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Part 1

You have two assets and must calculate their values today based on their payment streams and required returns. Asset 1 has a required return of

6

​% 

and will produce a stream of

​$700
 
starting at year 1 and continuing indefinitely. Asset 2 has a required return of

8

​% 

and will produce an​ end-of-year cash flow of

​$1 comma 000
 
in 1​ year,

$ 1 comma 500
 
in 2​ years, and

​$900
 
in 3 years.

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Part 1

The value of Asset 1 today is

​$enter your response here

. 

​(Round to the nearest​ cent.)

To calculate the value of the two assets, we will use the Present Value (PV) formula.

### **Part 1: Asset 1**

Asset 1 pays a stream of cash flows of $700 starting at the end of year 1 and continuing indefinitely. This is essentially a perpetuity. The formula for the present value of a perpetuity is:

\[
PV = \frac{C}{r}
\]

Where:
- $C = 700$ (the annual cash flow),
- $r = 0.06$ (the required return of 6%).

Let's calculate:

\[
PV_1 = \frac{700}{0.06} = 11,666.67
\]

So, the present value of Asset 1 today is **$11,666.67**.

### **Part 2: Asset 2**

Asset 2 pays different amounts over the next three years. To calculate its value today, we must discount each cash flow to the present using the required return of 8%.

The present value of each cash flow is given by:

\[
PV = \frac{C}{(1+r)^t}
\]

Where:
- $C$ is the cash flow,
- $r = 0.08$ (the required return of 8%),
- $t$ is the year in which the cash flow occurs.

Let's calculate the present value for each year:

1. Year 1: $C = 1,000$
\[
PV_1 = \frac{1,000}{(1 + 0.08)^1} = \frac{1,000}{1.08} = 925.93
\]

2. Year 2: $C = 1,500$
\[
PV_2 = \frac{1,500}{(1 + 0.08)^2} = \frac{1,500}{1.1664} = 1,285.16
\]

3. Year 3: $C = 900$
\[
PV_3 = \frac{900}{(1 + 0.08)^3} = \frac{900}{1.2597} = 714.59
\]

Now, sum these present values to get the total present value of Asset 2:

\[
PV_2 = 925.93 + 1,285.16 + 714.59 = 2,925.68
\]

### **Summary:**
- The value of Asset 1 today is **$11,666.67**.
- The value of Asset 2 today is **$2,925.68**.

Would you like further details or clarification?

Here are 5 related questions to expand your understanding:
1. How would the value of Asset 1 change if the required return was 5%?
2. What if Asset 2 had a 4th year payment—how would you calculate that value?
3. Can you calculate the present value of an increasing perpetuity?
4. How does the discount rate affect the present value of future cash flows?
5. What is the present value of an annuity that pays $1000 annually for 10 years at 6%?

**Tip:** For a perpetuity, a small change in the discount rate can have a significant effect on the present value, especially with large cash flows!

You have two assets and must calculate their values today based on their payment streams and required returns. Asset 1 has a required return of 6% and will produce a stream of $700 starting at year 1 and continuing indefinitely. Asset 2 has a required return of 8% and will produce an end-of-year cash flow of $1,000 in 1 year, $1,500 in 2 years, and $900 in 3 years.

Learn how to calculate the present value of two assets with different cash flow structures. Asset 1 produces an infinite cash flow of $700 at a 6% required return, while Asset 2 has three end-of-year cash flows discounted at 8%. Understand the key formulas and concepts like present value and perpetuity.

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