Category: Management Notes

Method # 1. Based on Balance Sheet:

i. Book Value:

It is the net worth of a company divided by number of outstanding shares. Net worth is equal to paid-up equity capital plus reserves and surplus minus losses.

ii. Liquidation Value:

Liquidation value is different than a book valuation. In that it uses the value of the assets at liquidation, which is often less than market and sometimes book. Liabilities are deducted from the liquidation value of the assets to determine the liquidation value of the business. Liquidation value can be used to determine the bare bottom benchmark value of a business.

iii. Replacement Cost:

Replacement costs provide an alternative way of valuing a company’s assets. The replacement, or current, cost of an asset is the amount of money required to replace the asset by purchasing a similar asset with identical future service capabilities. In replacement cost, assets and liabilities are valued at their cost to replace.

Method # 2. Based on Dividends:

i. One Year Holding Period:

As per this model, the investor intends to purchase now, hold it for one year and sell it off at the end of one year. Thus, the investor would receive dividend of one year as well as the share price at the end of year one.

To value a stock, we have to first find the present discounted value of the expected cash flows.

Where,

Po = the current price of the stock

D1 = the dividend paid at the end of year 1

ke = required return on equity investments (Discounting factor)

P1 = the price at the end of period one

Let ke = 12%, Div = 0.16 and P1 = Rs.60.

Po = Rs. 53.71

If the stock was selling for Rs. 53.71 or less, the share should be purchased

ii. Multiple Year Holding Period:

As per this model, an investor may hold the shares for a number of years and sell it off at the end of it. Thus, he receives dividends for these periods as well as market price of the share after it.

Where,

Po = the current price of the stock

D1, D2, D3……. Dn = annual dividend paid at the end of year 1, 2, 3…n

ke = required return on equity investments (Discounting factor)

Pn = the price at the end of period n

For example:

If an investor expects to get Rs.3.5, Rs.4 and Rs.4.50 as dividend from a share during the next 3 years and hopes to sell it off at Rs.75 at the end of the third year, and if required rate of return is 15%, the present value of the share will be

iii. Constant Growth Model (Gordon’s Share Valuation Model):

As per this model, dividends will grow at the same rate (g) into the indefinite future and the discount rate (k) is greater than growth rate

Where,

k = discount factor

g = growth rate

D_o = current dividend

D1 = Dividend at end of year one

For example:

Alembic Company has declared a dividend of Rs. 2.5 per share for the current year. The company has been following a policy of enhancing its dividends by 10% every year and is expected to continue its policy in future also. The investor’s required rate of return is 15%. The value of the share will be

iv. Multiple Growth Model (Also called as the Two Stage Growth Model):

The constant growth model has a very unrealistic assumption of constant growth. The growth may take place at varying rates. In the multiple growth model, the future time period is viewed as divisible into two different growth segments, the initial extraordinary growth period and the subsequent constant growth period.

Where,

Po = the current price of the stock

D1, D2, D3……. Dn = annual dividend paid at the end of year 1, 2, 3…n

ke = required return on equity investments (Discounting factor)

g = constant growth rate of dividends at the start of the second stage

For example:

Hindalco paid a dividend of Rs.1.75 per share during the current year. It is expected to pay a dividend of Rs.2 per share during the next year. Investors forecast a dividend of Rs.3 and Rs.3.5 per share respectively during the two subsequent years. After that, it is expected that annual dividends would grow at 10% per year into an indefinite future. The investor’s required rate of return is 20%. 

Method # 3. Other Approaches:

i. Price to Book Value Ratio:

The book value of a company is the value of the net assets expressed in the balance sheet. Net assets means total assets minus intangible assets and liabilities. This ratio gives the investor an idea of how much he is actually paying for the share.

ii. Earnings Multiplier Approach:

Under this approach, the value of equity share is estimated as follows:

Po = EPS × P/E ratio.

Where,

EPS = Earning Per share

P/E ratio = Price Earning Ratio

P/E ratio = Market price per share / earnings per share

iii. Price to Sales Ratio:

It is calculated by dividing a company’s current stock price by its revenue per share for the recent twelve months. This ratio reflects what the market is willing to pay per rupee of sales.

iv. Market Value Method:

This method is used only in case of listed companies, since they have a market value.

