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P6-14 Asset valuation and riskLaura Drake wishes to estimate the value of an asset expected to provide cash inflows of $3,000 per year for each of the next 4 years and $15,000 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.

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.

The valuation of assets can be computed using the basic valuation model: the value of the asset when the cash flows associated with the asset is given thus, the value of the asset can be calculated by using formula

V₀= CF₁/(1+r)¹ + CF₂/(1+r)² . CF_n/(1+r)ⁿ

V_{0 =} Value of asset at time zero_, CF₁ = Cash flow expected at the end of year t, r = required rate of return, n = time period

Solution:

(1) Calculate the value of the asset should Laura pay, if it is at low-risk:

Value of asset at low risk the required rate of interest is 4%.

V₀= CF₁/(1+r)¹ + CF₂/(1+r)² + CF₃/(1+r)³+ CF₄/(1+r)⁴+ CF₅/(1+r)⁵

= $3,000/(1.04)¹ + $3,000/(1.04)² + $3,000/(1.04)³ + $3,000/(1.04)⁴+ $15,000/(1.04)⁵

= $3,000/1.04+ $3,000/1.08+ $3,000/1.12+ $3,000/1.16 + $15,000/1.21

= $2,884.61 + $2,777.77 + $2,678.57 + $2,586.20 + $12,396.69

Therefore, the amount Laura should pay for the low-risk asset is $23,323.84

(2) Calculate the value of asset should Laura pay, if it is at average-risk:

Value of asset at low risk the required rate of interest is 7%.

V₀= CF₁/(1+r)¹ + CF₂/(1+r)² + CF₃/(1+r)³+ CF₄/(1+r)⁴+ CF₅/(1+r)⁵

= $3,000/(1.07)¹ + $3,000/(1.07)² + $3,000/(1.07)³ + $3,000/(1.07)⁴+ $15,000/(1.07)⁵

= $3,000/1.07+ $3,000/1.14+ $3,000/1.22+ $3,000/1.31+ $15,000/1.40

= $2,803.73 + $2,631.57+ $2,459.01 + $2,290.07 + $10,714.28

Therefore, the amount Laura should pay for the average-risk asset is $20,898.66

(3) Calculate the value of asset should Laura pay, if it is at high-risk:

Value of asset at low risk the required rate of interest is 14%.

V₀= CF₁/(1+r)¹ + CF₂/(1+r)² + CF₃/(1+r)³+ CF₄/(1+r)⁴+ CF₅/(1+r)⁵

= $3,000/(1.14)¹ + $3,000/(1.14)² + $3,000/(1.14)³ + $3,000/(1.14)⁴+ $15,000/(1.14)⁵

= $3,000/1.14+ $3,000/1.29+ $3,000/1.48+ $3,000/1.68+ $15,000/1.92

= $2,631.57 + $2,325.58 + $2,027.02 + $1,785.71 + $7,812.50

Therefore, the amount Laura should pay for the low-risk asset is $16,582.38

Suppose that Laura is unable to assess the risk of the asset and wants to be certain shes making a good deal. On the basis of your findings in part a, what is the most she should pay? Why?

- Since Laura is unable to assess the risk of the asset and wants to make certain shes making a good deal from the calculations above it is evident that the asset has the lowest price at the highest risk point of 14%, required the rate of return. Therefore, Laura should select the price of $16,582.38, presuming the highest risk.

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.

- As the required rate of return increases, the value of asset decreases. It is evident from the above calculations that the asset has the highest value, $23,323.84 at the rate of return of 4%. The value of the asset is decreasing with the increase in the rate and it is the lowest at 14%.