2.6 Fixed Income Securities: Dollar Price and Yield-to-Maturity Calculation
Since the coupon cash flow is an annuity, a simple valuation solution would utilize the following formula. Take note, that it does not matter how many zeros you use although, we shall always figure a face value in this text of $1,000 for consistency and convenience, unless otherwise noted:
| Example: | Coupon | .10 (Semi-annual) |
|---|---|---|
| Term-to-Maturity | 5 years | |
| Discount Rates (Y-T-M) | .08, .10, and .12 |
You’ll need calculators and interest rate tables for this!
Discount Rates
Here you shall need to insert the appropriate present value annuity factor (PVAF) and the present value factor (PVF).
| .08 | .10 | .12 | |
| Coupon (PVAF) | |||
| Par Value (PVF) |
Dollar Values
Here you shall need to multiply the above factors by the dollar amounts of the coupon / annuity and the face value respectively.
| Coupon ($50) | |||
| Par ($1,000) | |||
| Total/Price | |||
| Price Characteristics (Discount/Par/Premium) |
The “true” price of the bond may, in fact, be considered the YTM. It is conceivable that there exist two bonds with the same maturity and creditability (or even issued by the same company) but due to having been issued at different times, the two bonds carry different coupons. Thus, the YTM will be the same for each, but the dollar prices will be different. Therefore, YTM is the true market price, at which bonds are assessed.
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