Market value of a company = No. of shares outstanding × market price per share

The method for valuation of bonds involves three steps as follows:

Step 1: Estimate the expected cash flows

Step 2: Determine the appropriate interest rate that should be used to discount the cash flows.

& Step 3: Calculate the present value of the expected cash flows (step-1) using appropriate interest rate (step- 2) i.e. discounting the expected cash flows

STEP 1: Estimating cash flows

Cash flow is the cash that is estimated to be received in future from investment in a bond. There are only two types of cash flows that can be received from investment in bonds i.e. coupon payments and principal payment at maturity.

The usual cash flow cycle of the bond is coupon payments are received at regular intervals as per the bond agreement, and final coupon plus principle payment is received at the maturity. There are some instances when bonds don’t follow these regular patterns. Unusual patterns maybe a result of the different type of bond such as zero-coupon bonds, in which there are no coupon payments. Considering such factors, it is important for an analyst to estimate accurate cash flow for the purpose of bond valuation.

STEP 2: Determine the appropriate interest rate to discount the cash flows

Once the cash flow for the bond is estimated, the next step is to determine the appropriate interest rate to discount cash flows. The minimum interest rate that an investor should require is the interest available in the marketplace for default-free cash flow. Default-free cash flows are cash flows from debt security which are completely safe and has zero chances default. Such securities are usually issued by the central bank of a country, for example, in the USA it is bonds by U.S. Treasury Security.

Consider a situation where an investor wants to invest in bonds. If he is considering to invest corporate bonds, he is expecting to earn higher return from these corporate bond compared to rate of returns of U.S. Treasury Security bonds. This is because chances are that a corporate bond might default, whereas the U.S. Security Treasury bond is never going to default. As he is taking a higher risk by investing in corporate bonds, he expects a higher return.

One may use single interest rate or multiple interest rates for valuation.

STEP 3: Discounting the expected cash flows

Now that we already have values of expected future cash flows and interest rate used to discount the cash flow, it is time to find the present value of cash flows. Present Value of a cash flow is the amount of money that must be invested today to generate a specific future value. The present value of a cash flow is more commonly known as discounted value.

The present value of a cash flow depends on two determinants:

• When a cash flow will be received i.e. timing of a cash flow
• The required interest rate, more widely known as Discount Rate (rate as per Step-2)

First, we calculate the present value of each expected cash flow. Then we add all the individual present values and the resultant sum is the value of the bond.

The formula to find the present value of one cash flow is:

PRESENT VALUE FORMULA FOR BOND VALUATION

Present Value _n = Expected cash flow in the period n/ (1+i) ⁿ

Here,

i = rate of return/discount rate on bond
n = expected time to receive the cash flow

By this formula, we will get the present value of each individual cash flow t years from now. The next step is to add all individual cash flows.

Bond Value = Present Value ₁ + Present Value ₂ + ……. + Present Value _n

One of the most important skills an investor can learn is how to value a stock. It can be a big challenge though, especially when it comes to stocks that have supernormal growth rates. These are stocks that go through rapid growth for an extended period of time, say, for a year or more.

Many formulas in investing, though, are a little too simplistic given the constantly changing markets and evolving companies. Sometimes when you’re presented with a growth company, you can’t use a constant growth rate. In these cases, you need to know how to calculate value through both the company’s early, high growth years, and its later, lower constant growth years. It can mean the difference between getting the right value or losing your shirt.

Supernormal Growth Model

The supernormal growth model is most commonly seen in finance classes or more advanced investing certificate exams. It is based on discounting cash flows. The purpose of the supernormal growth model is to value a stock that is expected to have higher than normal growth in dividend payments for some period in the future. After this supernormal growth, the dividend is expected to go back to normal with constant growth.

To understand the supernormal growth model we will go through three steps:

• Dividend discount model (no growth in dividend payments)
• Dividend growth model with constant growth (Gordon Growth Model)
• Dividend discount model with supernormal growth

Dividend Discount Model: No Dividend Payments Growth

Preferred equity will usually pay the stockholder a fixed dividend, unlike common shares. If you take this payment and find the present value of the perpetuity, you will find the implied value of the stock.

For example, if ABC Company is set to pay a $1.45 dividend during the next period and the required rate of return is 9%, then the expected value of the stock using this method would be $1.45/0.09 = $16.11. Every dividend payment in the future was discounted back to the present and added together.

