Python for Finance

Bond and Stock Valuation
In the preceding codes, we drop the last cash flow since it is used to calculate the
selling price of P5. Because the scipy.npv() treats the first cash flow happening
at time zero, we have to adjust the result by timing it by (1+R). Calculating the
present of five future dividends separated with the calculation of the present value
of the selling price is to remind readers of the existence of so-called Excel sign
convention. The stock price is 17.47 (=9.52+7.95). Alternatively, we could use the
p4f.pvPriceNperiodModel() function, see the following code. The Python program
is included in Appendix D:
>>>import p4f
>>> r=0.182
>>> g=0.03
>>> d=[1.8,2.07,2.277,2.48193,2.68,2.7877]
>>> p4f.pvValueNperiodModel(r,g,d)
17.472364312825711
The preceding model depends on an important assumption, the number of shares
is constant. Thus, if a company uses a part of its earnings to buy back shares, this
assumption is violated. Thus, we could not use the dividend discount model. For those
cases, we could apply a so-called share repurchase and the total payout model. Here
is the formula. The present value of all of the firm's equity, rather than a single share,
is calculated first:
Logic Solution expects its total earnings at the end of the year to be about $400
million. The company plans to payout 45% of its total earnings: 30% for dividends
and 15% for shares repurchases. If the company's long-term growth rate is 3%, the
cost of equity is 18%, and the number of shares outstanding is 50 million, what is its
stock price today? The solution is shown here:
>>> 400*0.45/(0.18-0.03)/50
>>>
24.0
The third method is to estimate the total value of the firm, that is, the enterprise
value. Then we estimate the total value of the equity. Finally, we divide the
total value of equity by the number of shares outstanding to reach the price. The
enterprise value is defined here:
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