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Valuation is the process that links risk and return to determine the worth of an asset. To determine an asset’s worth at a given point in time, a financial manager uses time value of money techniques. This topic shows how present value concepts can be applied to the valuation of bonds and common stocks. The value of an asset is the present value of all future cash flows it is expected to provide over the relevant time period. An explanation will be provided of how bond prices vary with interest rates, the term structure of interest rates and the effect of inflation on the interest rate. This topic also provides a detailed understanding of the constant dividend growth model. It explores the relationship between stock price, earnings per share and growth opportunity and also how a business can be valued using DCFs.

The following parts are covered in this topic:

Using the present value formula to value bonds?

How bond prices vary with interest rates?

The term structure of interest rates?

Explaining the term structure ?

Real and nominal rate of interest ?

How common stocks are traded?

How common stocks are valued?

Estimating the cost of equity capital?

The link between stock price and earnings per share?

Valuing a business by discounted cash flow (DCF)?

As an introduction to using the present value formula to value bonds read pages 47–50 of your textbook (pages 46–49 of the 11th edition). This section also introduces the US semiannual coupons and bond prices.

Calculate the value of a bond that expects to mature in 12 years and has a \$1,000 face value. The coupon interest rate is 8% paid annually and the investors’ required rate of return is 12%.

Enterprise Ltd has issued debentures with a par value of \$1,000 and a 9% p.a. coupon rate. The coupon interest amounts are paid semi-annually and the debentures mature in 8 years.

If your required rate of return to invest in these debentures is 8% p.a., what is your valuation of the debenture? What would your valuation be if the debenture paid the coupon interest amount annually?

## Using the present value formula to value bonds?

1. a) The forward P/E ratios of the FANG stocks has been obtained from Yahoo Finance and summarised below.

It is apparent that the forward P/E for the four stocks highlighted above is different. The reasons attributed to the difference of these are highlighted below.

1) The main reason for difference in forward P/E is the difference in growth expectations that shareholders tend to have from the four shares listed above. Consider for example Netflix for which the key aspect is the addition of subscriber especially in the international market. In the Q2 2018, the company missed the estimates with regards to international subscribers added on account of higher competition (Steigard, 2018). However, the company has beaten the estimates for Q3 when it added the highest ever 7 million subscribers in a quarter. The company has also raised the guidance and expects that total subscriber addition in Q4 is likely to be in excess of 9 million (Lahiff, 2018). The company is well and truly on explosive growth especially in the largely untapped international markets which is also reflected in the high forward P/E.

With regards to Amazon, the business of the company continues to grow especially in the international markets and also the company is aggressively pushing the various product offerings. A key aspect of the recent results is the improved operating profit margins which have led to company reporting a healthy profit growth. In the Q3 2018 also, the company was able to beat the revenue and profit estimates. Although the management has lowered the estimates for Q3 and Q4, the growth story for the company continues to remain lucrative particularly on the back of international markets (Kim, 2018).

Facebook has in the past six months has faced several issues such as data leaks along with fake news. Further, the company has posted lacklustre results in both Q2 and Q3 owing to which the stock price has been hammered which has adversely impacted the forward P/E (Frier, 2018). Another major dampener is the management commentary which expects the growth to considerably lower down in subsequent quarters to high single digit values. Clearly, this has led the investors to lower the growth projections as the company grapples with the issues which lead to lower forward P/E ratio (Castillo, 2018).

Google also has shown tepid revenue growth in the current year which is caused concerns of future growth for the company. Also, the advertisement business is still going strong but the hardware & cloud business which is expected to be the future is still showing lesser growth than expected. The stock has also seen significant correction in the recent time and hence the low forward P/E ratio (D’Onfro, 2018).

Out of the FANG stock, the maximum growth seems to be likely in Netflix in the year term which is shown very significant quarter on quarter growth which therefore is captured in the highest forward P/E ratio.

2) A secondary reason for distortion in the forward P/E of the above stocks is the changes in the market price which is not uniform. As a result, a stock which is beaten severely would have a lower forward P/E ratio assuming other factors are constant. Thus, the recent price trends also need to be taken into consideration as price also plays a crucial factor.

1. b) The most recent price and the EPS estimates for each of the FANG stocks is summarised in the table below.

## How bond prices vary with interest rates?

Source: Yahoo Finance

The average P/E for the above companies is obtained from Damodaran website and is listed below.

Facebook –Relevant Industry is software (internet) and the current average P/E is 205.58.

Amazon – Relevant Industry is retailer (online) and the current average P/E is 73.27.

Netflix – Relevant Industry is retailer (online) and the current average P/E is 73.27.

