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Part 1

Asset valuation and risk  Personal Finance Problem   Laura Drake wishes to estimate the value of an asset expected to provide cash inflows of

$ 4 comma 200

for each of the next 4 years and

​$23 comma 997
 
in 5 years. Her research indicates that she must earn

4

​% 

on​ low-risk assets,

7

​% 

on​ average-risk assets, and

14

​% 

on​ high-risk assets.

a.  Determine what is the most Laura should pay for the asset if it is classified as​ (1) low-risk,​ (2) average-risk, and​ (3) high-risk.

b.  Suppose Laura is unable to assess the risk of the asset and wants to be certain​ she's making a good deal. On the basis of your findings in part

a​, 

what is the most she should​ pay? Why?

c. All else being the​ same, what effect does increasing risk have on the value of an​ asset? Explain in light of your findings in part

 a.

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Part 1

a. ​ (1) The most Laura should pay for the asset if it is classified as​ low-risk is

​$34,983.85

. 

​(Round to the nearest​ cent.)

To solve this asset valuation problem, we need to use the **present value** (PV) concept, which calculates the value of future cash flows in today's terms. The formula for calculating the present value of future cash flows is:

\[
PV = \frac{{CF_1}}{{(1 + r)^1}} + \frac{{CF_2}}{{(1 + r)^2}} + \dots + \frac{{CF_n}}{{(1 + r)^n}}
\]
Where:
- $ CF_i $ is the cash flow in year $ i $,
- $ r $ is the required rate of return (based on risk level),
- $ n $ is the number of years.

### Part a
Let's compute the present value of the asset for three different risk levels.

#### Cash flows:
- $ CF_1 = CF_2 = CF_3 = CF_4 = 4,200 $ for the next 4 years.
- $ CF_5 = 23,997 $ in year 5.

#### (1) Low-risk asset: $ r = 4\% $
\[
PV_{\text{low-risk}} = \frac{{4200}}{{(1 + 0.04)^1}} + \frac{{4200}}{{(1 + 0.04)^2}} + \frac{{4200}}{{(1 + 0.04)^3}} + \frac{{4200}}{{(1 + 0.04)^4}} + \frac{{23997}}{{(1 + 0.04)^5}}
\]

#### (2) Average-risk asset: $ r = 7\% $
\[
PV_{\text{average-risk}} = \frac{{4200}}{{(1 + 0.07)^1}} + \frac{{4200}}{{(1 + 0.07)^2}} + \frac{{4200}}{{(1 + 0.07)^3}} + \frac{{4200}}{{(1 + 0.07)^4}} + \frac{{23997}}{{(1 + 0.07)^5}}
\]

#### (3) High-risk asset: $ r = 14\% $
\[
PV_{\text{high-risk}} = \frac{{4200}}{{(1 + 0.14)^1}} + \frac{{4200}}{{(1 + 0.14)^2}} + \frac{{4200}}{{(1 + 0.14)^3}} + \frac{{4200}}{{(1 + 0.14)^4}} + \frac{{23997}}{{(1 + 0.14)^5}}
\]

Let's calculate the present values for each risk level. I'll start with the low-risk scenario.The present values for the asset based on the different risk levels are:

1. **Low-risk asset (4%)**: \$34,969.34
2. **Average-risk asset (7%)**: \$31,335.82
3. **High-risk asset (14%)**: \$24,700.88

### Part b
If Laura is uncertain about the asset's risk and wants to ensure she's making a good deal, she should base her decision on the most conservative estimate. In this case, the asset should be considered as high-risk to avoid overpaying. Therefore, the most Laura should pay is **\$24,700.88**, which corresponds to the high-risk valuation.

### Part c
Increasing the risk of an asset decreases its present value. This happens because higher risk demands a higher rate of return, which increases the discount rate applied to future cash flows. As a result, the future cash flows are worth less in today's terms. In this case, as risk increased from low (4%) to high (14%), the asset's value dropped significantly from \$34,969.34 to \$24,700.88.

---

Do you want more details or have any questions?

Here are 5 questions to deepen your understanding:

1. How does the time value of money affect asset valuation?
2. What other methods can be used for risk assessment besides discount rates?
3. Can you compare how inflation might influence cash flow valuation?
4. How does the present value concept apply to other financial instruments like bonds?
5. What would happen if the cash flows were not guaranteed (i.e., uncertain)?

**Tip**: Understanding how to adjust for risk using discount rates is essential for sound financial decision-making.

Laura Drake wishes to estimate the value of an asset expected to provide cash inflows of $4,200 for each of the next 4 years and $23,997 in 5 years. She must earn 4% on low-risk assets, 7% on average-risk assets, and 14% on high-risk assets. a) Determine the most she should pay for the asset if it is classified as (1) low-risk, (2) average-risk, and (3) high-risk. b) If she is unsure of the risk, what is the most she should pay based on these findings? c) How does increasing risk affect the value of the asset?

Learn how to calculate the present value of future cash flows under different risk conditions. This problem helps you understand the relationship between risk and asset valuation, covering key finance concepts like present value and time value of money.

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