To calculate the present value (PV) of a series of future cash flows, we need to discount each payment back to the present using the formula:

$PV = \frac{{CF_1}}{{(1 + r)^1}} + \frac{{CF_2}}{{(1 + r)^2}} + \dots + \frac{{CF_n}}{{(1 + r)^n}}$

Where:

• $CF_n$ = Cash flow in year $n$
• $r$ = Discount rate (7% or 0.07)
• $n$ = Year number

Now, let's calculate the present value for each year:

Given Data:

• Year 1: $CF_1 = 10,000$
• Year 2: $CF_2 = 6,000$
• Year 3: $CF_3 = 9,000$
• Year 4: $CF_4 = 0$
• Year 5: $CF_5 = 25,000$
• Year 6: $CF_6 = 8,000$
• Discount rate $r = 0.07$

Calculation of Present Values:

1. $PV_1 = \frac{10,000}{{(1 + 0.07)^1}} = \frac{10,000}{1.07} = 9,345.79$
2. $PV_2 = \frac{6,000}{{(1 + 0.07)^2}} = \frac{6,000}{1.1449} = 5,241.48$
3. $PV_3 = \frac{9,000}{{(1 + 0.07)^3}} = \frac{9,000}{1.2250} = 7,346.94$
4. $PV_4 = \frac{0}{{(1 + 0.07)^4}} = 0$
5. $PV_5 = \frac{25,000}{{(1 + 0.07)^5}} = \frac{25,000}{1.4026} = 17,818.71$
6. $PV_6 = \frac{8,000}{{(1 + 0.07)^6}} = \frac{8,000}{1.5007} = 5,330.86$

Total Present Value:

Now, summing all the present values:

$PV = 9,345.79 + 5,241.48 + 7,346.94 + 0 + 17,818.71 + 5,330.86 = 45,083.78$

Conclusion:

The total present value of the future payments is $45,083.78.

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

Here are 5 related questions:

1. What if the discount rate changes to 10%?
2. How does changing the timing of payments affect present value?
3. How is present value applied in financial decision-making?
4. Can you calculate present value for perpetuities?
5. How do annuities differ from the above example?

Tip: The further away a cash flow occurs, the lower its present value due to the time value of money.