Bond Cash Flows

Pricing a Bond

Bond value is the discounted sum of all contractual cash flows.

highlighted = computed this step

Bond valuation

Price is the present value of each fixed future payment. At period 1 it is $90.91, at period 2 it is $82.64, and at period 3 it is $826.45.

PV=∑t=13Ct(1+y)t\text{PV}=\sum_{t=1}^{3}\frac{C_t}{(1+y)^t}
Price a bondDiscount each future payment by the yield.PeriodCouponPrincipalCash flowPV1$100.00$0.00$100.00$90.912$100.00$0.00$100.00$82.643$100.00$1,000.00$1,100.00$826.45Price = Σ PV$1,000.00

Reconcile to par

The discounted terms are $90.91, $82.64, and $826.45, which sum to $1,000.00.

$90.91+$82.64+$826.45=$1,000.00\$90.91+\$82.64+\$826.45=\$1,000.00

Model note

This discounts fixed future payments at one flat yield, displayed half-up to the cent; it models no default risk, taxes, or fees.

PV model: P=∑tdiscounted cash flows\text{PV model: }P=\sum_t\text{discounted cash flows}