spring_attempt_25-4-10

Below are two separate tables that outline the cash‐flow details for each hypothetical scenario over 30 years. These tables assume that in the bond scenario you receive a fixed 5% coupon on a $1,000,000 investment every year (with the principal returned at maturity), and in the stock scenario you have an asset that grows by 30% per year while paying a dividend equal to 1% of its beginning‐of‐year value (with dividends paid out and not reinvested).

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For a $1,000,000 bond at 5% annual yield:

• Annual Coupon: $1,000,000 × 5% = $50,000 each year (for years 1–29).
• At Maturity (Year 30): You receive the final coupon ($50,000) plus the $1,000,000 principal return, for a total payment of $1,050,000.
• Cumulative Total Over 30 Years: $50,000 × 29 + $1,050,000 = $2,500,000.

A representative table (with a few rows shown and ellipsis for brevity):

Year	Annual Payment ($)	Cumulative Payment ($)	Note
1	50,000	50,000	Annual coupon only
2	50,000	100,000	Annual coupon only
3	50,000	150,000	Annual coupon only
…	…	…	…
29	50,000	1,450,000	Annual coupon only
30	1,050,000	2,500,000	Coupon + Return of $1,000,000 principal

Note: The table shows that over 30 years, you receive a total of $2.5 million from the bond—$1.5 million in interest (coupons) plus your original $1 million returned at the end.

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In this scenario, you start with $1,000,000. Each year:

• Beginning Value: Grows by a factor of 1.30 (i.e. increases by 30%).
• Dividend Payment: 1% of the beginning value of that year.
• End-of-Year Value: The beginning value multiplied by 1.30.
• Cumulative Dividends: Sum of each year's dividend (paid out, not reinvested).

Because the 30% annual growth is very powerful, the asset's value compounds dramatically over 30 years. (The mathematical formula for the end value is:
Final Value = $1,000,000 × 1.3^30, which is approximately $2.62 billion.)

Below is a sample table that shows selected years. (All values are approximate due to rounding.)

Year	Beginning Value ($)	Dividend ($)	End-of-Year Value ($)	Cumulative Dividends ($)
1	1,000,000	10,000 (1% of 1,000,000)	1,300,000 (1,000,000 × 1.3)	10,000
2	1,300,000	13,000 (1% of 1,300,000)	1,690,000 (1,300,000 × 1.3)	23,000 (10,000 + 13,000)
3	1,690,000	16,900	2,197,000	39,900
10	~10,608,000	~106,080	~13,790,000	~426,300
20	~146,150,000	~1,461,500	~190,000,000	~6,300,000
30	~2,019,600	~20,196	~2,625,480,000	~87,470,000

How the Numbers Work:

• Year 1:

  • Start with $1,000,000.
  • Dividend = 1% × $1,000,000 = $10,000.
  • End-of-Year Value = $1,000,000 × 1.30 = $1,300,000.

• Year 30:

  • The beginning value is $1,000,000 × 1.3^(29) ≈ $2,019,600.
  • Dividend = 1% × $2,019,600 ≈ $20,196.
  • End-of-Year Value = $2,019,600 × 1.30 ≈ $2,625,480,000.
  • The cumulative dividends over 30 years sum to roughly $87.5 million, using the geometric series formula.

Note: Because of the very high assumed annual growth rate (30%), the final asset value becomes extraordinarily large, even though the yearly dividend payments remain a small percentage of an ever-growing base.

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• Bond Scenario: You steadily receive $50,000 each year, with a total return of $2.5 million over 30 years (including the returned principal).
• Stock Scenario: With 30% annual price appreciation and a 1% annual dividend, the asset's value compounds to approximately $2.62 billion by Year 30, plus cumulative dividends of roughly $87.5 million.

These tables help illustrate how dramatically different the outcomes can be when comparing a stable fixed-income investment with an extraordinarily high growth stock (noting that a consistent 30% annual growth rate is exceedingly rare and comes with significantly higher risk).

Feel free to adjust or expand these tables further depending on the level of detail you need for your analysis.