To get discount factors from the new object, a time list with year fractions is needed:
In [ 52 ]: time_list = [0.0, 0.5, 1.0, 1.25, 1.75, 2.0] # in year fractions
In [ 53 ]: sr.get_discount_factors(time_list)
Out[53]: array([ 1. , 0.97530991, 0.95122942, 0.93941306, 0.91621887,
0.90483742])
Using this object, it is quite simple to generate a plot as before (see Figure 13-2). The
major difference is that we first update the attribute rate and then provide the time list t
to the method get_discount_factors:
In [ 54 ]: for r in [0.025, 0.05, 0.1, 0.15]:
sr.rate = r
plt.plot(t, sr.get_discount_factors(t),
label=‘r=%4.2f’ % sr.rate, lw=1.5)
plt.xlabel(‘years’)
plt.ylabel(‘discount factor’)
plt.grid(True)
plt.legend(loc= 0 )
Figure 13-2. Discount factors for different short rates over five years
Generally, discount factors are “only” a means to an end. For example, you might want to
use them to discount future cash flows. With our short rate object, this is an easy exercise
when we have the cash flows and the dates/times of their occurrence available. Consider
the following cash flow example, where there is a negative cash flow today and positive
cash flows after one year and two years, respectively. This could be the cash flow profile
of an investment opportunity:
In [ 55 ]: sr.rate = 0.05
cash_flows = np.array([- 100 , 50 , 75 ])
time_list = [0.0, 1.0, 2.0]
With the time_list object, discount factors are only one method call away:
In [ 56 ]: disc_facts = sr.get_discount_factors(time_list)
In [ 57 ]: disc_facts
Out[57]: array([ 1. , 0.95122942, 0.90483742])
Present values for all cash flows are obtained by multiplying the discount factors by the
cash flows:
In [ 58 ]: # present values
disc_facts * cash_flows
Out[58]: array([-100. , 47.56147123, 67.86280635])
A typical decision rule in investment theory says that a decision maker should invest into a
project whenever the net present value (NPV), given a certain (short) rate representing the
