$15-18.668M gain over 4 years from $1M loan
100% ARR, each year a $1M gain?
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Yearly Gains for 100% ARR:
• Year 1: $2,000,000 (Gain: $1,000,000)
• Year 2: $4,000,000 (Gain: $2,000,000)
• Year 3: $8,000,000 (Gain: $4,000,000)
• Year 4: $16,000,000 (Gain: $8,000,000)
Yearly Gains for 120% ARR:
• Year 1: $2,200,000 (Gain: $1,200,000)
• Year 2: $4,840,000 (Gain: $2,640,000)
• Year 3: $10,648,000 (Gain: $5,808,000)
• Year 4: $23,425,600 (Gain: $12,777,600)
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Let’s break this down:
Definitions:
• $1M ARR (Annual Recurring Revenue): Starting revenue in year 1 is $1M.
• ARR Growth Rate 100% YoY (Year over Year): Revenue doubles each year.
• ARR Growth Rate 120% YoY: Revenue increases by 120% of the previous year’s revenue each year.
Now let’s calculate the ARR for 4 years under both growth rates:
1. 100% Growth Rate (Revenue Doubles Yearly):
• Year 1: $1M
• Year 2: $1M × 2 = $2M
• Year 3: $2M × 2 = $4M
• Year 4: $4M × 2 = $8M
Total ARR Over 4 Years: $1M + $2M + $4M + $8M = $15M
2. 120% Growth Rate:
Growth formula: New ARR = Previous ARR × (1 + Growth Rate)
• Year 1: $1M
• Year 2: $1M × (1 + 1.2) = $1M × 2.2 = $2.2M
• Year 3: $2.2M × (1 + 1.2) = $2.2M × 2.2 = $4.84M
• Year 4: $4.84M × (1 + 1.2) = $4.84M × 2.2 = $10.648M
Total ARR Over 4 Years: $1M + $2.2M + $4.84M + $10.648M = $18.688M
Summary:
• 100% Growth: Total ARR over 4 years = $15M
• 120% Growth: Total ARR over 4 years = $18.688M
Would you like this broken down further?
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Certainly! Let’s calculate the future value of a $1 million investment over 4 years at two different annual rates of return (ARR): 100% and 120%.
At 100% ARR over 4 years
Formula:
Where:
• Present Value (PV) = $1,000,000
• ARR = 100% or 1.0
• n = 4 years
Calculation:
So, after 4 years at 100% ARR, your investment grows to $16 million.
At 120% ARR over 4 years
ARR Conversion:
• ARR = 120% or 1.2
Calculation:
First, compute :
1.
2.
Alternatively:
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Final Calculation:
So, after 4 years at 120% ARR, your investment grows to approximately $23.43 million.
Summary
• 100% ARR over 4 years: $1 million grows to $16 million
• 120% ARR over 4 years: $1 million grows to $23.43 million
Difference: The higher ARR of 120% results in an additional $7.43 million over the 4-year period compared to the 100% ARR.
Understanding the Impact
The calculations show how significant the impact of a higher annual rate of return is over multiple years due to the effect of compounding. Even a 20% increase in the ARR (from 100% to 120%) results in a substantial increase in the future value over 4 years.