Finman - Ytm & Stock Valuation

YIELD TO MATURITY (YTM) OF A BOND

(This represents the rate of return to the investor assuming the bond will be held until maturity) EXAMPLE: Assume a 20-year bond (PHP1,000 (PHP1,000 par value) with annual annual interest of PHP118 (or 11.8% coupon rate) is selling selling today at PHP1,085. Compute the yield to maturity of the bond. bond. Trial 1: Since the bond is selling at a premium, the YTM must be below the coupon rate. Try 10%. Present value of interest (annuity due) = 118 x 8.514 = Present value of principal payment = 1,000 x .149 = TOTAL PRESENT VALUE AT 10%

1,004.65 149.00 1,153.65

Since PHP1,153.65 is higher than the present price of PHP1,085, the YTM must be higher than 10% but below 11.80%. Trial 2: Try 11% Present value of interest (annuity due) = 118 x 7.963 = Present value of principal payment = 1,000 x .124 = TOTAL PRESENT VALUE AT 11%

939.63 124.00 1,063.63

The discount rate of 11% gives a value of PHP1,063.63 slightly lower than the price of the bond of PHP1,085. The YTM must then be between 11% and 11.8%. The exact YTM can be computed using interpolation. 1,153.65 PV @ 10% (1,063.63) PV @ 11%   90.02

1,153.65 PV @ 10% (1,085.00) bond price 68.65

YTM = 10% + 1% (68.65/90.02) = 10.76% Note: The 1% represents the difference difference of the rates being interpolated (11% minus 10%) 10%) APPROXIMATION OF THE YIELD TO MATURITY

(Trial & error method is quite tedious. The formula below can be used to approximate the YTM)

Approximate YTM =

Approximate YTM =

Approximate YTM =

Approximate YTM =

Principal payment - Price of the bond Annual interest + Number of years to maturity .60 (Price of the bond) + .40 (Principal payment) 1,000 - 1,085 118 + 20 .60(1,085) + .40(1,000) 118 - 4.25 651 + 400 10.82%

PREFERRED STOCK VALUATION 1) The preferred stock has maturity date

(The value of preferred stock is computed similar to bond valuation wherein the preferred dividends during the remaining term of the preferred stock and the face value of the preferred stock are discounted using a required rate of return) Example: Assume a PHP10 annual dividend for a PHP100 par value preferred stock maturing 5 years from now. What is the value of the preferred stock if the investor investor wants a 12% rate of return.

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Year 1

Value =

 

10.00

(1 + .12) Value =

Year 2

 

8.93

Value =

 

1

Year 3

10.00 (1 + .12)

 

 

2

7.97

10.00 (1 + .12)

 

Year 4 3

7.12

 

10.00

(1 + .12)  

Year 5 4

6.36

110.00 (1 + .12)

5

62.42

92.79

2) The preferred stock has no maturity date

(The value of the preferred stock is simply equal to the present value of perpetuity) Example: Using the example above except that the preferred stock has no maturity, what is the value of the preferred stock? Value =

10.00 = 83.33 0.12

COMMON STOCK VALUATION METHODS

1) Dividend valuation model (this valuation model is applicable when you intend to hold the stocks indefinitely) 1) No growth in dividends (Periodic dividend is fixed) 2) Constant growth in dividends (also known as the Gordon Growth Formula) 3) Variable growth in dividends 2) Enterprise valuation or the free cash flow valuation 3) Price Earnings (PE) valuation 4) Accounting valuation (or the book value per share) 1)No growth in dividends

(The value of the common stock is calculated similar to preferred stock valuation with no maturity date) Example: Fixed dividend is PHP1.87 and the required rate of return is 12%, what is the price or the value of the common stock? Value =

1.87 = 15.58 0.12

2) Constant growth in dividends

(This valuation approach is used when dividend is increasing at a constant rate. The formula is Value =

Example:

 Previous dividend x ( 1 + growth rate) Required rate of return - growth rate

At 7% increase in dividend and required rate of return of 12%, what is the value of the common stock or the price of the common stock if the dividend last year was PHP1.87? Value =

Value =

1.87 (1 + .07) .12 - .07 40

3) Variable growth rate in dividends

(This valuation applies more to companies that are in the growth stage wherein dividends fluctuate during this period. During the growth period, the present value of the dividends are computed to determine the value of the common stock during the growth stage. At the end of the growth stage (when companies are assumed to be at stable or at normal stage, the value of the common stock during this stable or normal stage is determined by applying the constant growth valuation model. The total of the two present values represents then the value of the common stock today.)

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Example:

Assume a dividend payment last year of PHP1.67. The dividends are expected to grow by 20% per year over the next three years while on the fourth year and years thereafter, the dividend is expected to grow at a constant rate of 5%. What is the value of the common stock if the investor wishes to have a return of 9%? Year 1 dividend = Year 2 dividend = Year 3 dividend = Year 4 and onwards =

1.67 x 1.20 = 2.00 2.00 x 1.20 = 2.40 2.40 x 1.20 = 2.88 (2.88 x 1.05)/(.09 - .05) = 86.40

Year 1

Value =

 

2.00

(1 + .12) Value = Value =

Year 2

 

2.40

1

1.79

Year 3

(1 + .12)  

2.88 + 86.40

2

1.91

(1 + .12)

