Question

Asset valuation and risk Personal Finance Problem Laura Drake wishes to estimate the value of an asset expected to provide cash inflows of $3,400 for each of the next 4 years and $15,139 in 5 years. Her research indicates that she must earn 3% on low-risk assets, 8% on average-risk assets, and 13% 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. a. (1) The most Laura should pay for the asset if it is classified as low-risk is $ (Round to the nearest cent.) (2) The most Laura should pay for the asset if it is classified as average-risk is $ (Round to the nearest cent.) (3) The most Laura should pay for the asset if it is classified as high-risk is $ . (Round to the nearest cent.) 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, the most she should pay is $ . (Round to the nearest cent.) 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. (Select the best answer below.) O A. By increasing the risk of cash flows received from an asset, the required rate of return increases, which reduces the value of the asset. O B. By increasing the risk of cash flows received from an asset, the required rate of return increases, which increases the value of the asset. O C. By increasing the risk of cash flows received from an asset, the required rate of return decreases, which reduces the value of the asset.

Answer 1

a) the price that Laura should pay = PV of the asset's CFs

1) If risk is low, the PV of the asset is calculated below:

Year	CF	Discount Factor		Discounted CF
1	$   3,400.00	1/(1+0.03)^1=	0.970873786	0.970873786407767*3400=	$   3,300.97
2	$   3,400.00	1/(1+0.03)^2=	0.942595909	0.942595909133754*3400=	$   3,204.83
3	$   3,400.00	1/(1+0.03)^3=	0.915141659	0.91514165935316*3400=	$   3,111.48
4	$   3,400.00	1/(1+0.03)^4=	0.888487048	0.888487047915689*3400=	$   3,020.86
5	$15,139.00	1/(1+0.03)^5=	0.862608784	0.862608784384164*15139=	$ 13,059.03
				PV = Sum of all Discounted CF	$ 25,697.17

2) If risk is average, the PV of the asset is calculated below:

Year	CF	Discount Factor		Discounted CF
1	$   3,400.00	1/(1+0.08)^1=	0.925925926	0.925925925925926*3400=	$   3,148.15
2	$   3,400.00	1/(1+0.08)^2=	0.85733882	0.857338820301783*3400=	$   2,914.95
3	$   3,400.00	1/(1+0.08)^3=	0.793832241	0.79383224102017*3400=	$   2,699.03
4	$   3,400.00	1/(1+0.08)^4=	0.735029853	0.735029852796453*3400=	$   2,499.10
5	$15,139.00	1/(1+0.08)^5=	0.680583197	0.680583197033753*15139=	$ 10,303.35
				PV = Sum of all Discounted CF	$ 21,564.58

3) If risk is high, the PV of the asset is calculated below:

Year	CF	Discount Factor		Discounted CF
1	$   3,400.00	1/(1+0.13)^1=	0.884955752	0.884955752212389*3400=	$   3,008.85
2	$   3,400.00	1/(1+0.13)^2=	0.783146683	0.783146683373796*3400=	$   2,662.70
3	$   3,400.00	1/(1+0.13)^3=	0.693050162	0.693050162277696*3400=	$   2,356.37
4	$   3,400.00	1/(1+0.13)^4=	0.613318728	0.613318727679377*3400=	$   2,085.28
5	$15,139.00	1/(1+0.13)^5=	0.542759936	0.542759935999449*15139=	$   8,216.84
				PV = Sum of all Discounted CF	$ 18,330.05

b) If Laura is not able to assess risk and wants to be certain then she should assume the highest possible risk and pay $18330.05

c) As risk increases the value of the asset falls as we can see in the above calculations. Therefore the correct option is the first option that when risk increases, required rate increases and asset value falls.