To find the present value of each alternative and determine which is preferred using the discounted cash flow criterion, we'll proceed with the detailed calculations again based on the given conditions:

Part 1: Present Value of Alternative 1

Alternative 1 involves:

• A payment of $1,000 now (immediate payment).
• A final payment of $13,000 in two years.

The formula for the present value (PV) of a future payment is:

$PV = \frac{FV}{(1 + i)^n}$

Where:

• $FV = 13,000$ (future payment).
• $i = 0.045$ (interest rate per period, since 9% is compounded semi-annually).
• $n = 4$ periods (2 years with semi-annual compounding).

We already calculated:

• Immediate payment of $1,000 has a PV of $1,000.
• The discounted value of $13,000 needs to be recalculated.

Part 2: Present Value of Alternative 2

Alternative 2 involves:

• Payments of $1,300 at the end of every six months for six years.

Since this is an annuity, the formula used is:

$PV = P \times \frac{1 - (1 + i)^{-n}}{i}$

Where:

• $P = 1,300$ (payment).
• $i = 0.045$ (semi-annual interest rate).
• $n = 12$ (total number of payments).

Let's confirm the calculations for present values.### Calculation Results:

1. Present Value of Alternative 1: $11,901 (rounded to the nearest dollar)
2. Present Value of Alternative 2: $11,854 (rounded to the nearest dollar)

Conclusion:

Since Alternative 1 has a higher present value, Alternative 1 is the preferred choice according to the discounted cash flow criterion.

Would you like to explore more, or do you have any questions? Here are some related questions:

1. How would the calculations change if the interest rate was compounded quarterly?
2. What if the payment schedule for Alternative 2 changed to yearly payments?
3. How would inflation affect the decision between these two alternatives?
4. What is the impact of making the final payment in Alternative 1 earlier or later?
5. How does changing the frequency of compounding affect the present value?

Tip: When comparing financial options, always consider the effect of compounding intervals on the overall cost or value.