Google – Relevant Industry is software (internet) and the current average P/E is 205.58.

Considering the above average P/E, the computation the current theoretical prices of the FANG stocks is indicated below.

Facebook = 205.58*7.37 = \$ 1,515.25

Amazon – 73.27*19.8 = \$ 1,450.75

Netflix – 73.27*2.66 = \$ 194.90

Google = 205.58*41.78 = \$ 8,589.13

It is apparent that theoretical prices of Facebook and Google are at significant premium to the market prices primarily because of the exorbitant prices. The theoretical price of Amazon and Netflix are lower than the corresponding price. The above variation between theoretical price and market price can be attributed owing to the following lines.

1) The above data corresponds to values as on January 5, 2018 while the current price taken into consideration is November 2018 price. Significant price fluctuations and also growth estimation has taken place between the beginning of the year and the current situation. The growth of companies such as Google and Facebook has been downgraded and additionally there has been price movements and hence it is expected that deviation between theoretical and market price would be expected (D’Onfro, 2018;Castillo, 2018).

2) Another main contributor is the fact that the P/E considered to arrive at the prices are industry average. With regards to the software (internet), there are other companies which are significantly smaller than Facebook and Google and are clocking a significantly higher growth rates owing. Further, a lot of these typically have low earnings as these are in their growth phase. However, this is not the case with Google and Facebook whose primary business has matured and is not growing very rapidly. The performance of Facebook in this regards even worse as it considers high single digit growth in the near term which clearly would be at the lower end of growths in this sector (Castillo,2018). Similarly, Netflix and Amazon in terms of their growth would be growing at above average pace in their respective industry and hence the undervaluation.

3) Even though two companies belong to the same industry, but the business challenges and growth prospects may be significantly different. Consider for example Google and Facebook which tend to belong to the same industry group but the latter is going through a much more challenging business environment both domestically and globally. These aspects are reflected in the market price owing to which Facebook stock price has significantly underperformed the other components of FANG stocks. Thus, using of the average P/E of the industry to determine price completely ignores these varied challenges that may be faced by firms belonging to the same industry.

1. c) The cost of equity capital for each of the FANG stocks can be computed using the Capital Asset Pricing Model (CAPM) which states the following (Petty et. al., 2015).

Cost of equity = Risk free rate + Beta * Market Risk Premium

## The term structure of interest rates?

Risk free rate (10 year Treasury bond) = 3.14%

Market Risk Premium = 7.17% (Considering the period from 1968-2017 https://www.stern.nyu.edu/~adamodar/pc/datasets/histretSP.xls )

The respective beta of the FANG stocks is as stated below.

Cost of equity (Facebook) = 3.14 + 0.546*7.17 = 7.05%

Cost of equity (Amazon) = 3.14 + 1.7*7.17 = 15.33%

Cost of equity (Netflix) = 3.14 + 1.17*7.17 = 11.53%

Cost of equity (Google) = 3.14 + 1.32*7.17 = 12.60%

Neither of the FANG stocks pay any dividend, hence the dividend yield for all these stocks is zero. Further, considering the rapid growth path on which these companies are currently on, it is unlikely that they would pay any dividends in the near future also. This is not surprising also, considering their stock prices where the even after giving out more than \$ 1 billion as dividends to investors, the dividend yield would be very small and hence the main focus of the business should be growing the EPS of the firm (Damodaran, 2015).

In order to estimate the theoretical price of the FANG stocks, the EPS would be used which would be discounted at the respective cost of equity to yield a theoretical stock price (Parinno and Kidwell, 2014). The EPS trend for the FANG stocks for the last four year is reflected below.

Clearly, as the base becomes higher and also international markets saturate, the growth would become considerably lower and the above growth cannot be expected to continue. Also, considering the above growth trajectory, it is expected that the companies would continue to witness at a higher growth rate for some years before slowing down to more realistic rates (Brealey, Myers and Allen, 2014). The following assumptions are made for the stocks.

1) It is expected that Amazon and Netflix would register a 100% growth in EPS for the next four years and then the growth would moderate to 10% p.a. till perpetuity.

2) It is expected that Google would register a 50% growth in EPS for the next four years and post that the growth rate would be moderated to 7.5% p.a. till perpetuity.

3) It is expected that Facebook would register a 40% growth in EPS for the next four years and post that the growth rate would be moderated to 5 % p.a. till perpetuity.

