT x (1-t ) = 80 x (1-0.4) = 48

EVA = NOPLAT – Kc x invested capital

                48 – 15% x 300 = 3

Alternatively, PAT = (EBIT – Interest) x (1-t)

                                                (80 – 15) x (1-0.4) = 39

EVA = PAT – Ke x Networth = 39 – 18% x 200 = 3

Suppose, the firm has 4 lac shares outstanding. Find out the IV of the share in following cases:

1. EVA is perpetual
2. EVA will grow perpetually @3%

Solution : Case 1

MVA = EVA/Re   {P= A/i)

                3/0.18 = 16.67

Value of equity = Net worth + MVA

                                200 + 16.67 = 216.67

IV of share = 216.67/4 = Rs. 54.17