Question

2. Laura Drake wishes to estimate the value of an asset expected to provide cash inflows of $ 2400 per year at the end of years 1 through 4 and $13747 at the end of year 5. Her research indicates that she must earn 11 % on low-risk assets, 13 % on average-risk assets, and 24 % 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

Irrespective of the risk-level chosen, the fair value (maximum amount Laura should pay) of any asset should equal the total present value of the cash inflows generated by the asset, discounted at a rate corresponding to the asset's pre-determined risk level. In this case, the risk-level and along with it the discount rate (return earned) can be any one of the three given options.

Annual Cash Inflows from Year 1 to Year 4 = $ 2400 and Year 5 Cash Inflows = $ 13747

(a) Low-Risk: Return Earned = 11 %

Total Present Value of Annual Cash Inflows = 2400 x (1/0.11) x [1-{1/(1.11)^(4)}] + 13747/(1.11)^(5) = $ 15604.05

Average Risk: Return Earned = 13 %

Total Present Value of Annual Cash Inflows = 2400 x (1/0.13) x [1-{1/(1.13)^(4)}] + 13747/(1.13)^(5) = $ 14600.05

High Risk: Return Earned = 24 %

Total Present Value of Annual Cash Inflows = 2400 x (1/0.24) x [1-{1/(1.24)^(4)}] + 13747/(1.24)^(5) = $ 10459.47

(b) If Laura is unable to determine the risk level of the asset, she should go ahead with the conservative assumption that the asset has the highest possible level of risk. This would imply paying a maximum price of $ 10459.47 for the asset which naturally is the lowest among the three possible prices calculated in part(a). If the lowest possible price is paid (by assuming the highest possible level of risk), the investor assures for herself a greater degree of safety.

(c) All else remaining constant, increasing the risk level increases the required rate of return for the investor, thereby pushing down the maximum possible price of the asset for a given level of asset cashflows.