2.14 Dollar Price and Yield-to-Maturity: Solutions
Solutions
The following are the solutions to the problems on the prior page.
| Problem 1 | Problem 2 | Problem 3 | |
|---|---|---|---|
| Coupon Cash Flow | $70 | $50 | $35 |
| PV Annuity Factor | |||
| PV of the Coupon | $183.70 | $679.52 | $692.75 |
| Par Value | $1,000 | $1,000 | $1,000 |
| PV Factor | |||
| PV of the Par Value | $816.30 | $456.40 | $208.30 |
| Total PV | $1,000 | $1,135.92 | $901.05 |
| Price (% of Par) | 100 | 113.592 | 90.105 |
| Discount/Par/Premium? | Par | Premium | Discount |
Questions:
- What would be the price of each of the bonds if the coupon rates were equal to 0%?
- What do you note about the prices of the above bonds?
Answers:
- The coupon would be zero dollars, and the bond’s price would be solely determined by the row in the table entitled Present Value of the Cash flow of the Par value.
- Prices are Par, Premium, Discount. While the dollar coupon payment goes down (from left to right above) the present values go up. These are annuities, and the longer annuities are to the right. Annuity PVs go up with time as there are more payments. The PVs of the respective par payments go down from left to right, as simple PVs ought to.
Summary Rules
| Par | Coupon Rate = YTM |
| Premium | Coupon > YTM |
| Discount | Coupon > YTM |
By owning a (an “old”) bond whose coupon exceeds the current market rate, one is receiving a greater coupon interest payment than the market is now providing for (newly issued) bonds of that same maturity and creditability. New bonds are usually offered at around the going market YTM. For this superior cash flow, the investor pays more, i.e., a premium. To get more – you pay more. The opposite holds for discount bonds. Can you express this discount notion in words?
