A company has two investment opportunities. Alternative 1 (Alt. 1) pays  $12,000 (inflow) two years from now, and $18,000 (inflow) four years from now.
Alternative 2 (Alt. 2) pays  $7,000 (inflow) at the end of every year for five years.
Interest is 7.88% compounded annually. Which is the preferable alternative? 

Round the values for PV to the nearest cent. 

 	TWO YEARS	FOUR YEARS	FIVE YEARS
P/Y = 	
C/Y =	
N =	
I/Y =	
%	
%	
%
PV =	$
$
$
PMT =	$
$
$
FV = 	$
$
$
Write the Discounted Cash Flow (DCF) for Alt. 1 and Alt. 2.

Enter positive values for Alt. 1, and Alt. 2, rounded to the nearest dollar.

Let's calculate the Discounted Cash Flow (DCF) for both alternatives with the given interest rate and round the values to the nearest cent.

**Alternative 1:**

1. $12,000 received 2 years from now
2. $18,000 received 4 years from now

For each cash flow, we use the present value formula:

\[ PV = \frac{FV}{(1 + r)^n} \]

where:
- $ r = 7.88\% = 0.0788 $

Calculating for each cash flow:

\[ PV_1 = \frac{12,000}{(1 + 0.0788)^2} = \frac{12,000}{1.16343904} = 10,313.35 \]
\[ PV_2 = \frac{18,000}{(1 + 0.0788)^4} = \frac{18,000}{1.35808858} = 13,255.85 \]

Sum of the present values for Alternative 1:

\[ PV_{\text{Alt1}} = 10,313.35 + 13,255.85 = 23,569.20 \]

**Alternative 2:**

We have an annuity of $7,000 received at the end of each year for 5 years. The present value of an annuity can be calculated using the formula:

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

where:
- $ P = 7,000 $
- $ r = 0.0788 $
- $ n = 5 $

Substitute the given values:

\[ PV_{\text{Alt2}} = 7,000 \times \frac{1 - (1 + 0.0788)^{-5}}{0.0788} \]

Calculate the value:

\[ PV_{\text{Alt2}} = 7,000 \times \frac{1 - (1.0788)^{-5}}{0.0788} \]
\[ PV_{\text{Alt2}} = 7,000 \times \frac{1 - 0.672} {0.0788} \approx 7,000 \times 4.156 \approx 29,092.00 \]

**Comparison:**

- Present value of Alternative 1: $ 23,569.20 $
- Present value of Alternative 2: $ 29,092.00 $

Since $ 29,092.00 $ is greater than $ 23,569.20 $, Alternative 2 is the preferable investment.

**Discounted Cash Flow (DCF) for Alternative 1:**

\[ \text{Year 2: } \frac{12,000}{(1.0788)^2} = 10,313.35 \]
\[ \text{Year 4: } \frac{18,000}{(1.0788)^4} = 13,255.85 \]

\[ \text{Total DCF for Alt. 1: } 23,569.20 \]

**Discounted Cash Flow (DCF) for Alternative 2:**

\[ \text{Year 1: } \frac{7,000}{(1.0788)^1} = 6,487.16 \]
\[ \text{Year 2: } \frac{7,000}{(1.0788)^2} = 6,014.96 \]
\[ \text{Year 3: } \frac{7,000}{(1.0788)^3} = 5,575.15 \]
\[ \text{Year 4: } \frac{7,000}{(1.0788)^4} = 5,166.61 \]
\[ \text{Year 5: } \frac{7,000}{(1.0788)^5} = 4,787.99 \]

\[ \text{Total DCF for Alt. 2: } 29,031.87 \]

Since the value of $ 29,031.87 $ for Alternative 2 is greater than $ 23,569.20 $ for Alternative 1, Alternative 2 is preferable.

Do you have any questions or need further details on the calculations?

Here are 5 numbered questions you might want to ask:
1. How is the present value of a series of cash flows calculated?
2. What is the formula for the present value of an annuity?
3. Can you explain the significance of the interest rate in present value calculations?
4. How does compounding frequency affect the present value of future cash flows?
5. What are some common applications of present value calculations in finance?

**Tip:** Always ensure you are using the correct formula and values for the specific type of cash flow (single lump sum vs. annuity) when calculating present value.

Learn how to calculate the Discounted Cash Flow (DCF) for investment alternatives using the Time Value of Money concept. Compare two investment options based on their present values with a detailed explanation. Suitable for finance professionals and students.

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