Present Value - Weighted Discount Rate
Overview
The present value calculation applied to the cash flows of a bond, using the bonds contractual interest rate will yield the
bonds principal as a result.
When given a portfolio of bonds, the same calculation can be performed, however, there multiple contractual interest rates.
A weighted average of the contractual interest rates yields a rate that return the sum of the principals in a present value calculation.
Two Bond Portfolio Calculations
The weighted average rate is given by
{% r = \frac{ B_1 \times r_1 + B_2 \times r_2}{B_1 + B_2} %}
When the weighted average rate is applied to the total bond balance, the result is the total
interest payment.
{% (B_1 + B_2) \times r = B_1 \times r_1 + B_2 \times r_2 %}
Weighted Average Discount Rate
When valuing a portfolio of different types of risky instruments for which a discount rate is known for each asset,
a weighted average discount rate is the appropriate rate to apply to the portfolio.
