Problem $6-17$

Asset valuation and risk. Laura Drake wishes to estimate the value of an asset expected to provide cash inflows of $\backslash (\backslash$$ $3,000\backslash )$ per year for each of the next four years and $\backslash (\backslash$$ $15,000\backslash )$ in five years. Her research indicates that she must earn $\backslash (4\backslash \%\backslash )$ on low$-$risk assets, $\backslash (7\backslash \%\backslash )$ on average$-$risk assets, and $\backslash (14\backslash \%\backslash )$ 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$.$

Solution

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?

To be sure of a good deal, Laura must take care to not understate risk. A conservative approach is to pay no more than $,$ the present value of the asset assuming the highest possible risk $($and highest discount rate$).$

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$.$