Theoretical price of Facebook stock = (7.37*1.4/1.0705) + (7.37*1.42/1.07052) + (7.37*1.43/1.07053) + (7.37*1.44/1.07054) + (7.37*1.44*1.05/((1.07054*(0.0705-0.05)) = \$901.14

Theoretical price of Amazon stock = (19.8*2/1.1533) + (19.8*4/1.15332) + (19.8*8/1.15333) + (19.8*16/1.15334)+ (19.8*16*1.1/((1.15334*(0.1533-0.1)) = \$ 2,465.08

Theoretical price of Netflix stock = (2.66*2/1.1153) + (2.66*4/1.11532) + (2.66*8/1.11533) + (2.66*16/1.11534)+ (2.66*16*1.1/((1.11534*(0.1133-0.1)) = \$ 1,450.75

Theoretical price of Google stock = (41.78*1.5/1.126) + (41.78*1.52/1.1262) + (41.78*1.53/1.1263) + (41.78*1.54/1.1264) + (41.78*1.54*1.075/((1.1264*(0.126-0.075)) = \$1,652.18

1. d) For determining the theoretical price of the FANG stocks, the Gordon growth model has been used. The model is based on the following assumptions (Damodaran, 2015).

1) The company has a stable business model and there are no major changes in business operations.

2) The company is growing at a constant rate.

3) The financial leverage of the company is stable.

4) The free cash flow of the company is paid as dividends.

The assumptions in this model do not seem to concur for the given companies as explained below.

1) The business model of companies like Google is still evolving considering that the company is trying to move into businesses other than advertising which can propel the company forward. Additionally, considering the nature of ecosystem which is quite dynamic, the FANG companies need to be quite agile in order to maintain their growths (Parrino and Kidwell, 2015).

2) The growth rates of these companies is quite volatile as is apparent from the empirical data. Also, while these are going at more than 100% for the last few years on a CAGR basis, this cannot be expected over the long term when growth will moderate. As a result, assumptions are made regarding the future growth rate and moderation of growth. However, a constant growth rate is very difficult to predict especially for growing businesses. Thus, assumptions have been taken based on the current performance of companies and potential future growth rate.

3) The companies do not pay any dividends and hence the EPS of the companies have been taken instead considering that the companies are unlikely to pay any dividends in the near future.

From the above analysis, it may be concluded that valuing companies that are growing at a fast non-uniform pace through the Gordon growth model is a challenge owing to the assumptions not being satisfied. Also, a greater challenge is to draw an estimate of the future growth potential and also the constant growth rate and the timeline of achieving the same (Petty et. al., 2015). These difficulties are apparent in the determination of theoretical prices which are at a premium to the current market prices.

References

Brealey, R. A., Myers, S. C. and Allen, F. (2014) Principles of corporate finance, 6th ed. New York: McGraw-Hill Publications

Castillo, M. (2018) Facebook plunges more than 24 percent on revenue miss and projected slowdown, [online] Available at https://www.cnbc.com/2018/07/25/facebook-earnings-q2-2018.html [Accessed November 14, 2018]

D’Onfro. E. (2018) Alphabet stock sinks on revenue miss, [online] Available at https://www.cnbc.com/2018/10/25/alphabet-google-earnings-q3-2018.html [Accessed November 14, 2018]

Damodaran, A. (2015). Applied corporate finance: A user’s manual 3rd ed. New York: Wiley, John & Sons.

Frier, S. (2018) Facebook results miss revenue estimates, shares slide, [online] Available at https://www.livemint.com/Companies/agc0dbYkDYcdocZ5crWtiN/Facebook-results-miss-revenue-estimates-shares-slide.html [Accessed November 14, 2018]

Kim, E. (2018) Amazon plunges 10% on revenue and guidance miss, [online] Available at https://www.cnbc.com/2018/10/25/amazon-earnings-q3-2018.html [Accessed November 14, 2018]

Lahiff, K. (2018)  Netflix is rocketing higher in extended trading after clearing one of its biggest hurdles, [online] Available at https://www.cnbc.com/2018/10/16/netflix-is-about-to-release-earnings-and-one-analyst-has-a-warning.html [Accessed November 14, 2018]

Parrino, R. and Kidwell, D. (2014) Fundamentals of Corporate Finance, 3rd ed. London: Wiley Publications

Petty, J.W., Titman, S., Keown, A., Martin, J.D., Martin, P., Burrow, M. and Nguyen, H. (2015). Financial Management, Principles and Applications, 6th ed..  NSW: Pearson Education, French Forest Australia

Steigard, A. (2018)  Netflix shares dive after disappointing quarterly results, [online] Available at https://nypost.com/2018/07/16/netflix-shares-dive-after-disappointing-quarterly-results/ [Accessed November 14, 2018]

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