What is the present value of the following future payments you will receive if the discount rate is 7%? Yr 1 $10,000.00 Yr 2 $6000.00, Yr 3 $9000.00, Yr 4 $0.00, Yr 5 $25,000.00 and Yr 6 $ 8000.00.

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.

What is the present value of the following future payments you will receive if the discount rate is 7%? Yr 1 $10,000.00 Yr 2 $6000.00, Yr 3 $9000.00, Yr 4 $0.00, Yr 5 $25,000.00 and Yr 6 $8000.00.

Calculate the present value of future payments at a 7% discount rate for amounts like $10,000 in Yr 1, $6,000 in Yr 2, and $25,000 in Yr 5. This problem involves the formula for present value (PV) and demonstrates how the time value of money affects future cash flows.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation