9.5 Average Life of the Cash Flow of a Bond (A Comparison of Two Bonds)
Below, we compare a 5% coupon to the 10% coupon bond we had just earlier.
| Period | Cash Flow (10% Cpn.) Bond “A” | Cumulative Cash Flow = (p) × CF |
Cash Flow (5% Cpn.) Bond “B” | Cumulative Cash Flow = (p) × CF |
|---|---|---|---|---|
| 1 | 100 | 100 | 50 | 50 |
| 2 | 100 | 200 | 50 | 100 |
| 3 | 100 | 300 | 50 | 150 |
| 4 | 100 | 400 | 50 | 200 |
| 5 | 100 | 500 | 50 | 250 |
| 6 | 100 | 600 | 50 | 300 |
| 7 | 100 | 700 | 50 | 350 |
| 8 | 100 | 800 | 50 | 400 |
| 9 | 100 | 900 | 50 | 450 |
| 10 | 100 | 1,000 | 50 | 500 |
| 1,000 | 10,000 | 1,000 | 10,000 | |
| Totals | 2,000 | 15,500 | 1,500 | 12,750 |
Note that, in the case of the 10% coupon, the ratio of the coupon cash flow to face value (i.e., the weights) is 1:10, whereas, in the case of the 5% coupon, the ratio is 0.5:10. With Bond A, more cash flows are received sooner (its numerator is larger).
(Weighted) Average Life of the Bond’s Cash Flow
“A” = 15,500 ÷ 2,000 = 7.75 periods
“B” = 12,750 ÷ 1,500 = 8.5 periods
Note: The higher the coupon the shorter the average life of the bond’s cash flow.
Questions and Answers
Question 1:
Answer 1:
Question 2:
Answer 2:
Solution: (10 × 1,000) / 1,000 = 10 years
Answer: The average life of the cash flow of a Zero-coupon bond is equal to its maturity! This would be our base case. As the coupon increases from Zero, the ALCF decreases.
This analysis has not been adjusted for the Time Value of Money! Yes! … and that is where we are going!
