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

7

​% 

and will produce a stream of

​$300
 
starting at year 1 and continuing indefinitely. Asset 2 has a required return of

10

​% 

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

​$1 comma 200
 
in 1​ year,

$ 1 comma 300
 
in 2​ years, and

​$800
 
in 3 years.

Question content area bottom

Part 1

The value of Asset 1 today is

​$4285.71

. 

​(Round to the nearest​ cent.)

Part 2

The value of Asset 2 today is

​$enter your response here

. 

​(Round to the nearest​ cent.)

Let's calculate the present value of both assets.

### **Part 1: Asset 1**
- Asset 1 has a required return of 7% and produces a perpetual stream of $300 starting at year 1.

This is a perpetuity, and the present value of a perpetuity is calculated by:

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

Where:
- $C$ is the annual cash flow ($300),
- $r$ is the required return (7% or 0.07).

\[
PV = \frac{300}{0.07} = 4285.71
\]

This matches the provided value of $4,285.71.

### **Part 2: Asset 2**
- Asset 2 has a required return of 10% and will produce the following cash flows:
  - $1,200 in 1 year,
  - $1,300 in 2 years,
  - $800 in 3 years.

We need to calculate the present value of each cash flow using the formula for the present value of future cash flows:

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

Where:
- $CF$ is the cash flow,
- $r$ is the required return (10% or 0.10),
- $t$ is the time period.

Let's calculate the present value of each cash flow separately:

1. Present value of $1,200 in 1 year:
\[
PV_1 = \frac{1200}{(1 + 0.10)^1} = \frac{1200}{1.10} \approx 1090.91
\]

2. Present value of $1,300 in 2 years:
\[
PV_2 = \frac{1300}{(1 + 0.10)^2} = \frac{1300}{1.21} \approx 1074.38
\]

3. Present value of $800 in 3 years:
\[
PV_3 = \frac{800}{(1 + 0.10)^3} = \frac{800}{1.331} \approx 601.80
\]

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

\[
PV_{\text{Total}} = 1090.91 + 1074.38 + 601.80 \approx 2767.09
\]

So, the value of **Asset 2 today is $2,767.09** (rounded to the nearest cent).

---

Would you like more details or have any questions?  
Here are 5 related questions for further exploration:
1. How would the value of Asset 1 change if the required return increased to 10%?
2. How does the present value formula change for semi-annual payments instead of annual payments?
3. How would Asset 2’s value be affected by an additional cash flow in year 4?
4. What happens to the present value of a perpetuity when the interest rate approaches zero?
5. How do bond pricing models relate to the present value of cash flow streams?

**Tip:** When calculating present values for multiple cash flows, handle each cash flow individually, then sum them up for accuracy.

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 7% and will produce a stream of $300 starting at year 1 and continuing indefinitely. Asset 2 has a required return of 10% and will produce an end-of-year cash flow of $1,200 in 1 year, $1,300 in 2 years, and $800 in 3 years.

Learn how to calculate the present value of two assets using the perpetuity formula and discounted cash flow approach. Asset 1 provides a perpetual stream of $300 with a 7% required return, and Asset 2 offers varying cash flows with a 10% required return. Detailed step-by-step calculations included.

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