We can use the following formula to determine this model:

V= Dn/K

Where:

V=Value

Dn​=Dividend in the next period

k= Required rate of return​

Constant Growth Model: Gordon Growth Model

Next, let’s assume there is a constant growth in the dividend. This would be best suited for evaluating larger, stable dividend-paying stocks. Look to the history of consistent dividend payments and predict the growth rate given the economy the industry and the company’s policy on retained earnings.

Again, we base the value on the present value of future cash flows:

V = D1/ (k-g)

Where:

V=Value

D1=Dividend in the first period

k= Required rate of return

g=Dividend growth rate​

Dividend Discount Model with Supernormal Growth

Now that we know how to calculate the value of a stock with a constantly growing dividend, we can move on to a supernormal growth dividend.

One way to think about the dividend payments is in two parts: A and B. Part A has a higher growth dividend, while Part B has a constant growth dividend.

A) Higher Growth

This part is pretty straight forward. Calculate each dividend amount at the higher growth rate and discount it back to the present period. This takes care of the supernormal growth period. All that is left is the value of the dividend payments which will grow at a continuous rate.

B) Regular Growth

Still working with the last period of higher growth, calculate the value of the remaining dividends using the V = D₁ ÷ (k – g) equation from the previous section. But D₁, in this case, would be next year’s dividend, expected to be growing at the constant rate. Now the discount goes back to the present value through four periods.

A common mistake is discounting back five periods instead of four. But we use the fourth period because the valuation of the perpetuity of dividends is based on the end of year dividend in period four, which takes into account dividends in year five and on.

The values of all discounted dividend payments are added up to get the net present value. For example, if you have a stock that pays a $1.45 dividend which is expected to grow at 15% for four years, then at a constant 6% into the future, the discount rate is 11%.

An annuity due is a series of equal consecutive payments that you are either paying as a debtor or receiving as a lender. This differs from an annuity, as an annuity is a form of investment. Annuities are paid at the end of a period, while an annuity due payment is made at the beginning of a period. This payment covers the period to come.

Some examples of this could be a premium on insurance or rent due. If you were renting a house to someone, their monthly payments are an annuity due.

Time Value of Money 

Present value can be a difficult topic to digest. It refers to a concept called “the time value of money”. Time value of money can be explained thusly—if you were given $1 today, it is worth more than the same $1 five years from now. This is due to the changing value of money and inflation, and the potential of money to earn interest.

The present value of an annuity due (PVAD) is calculating the value at the end of the number of periods given, using the current value of money. Another way to think of it is how much an annuity due would be worth when payments are complete in the future, brought to the present.

Calculating the PVAD

For this formula, the following values are used:

P = periodic payment

r = rate per period

n = number of periods

The formula used is:

PVAD = P + P [ (1 – (1 + r) ^{– (n – 1)} ) ÷ r ]

An annuity is essentially a finance related contract, which permits the person who is buying it to pay on a lump-sum basis or make payments in series, in return for acquiring disbursements at regular intervals in future. Deferred Payment Annuity is a type of an annuity in which the payments that are received start somewhere in the future instead of starting at the time it is initiated.

Deferred payment annuity generally provides tax-deferred development and growth at a variable or fixed rate of return, similar to a regular annuity. Deferred payment annuity is usually bought for under-age or small children so that the benefit payment amount can be postponed till they complete a certain or desired age. Such annuities are extremely helpful when it comes to planning for retirement.

Deferred annuities are a type of annuity contract that delays payments to the investor until the investor elects to receive them. When the investor is in savings mode, he makes payments into some sort of investment account. The investment grows and compounds in a tax-deferred manner, and the investor pays no taxes on its growth until he decides to convert the investment into an annuity and start receiving regular payments.

A deferred annuity is essentially an investment vehicle that is sold by companies that provide insurance to people. The value of a deferred annuity can typically be calculated in two different ways i.e. future based value or present based value. It is these particular values that can assist you in determining the amount you should invest in order to fulfill your investment related goals.

Deferred annuity formula is used to calculate the present value of the deferred annuity which is promised to be received after some time and it is calculated by determining the present value of the payment in the future by considering the rate of interest and period of time.

