Friday, October 25, 2013

Discounted Cash Flows and Present Value

By Tim Dulaney, PhD, FRM and Tim Husson, PhD

When determining the value of a bond, you start by thinking about the cash flows you're expected to recieve and when those cash flows are expected to occur.   We've created the following illustration of a simple $1,000 face-value bond that pays annual interest payments (also known as coupons).

Coupon Rate: 
For a year $1,000 face-value bond with an interest rate of , the total cash flow is .

The timing of the cashflows matters since obviously we'd prefer to have a dollar today than a dollar tomorrow.  The value today of a future payment today is called the present value of that payment.  We find the present value by discounting the future cash flow using a discount rate for an asset that matures at approximately the same time.    $$Present Value = {Cash Flow \over \left(1 + Discount Rate\right)^{Time}}$$ For example, if we use an interest rate of 3% to discount our cash flows, then a $30 coupon payment at the end of year one has a present value of $30/(1+3%) = $29.13. A $30 coupon payment at the end of year two has a present value of $30/((1+3%)*(1+3%)) = $28.28.  The total value of the bond is equal to the sum of the present values of the coupon payments.  

The present value of the payments an investor is expected to receive is dependent upon the interest rate with which those cash flows are discounted.  As the discount rate increases, the value of the payments (and therefore the value of the security) goes down.  As the discount rate decreases, the value of the payments goes up.

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