Question

Laura Drake wishes to estimate the value of an asset expected to provide cash inflows of $2,500 for each of the next 4 years and ​$12,328 in 5 years. Her research indicates that she must earn 4​% on​ low-risk assets, 9​% 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.

Answer 1

Answer (a):

(1) Low-risk, most Laura should pay = $19,207.46

(2) Average -risk, most Laura should pay = $16,111.65

(3) High -risk, most Laura should pay = $14,127.32

Workings:

Answer (b):

If 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​, most she should​ pay = $14,127.32

She should be conservative and pay assuming highest risk and NPV at highest risk is $14,127.32

Answer (c):

Increase in risk results in higher required rate of return since risk premium is factored in.

Discounting at higher required rate of return reduces the expected present value of cash flows and hence expected NPV is reduced.

Lesser NPV will result in lesser Value of Asset.

As we observe as risk increases from low to high, the required rate increases from 4% to 13% and value of assets decreases from $19,207.46 to $14,127.32