An obligation can be settled by making a payment of Sl ,000 now and a final payment of Sl 3,000 in two

years (Alternative 1). Alternatively the obligation can be settled by payments of $1 ,300 at the end of every six months

for six years (Alternative 2). Interest is 9% compounded semi-annually. Compute the present value of each alternative

and determine the preferred alternative according to the discounted cash flow criterion.

The present value of Alternative 1 is

(Round to the nearest dollar as needed. Round all intermediate values to six decimal places as needed.)

The present value of Alternative 2 is SD

(Round to the nearest dollar as needed. Round all intermediate values to six decimal places as needed.)

Therefore, the best alternative is

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.

Learn how to calculate present value and decide between two investment alternatives using discounted cash flow analysis. This problem involves determining present values under different payment schedules and interest rates. Suitable for college-level finance students.

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