Suppose you have a real estate investment opportunity that will generate $1,200 per month for the next year. What is the present value of this stream of cash flows if the annual discount rate is 6%?


To calculate the present value (PV) of a stream of monthly cash flows, we use the formula for the present value of an annuity:

\[
PV = \sum_{t=1}^{n} \frac{C}{(1 + r)^t}
\]

Where:
- $ C $ is the monthly cash flow ($1,200),
- $ r $ is the monthly discount rate (the annual discount rate divided by 12),
- $ t $ is the time period in months,
- $ n $ is the number of periods (12 months, in this case).

First, we need to calculate the monthly discount rate. Since the annual discount rate is 6%, the monthly rate $ r $ is:

\[
r = \frac{6\%}{12} = 0.5\% = 0.005
\]

Now, let's calculate the present value using the formula for the present value of an annuity, which is a more direct method for fixed periodic payments:

\[
PV = C \times \left[ \frac{1 - (1 + r)^{-n}}{r} \right]
\]

Substituting the known values:

\[
PV = 1200 \times \left[ \frac{1 - (1 + 0.005)^{-12}}{0.005} \right]
\]

Let's calculate the terms:

1. $ (1 + 0.005)^{-12} = (1.005)^{-12} \approx 0.94176 $,
2. $ 1 - 0.94176 = 0.05824 $,
3. $ \frac{0.05824}{0.005} = 11.648 $.

Finally:

\[
PV = 1200 \times 11.648 = 13,977.60
\]

The present value of the investment opportunity is approximately **$13,977.60**.

Would you like more details or have any questions?

Here are 5 related questions for deeper understanding:
1. How would the present value change if the discount rate was higher or lower?
2. What if the cash flows were uneven instead of fixed at $1,200 per month?
3. How does inflation affect the real value of these future cash flows?
4. How do we account for risk in calculating present value?
5. What is the difference between present value and net present value (NPV)?

**Tip**: Always ensure to use the same time unit for discount rates and cash flows when calculating present value.

Suppose you have a real estate investment opportunity that will generate $1,200 per month for the next year. What is the present value of this stream of cash flows if the annual discount rate is 6%?

Learn how to calculate the present value of a real estate investment that generates $1,200 per month over the next year, with an annual discount rate of 6%. Understand key concepts such as discounting cash flows and the present value of annuities, with step-by-step calculations.

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