Question

Personal Finance Problem P6-14 Asset valuation and risk. Laura Drake wishes to estimate the value of an asset expected to provide cash inflows of $3000 per year for each of the next 4 years and $15,000 in 5 years. Her research indicates that she must earn 4% low-risk assets, and 7% on average risk, 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 that 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 your answer in light of your findings in part a.

Please show the formula and your work.

Answer 1

Answer a(1):

If the asset is classified as (1) low-risk,

Required return = 4%

Cash inflows are $3000 per year for each of the next 4 years and $15,000 in 5 years.

NPV = 3000/1.04 + 3000/1.04^2 + 3000/1.04^3 + 3000/1.04^4 + 15000/1.04^5

= $23,218.59

Most Laura should pay for the asset if it is classified as low-risk is = $23,218.59

Answer a(2):

If the asset is classified as (2) average-risk,

Required return = 7%

Cash inflows are $3000 per year for each of the next 4 years and $15,000 in 5 years.

NPV = 3000/1.07 + 3000/1.07^2 + 3000/1.07^3 + 3000/1.07^4 + 15000/1.07^5

= $20,856.43

Most Laura should pay for the asset if it is classified as average-risk is = $20,856.43

Answer a(3):

If the asset is classified as (3) high-risk,

Required return = 14%

Cash inflows are $3000 per year for each of the next 4 years and $15,000 in 5 years.

NPV = 3000/1.14 + 3000/1.14^2 + 3000/1.14^3 + 3000/1.14^4 + 15000/1.14^5

= $16,531.67

Most Laura should pay for the asset if it is classified as high-risk is = $16,531.67

Answer b:

Suppose that 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 = $16,531.67

She should be conservative and should pay the value as calculated assuming the asset to be of high risk.

Answer c:

All else being the same, increasing risk reduces the value of an asset.

As we observe in part a, increase in risk results in investor factoring in higher risk premium in required return and as such the required return from 'low risk' to 'average risk' increases from 4% to 7%. Higher required return reduces the present value of cash inflows resulting in reduction in value.

We observe from part a the value of asset when classified as 'low risk' was $23,218.59 but it when risk level is increased to 'áverage risk' and 'high risk' the values are reduced to $20,856.43 and $16,531.67 respectively.