Present Value Calculation

As per this method, you need to take the present value i.e. the amount you are thinking of investing today, into consideration. Next, you will have to provide definitions for the variables. For example, if you wish to make a saving of 100,000 dollars by the time a decade comes to an end and you come across an annuity that would offer you a minimum of 5% return on an annual basis, then your present value would typically be a minimum of 61,391 dollars today.

Future Value Calculation

For this, you will have to make note of the future value, which is the amount that you would receive after the maturity of the annuity. Next, define all the variables. For example, if you are planning to make an investment of 10,000 dollars and wish to find out how your asset would grow in case you were to get a 5% rate of interest over a period of twenty years, then your investment’s future value would be 26,532 dollars.

An annuity is the series of periodic payments received by an investor on a future date and the term “deferred annuity” refers to the delayed annuity in the form of installment or lump-sum payments rather than an immediate stream of income. It is basically the present value of the future annuity payment. The formula for a deferred annuity based on an ordinary annuity (where the annuity payment is done at the end of each period) is calculated using ordinary annuity payment, the effective rate of interest, number of periods of payment and deferred periods.

Deferred Annuity = P _Ordinary * [1 – (1 + r)^-n] / [(1 + r)^t * r]

A perpetuity is a type of annuity that receives an infinite amount of periodic payments. An annuity is a financial instrument that pays consistent periodic payments. As with any annuity, the perpetuity value formula sums the present value of future cash flows.

Common examples of when the perpetuity value formula is used is in consols issued in the UK and preferred stocks. Preferred stocks in most circumstances receive their dividends prior to any dividends paid to common stocks and the dividends tend to be fixed, and in turn, their value can be calculated using the perpetuity formula.

The value of a perpetuity can change over time even though the payment remains the same. This occurs as the discount rate used may change. If the discount rate used lowers, the denominator of the formula lowers, and the value will increase.

It should be noted that the formula shown supposes that the cash flows per period never change.

Annuities are investment contracts sold by financial institutions like insurance companies and banks (generally referred to as the annuity issuer). When you purchase an annuity, you invest your money in a lump sum or gradually during an “accumulation period.” At a specified time the issuer must start making regular cash payments to you for a specified period of time. The future value of an annuity is an analytical tool an annuity issuer uses to estimate the total cost of making the required cash payments to you.

Identification

When you purchase an annuity, the issuer invests your money to produce income. Annuity issuers make their money by keeping a part of the investment income, which is referred to as the discount rate. However, as each payment is made to you, the income the annuity issuer makes decreases. For the issuer, the total cost of making the annuity payments is the sum of the cash payments made to you plus the total reduction of income the issuer incurs as the payments are made. Issuers calculate the future value of annuities to help them decide how to schedule payments and how large their share (the discount rate) must be to cover expenses and make a profit.

Types

The formula for the future value of an annuity varies slightly depending on the type of annuity. Ordinary annuities are paid at the end of each time period. Annuities paid at the start of each period are called annuities due. Many annuities are paid yearly. However, some annuities make payments on a semiannual, quarterly or monthly schedule.

Formula

The basic equation for the future value of an annuity is for an ordinary annuity paid once each year. The formula is F = P * ([1 + I]^N – 1 )/I. P is the payment amount. I is equal to the interest (discount) rate. N is the number of payments (the “^” means N is an exponent). F is the future value of the annuity. For example, if the annuity pays $500 annually for 10 years and the discount rate is 6 percent, you have $500 * ([1 + 0.06]^10 – 1 )/0.06. The future value works out to $6,590.40. This means that, at the end of 10 years, the issuer’s total cost is equal to $6,590.40 ($5,000 in payments plus $1,590.40 in interest not earned).

Payment Periods

In order to use the formula for the future value of an annuity when the payment interval is less than one year, you must make two adjustments. First, divide the discount rate (I) by the number of payments per year to find the rate of interest paid each month. Use this monthly rate as your value for I. Second, multiply the number of annual payments (N) by the number of payments each year to find the total number of payments and use this value for N.

Annuity Due

Because payments for an annuity due are made at the beginning of the payment period, the future value of the annuity is increased by the interest earned for one time period. Start by calculating the future value using the equation for an ordinary annuity for the appropriate time period. Then multiply the result by 1 + I where I is equal to the discount rate for the period.