Present Value of Income Streams

Business Calculus · Axiom Academy

EXAMPLE Present Value of Income Streams Calculating today's value of future income flows A commercial property generates 80,000/year in rental income. If the interest rate is 6% compounded continuously, what is the present value of the next 15 years of rent? For constant income rate R over T years at rate r Total rent collected = 80,000 × 15 = 1,200,000. Present value = 796,560. If you can buy this property for less than 796,560 (ignoring other costs), it's a good investment at 6% interest. A startup's income is projected to grow: f(t) = 100000e^ 0.08t dollars/year. Find the present value over 10 years at r = 5%. When growth rate (8%) exceeds discount rate (5%), present value is higher than simple totals suggest. The exponential e^(0.03t) factor grows over time, making later income valuable despite discounting. Patent royalties decline as: f(t) = 200000e^ -0.1t dollars/year. Calculate PV over 20 years at r = 4%. Two investment opportunities, both 10 years at r = 5%: Option A: 50,000/year constant Option B: 30,000/year growing at 10%/year Which has higher present value? Option B is worth 97,950 more in present value terms! Even though Option B starts with lower income ( 30,000 vs 50,000), its 10% growth rate creates much more value over time. When evaluating investments, growth potential can outweigh current returns. Based on the example above, which approach is correct?

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