8.5 The Realized Compound Yield (Solution to Problem)
Solution to Above Example:
Coupon CF = $4
FVAV (p = 14, r = .03) = 17.086
RCY = [($4) (17.086) + 100] ÷ 90.101 = 1.8684 ≈ 4.5% (semi-annual)
(1.8684) 1/14 – 1 = 4.566% (semi-annual)
9.132% (annual)
Questions (see answers below and discussion that follows):
- How much of the above represents interest-on-interest?
- If an investor’s tax bracket is 40%, what is the “net RCY” (i.e., after-tax)?
- What is the relationship between REIN, YTM, and RCY?
Solution (question #1):
| Interest-on-Interest | ||
| Coupon Cash Flow | 4 | |
| x Number of Periods | 14 | |
| Total Nominal Cash Flow | 56 | |
| Coupon CF x FVAF (above) | $68.344 | |
| Interest-on-interest | $12.344 |
Another solution for this is: ($4) (17.086 – 14.0) = $12.344.
Solution (question #2):
Here, one would multiply the coupon by the after-tax rate (T): (Coupon)(1 – T). Thus, the RCY would be equal to (4)(1 – T)(17.086) etc.