3

63.55

67.25

4) Enterprise valuation or the free cash flow valuation

This valuation approach is used for companies that declare no dividend or declare an irregular dividend. This valuation method is the focus of financial management. This is the valuation method that we always mentioned in our earlier discussions to determine the value of a company or any asset today. This method is widely used in practice to determine the intrinsic value of the stock today even if companies regularly declare dividends (because the level of dividends that companies will declare in the succeeding periods are difficult to estimate as these are subject to the discretion of their respective board of directors). This valuation method is used in a merger & acquisition transaction. This valuation method calculates the value of the company by discounting the free cash flow of the company and the terminal value of the company using the company's cost of capital (this is more appropriate than the investor's required rate of return as the cost of capital captures the total risk of the company). The interest bearing liability plus any preferred stocks of the company are then subtracted from the value of the company to get the intrinsic value of the stockholders' equity. The total stockholders' equity is then divided by the outstanding common shares to get the real value of the common stock. If the real value is higher than the prevailing market price in the stock market, the stock of the company today is said to be undervalued. If the real value is lower than the prevailing market price in the stock market, the stock of the company today is said to be overvalued. In formula, Present value of the free cash flows (the free cash flows are calculated from the projection) Add: Present value of the terminal value (the terminal value is determined at the end of the projection) Intrinsic value of the company Less: Market value of the interest bearing liability Less: Market value of the preferred stocks Intrinsic value of the stockholders' equity Divided by: common stock outstanding Intrinsic or the real value of the company per share Example:

See separate sheet

5) PE Valuation

(The value of the common stock is determined by multiplying the company's EPS against the PE ratio of the industry where the company belongs) Value = Example:

EPS x PE ratio of the industry

The EPS of the company is PHP5 while the PE ratio of the industry is PHP10 Value =

5 x 10 = 50

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6) Accounting Valuation (or the book value per share)

Value =

Total common stockholders' equity per books / outstanding common shares

7) Liquidation Value

Market value or the selling price of the company's asset, net of expenses related to disposal Less: Liabilities Less: Preferred stocks Remaining cash available to stockholders Divided by: common stock outstanding Liquidation value

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PROJECTED INCOME STATEMENT OF ABC COMPANY

Sales Cost of sales Gross margin General & administrative expenses Selling expenses EBIT Interest expense income before tax income tax Net income

                   

YEAR 1 130,000.00 (88,484.00) 41,516.00 (8,580.00) (15,898.00) 17,038.00 (1,280.00) 15,758.00 (4,727.40) 11,030.60

YEAR 2   463,920.00   (318,103.00)   145,817.00   (29,227.00)   (60,195.00)   56,395.00   (3,580.00)   52,815.00   (15,844.50)   36,970.50

YEAR 3   626,243.00   (426,802.00)   199,441.00   (38,201.00)   (91,314.00)   69,926.00   (4,870.00)   65,056.00   (19,516.80)   45,539.20

YEAR 4   762,257.00   (519,409.00)   242,848.00   (44,973.00)   (121,324.00)   76,551.00   (6,241.30)   70,309.70   (21,092.91)   49,216.79

YEAR 5 834,106.00 (569,906.00) 264,200.00 (46,710.00) (141,746.00) 75,744.00 (7,256.00) 68,488.00 (20,546.40) 47,941.60

Other information: 1) The general & administrative expense includes the following noncash items from year 1 to year 5

Noncash expenses   1,222.00   5,357.00   5,473.00 2) The capital expenditures and (disposal, net of tax) of the company from y ear 1 to year 5 are as follows:   CAPEX   11,097.00   815.00   (1,423.00) 3) The projected change (decrease) in working capital are as follows Working capital   (21,443.00)   3,807.00   7,867.00 4) The weighted cost of capital of the company is 15% 5) The company is expected to grow at 8% at the end of year 5 and beyond. 6) The market value of its outstanding liability to its creditors is PHP500,000.00 7) The common shares outstanding is 10,000 shares

 

5,545.00

5,637.00

 

3,103.00

2,132.00

  11,739.00

2,132.00

Required: Compute the value of the common stock

Solution: EBIT Tax on EBIT (30% of EBIT) Noncash expenses Cash flow from operation CAPEX Working capital Free cash flow

             

YEAR 1 17,038.00 (5,111.40) 1,222.00 13,148.60 (11,097.00) 21,443.00 23,494.60

FACTOR PRESENT VALUE TOTAL PRESENT VALUE = VALUE OF THE COMPANY LESS: MARKET VALUE OF INTEREST BEARING DEBT INTRINSIC VALUE OF STOCKHOLDERS EQUITY DIVIDE BY: OUTSTANDING COMMON SHARES VALUE OF THE COMMON STOCK

0.869565217   20,430.09 551,987.06 (500,000.00) 51,987.06 10,000 5.20

             

YEAR 2 56,395.00 (16,918.50) 5,357.00 44,833.50 (815.00) (3,807.00) 40,211.50

0.756143667   30,405.67

             

YEAR 3 69,926.00 (20,977.80) 5,473.00 54,421.20 1,423.00 (7,867.00) 47,977.20

0.657516232   31,545.79

             

YEAR 4 76,551.00 (22,965.30) 5,545.00 59,130.70 (3,103.00) (11,739.00) 44,288.70

0.571753246   25,322.21

YEAR 5 75,744.00 (22,723.20) 5,637.00 58,657.80 (2,132.00) (2,132.00)   54,393.80 0.497176735   27,043.33

TERMINAL VALUE AT THE END OF YEAR 5: Year 5 cash flow x (1 + growth rate) cost of capital - growth rate 54,393.80 x 1.08 .15 - .08 839,218.63 0.497176735 417,239.98