*Last updated: 2023-03-16.*
# tf_quant_finance.rates.analytics.cashflows.pv_from_yields
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Computes present value of cashflows given yields.
```python
tf_quant_finance.rates.analytics.cashflows.pv_from_yields(
cashflows, times, yields, groups=None, dtype=None, name=None
)
```
For a more complete description of the terminology as well as the mathematics
of pricing bonds, see Ref [1]. In particular, note that `yields` here refers
to the yield of the bond as defined in Section 4.4 of Ref [1]. This is
sometimes also referred to as the internal rate of return of a bond.
#### Example
The following example demonstrates the present value computation for two
bonds. Both bonds have 1000 face value with semi-annual coupons. The first
bond has 4% coupon rate and 2 year expiry. The second has 6% coupon rate and
3 year expiry. The yields to maturity (ytm) are 7% and 5% respectively.
```python
dtype = np.float64
# The first element is the ytm of the first bond and the second is the
# yield of the second bond.
yields_to_maturity = np.array([0.07, 0.05], dtype=dtype)
# 2 and 3 year bonds with 1000 face value and 4%, 6% semi-annual coupons.
# Note that the first four entries in the cashflows are the cashflows of
# the first bond (group=0) and the next six are the cashflows of the second
# bond (group=1).
cashflows = np.array([20, 20, 20, 1020, 30, 30, 30, 30, 30, 1030],
dtype=dtype)
# The times of the cashflows.
times = np.array([0.5, 1, 1.5, 2, 0.5, 1, 1.50, 2, 2.5, 3], dtype=dtype)
# Group entries take values between 0 and 1 (inclusive) as there are two
# bonds. One needs to assign each of the cashflow entries to one group or
# the other.
groups = np.array([0] * 4 + [1] * 6)
# Produces [942.712, 1025.778] as the values of the two bonds.
present_values = pv_from_yields(
cashflows, times, yields_to_maturity, groups=groups, dtype=dtype)
```
#### References:
[1]: John C. Hull. Options, Futures and Other Derivatives. Ninth Edition.
June 2006.
#### Args:
* `cashflows`: Real rank 1 `Tensor` of size `n`. The set of cashflows underlying
the bonds.
* `times`: Real positive rank 1 `Tensor` of size `n`. The set of times at which
the corresponding cashflows occur quoted in years.
* `yields`: Real rank 1 `Tensor` of size `1` if `groups` is None or of size `k`
if the maximum value in the `groups` is of `k-1`. The continuously
compounded yields to maturity/internal rate of returns corresponding to
each of the cashflow groups. The `i`th component is the yield to apply to
all the cashflows with group label `i` if `groups` is not None. If
`groups` is None, then this is a `Tensor` of size `[1]` and the only
component is the yield that applies to all the cashflows.
* `groups`: Optional int `Tensor` of size `n` containing values between 0 and
`k-1` where `k` is the number of related cashflows.
Default value: None. This implies that all the cashflows are treated as a
single group.
* `dtype`: `tf.Dtype`. If supplied the dtype for the input and output `Tensor`s.
Default value: None which maps to the default dtype inferred from
`cashflows`.
* `name`: Python str. The name to give to the ops created by this function.
Default value: None which maps to 'pv_from_yields'.
#### Returns:
Real rank 1 `Tensor` of size `k` if groups is not `None` else of size `[1]`.
The present value of the cashflows. The `i`th component is the present
value of the cashflows in group `i` or to the entirety of the cashflows
if `groups` is None.