Simes Innovations, Inc., is negotiating to purchase exclusive rights to manufacture and market a solar-powered compressor machine. The compressor machine's inventor has offered Simes the choice of either a one-time payment of 150,000php today or a series of 5 year-end payments of 38,500 PHP. If Simes has a cost of capital of 9%, which form of payment should it choose?

To determine which form of payment Simes Innovations, Inc. should choose, we need to compare the present value (PV) of the two options: 

1. A one-time payment of 150,000 PHP today.
2. A series of 5 year-end payments of 38,500 PHP each.

Since Simes has a cost of capital of 9%, we will discount the series of payments to their present value at a 9% discount rate.

### Step 1: Calculate the Present Value of the Series of Payments

The formula for the present value of an annuity (a series of equal payments) is:

\[
PV = \frac{P}{(1 + r)^1} + \frac{P}{(1 + r)^2} + \frac{P}{(1 + r)^3} + \cdots + \frac{P}{(1 + r)^n}
\]

where:
- \( P = 38,500 \) PHP (annual payment)
- \( r = 0.09 \) (cost of capital or discount rate)
- \( n = 5 \) years

Alternatively, we can use the formula for the present value of an ordinary annuity:

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

Substitute the values:

\[
PV = 38,500 \times \left( \frac{1 - (1 + 0.09)^{-5}}{0.09} \right)
\]

### Step 2: Calculate the Present Value

Let's compute the present value using the formula above.The present value of the series of 5 year-end payments of 38,500 PHP each, discounted at a 9% rate, is approximately **149,751.57 PHP**.

### Step 3: Compare the Two Options

- **One-time payment today**: 150,000 PHP
- **Present value of 5 payments**: 149,751.57 PHP

Since the present value of the 5-year payment series (149,751.57 PHP) is slightly less than the one-time payment of 150,000 PHP, Simes Innovations, Inc. should **choose the one-time payment of 150,000 PHP today** to minimize the cost.

Would you like more details on this calculation, or do you have any questions?

Here are 5 related questions you might find interesting:
1. What if the cost of capital was different, such as 7% or 10%?
2. How would inflation affect the decision between these two payment options?
3. What is the future value of the one-time payment after 5 years, assuming a 9% return?
4. How does the decision change if the payment series is made at the beginning of each year instead?
5. What is the impact of tax considerations on the choice between these two options?

**Tip:** Understanding the time value of money is crucial in finance; always consider the impact of interest rates when evaluating payment options.

Simes Innovations, Inc., is negotiating to purchase exclusive rights to manufacture and market a solar-powered compressor machine. The compressor machine's inventor has offered Simes the choice of either a one-time payment of 150,000 PHP today or a series of 5 year-end payments of 38,500 PHP. If Simes has a cost of capital of 9%, which form of payment should it choose?

Explore how Simes Innovations, Inc. can decide between a one-time payment of 150,000 PHP or a series of 5 year-end payments of 38,500 PHP, using the present value concept with a 9% cost of capital. This problem covers key financial concepts, such as the time value of money, present value, and annuities, suitable for high school and college finance students.

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