Lesson details
- Estimated study time
- 105 min
Learning objectives (4)
The same $2,000,000 face amount and 6 percent coupon can sell below, at, or above face. The supplied market yield explains which. Cedar Trail's market yield is 8 percent annually, or 4 percent for each of eight semiannual periods.
Price the streams separately:
coupon stream = $60,000 × ordinary-annuity factor(4%, 8)
principal stream = $2,000,000 × single-sum factor(4%, 8)
issue price = coupon present value + principal present value
With full precision, the price is $1,865,345.10. Face exceeds price by $134,654.90, so the bond is issued at a discount. Nothing was “lost” at issuance. Investors paid the present value of the promised cash flows at the supplied yield.
The two-rate test
Coupon cash uses face amount and 3 percent per period: $60,000. Effective interest later uses opening carrying amount and 4 percent. If a schedule uses 4 percent to calculate cash or 3 percent to calculate expense, the columns have changed roles.
If the supplied market yield were 5 percent annually while the coupon remained 6 percent, price would exceed face and the bond would carry a premium. The direction reverses; the method does not.
Exit check
Write the principal and coupon present-value equations with labels, not only function calls. Explain why issue price is neither face amount nor the sum of all undiscounted future cash. Recompute with a one-point yield change and describe the direction before looking at the number.