1. Sasha owns two investments, A and B, that have a combined total value of 30,4
ID: 2811105 • Letter: 1
Question
1. Sasha owns two investments, A and B, that have a combined total value of 30,400 dollars. Investment A is expected to pay 25,300 dollars in 7 year(s) from today and has an expected return of 7.7 percent per year. Investment B is expected to pay 22,374 dollars in T years from today and has an expected return of 4.74 percent per year. What is T, the number of years from today that investment B is expected to pay 22,374 dollars? Round your answer to 2 decimal places (for example, 2.89, 14.70, or 6.00).
2. Gomi Waste Disposal is planning to sell its Columbus, Memphis, and Detroit facilities. The firm expects to sell each of the three facilities for the same, positive cash flow of W dollars. The firm expects to sell its Columbus facility in Z years, its Memphis facility in Z years, and its Detroit facility in T years. The cost of capital for the Columbus facility is Q percent, the cost of capital for the Detroit facility is Q percent, and the cost of capital for the Memphis facility is P percent. We know that T > Z > 0 and Q > P > 0. The cash flows from the sales are the only cash flows associated with the various facilities. Based on the information in the preceding paragraph, which one of the following assertions is true?
The Detroit facility is the most valuable of the 3 facilities
The Memphis facility is the most valuable of the 3 facilities
None of the other assertions is true
The Columbus facility is the most valuable of the 3 facilities
Two of the three facilities have equal value and those two facilities are more valuable than the third facility or all three facilities have the same value
The Detroit facility is the most valuable of the 3 facilities
The Memphis facility is the most valuable of the 3 facilities
None of the other assertions is true
The Columbus facility is the most valuable of the 3 facilities
Two of the three facilities have equal value and those two facilities are more valuable than the third facility or all three facilities have the same value
Explanation / Answer
(1) Investment A and B together have a combined value of $ 30400. It must be noted that the combined value of the two investments are the sum of their respective future cash flows' present value discounted at their respective appropriate discount rate (expected return rate).
Investment A Expected Return = 7.7 % and Investment Tenure = 7 years.
Future Cash Flow Value = $ 25300
PV of Investment A's Cash Flow = 25300 / (1.077)^(7) = $ 15052.57
Therefore, PV of Investment B's Future Cash Flow = Combined Investment Value - PV Investment A's Future Cash Flow = 30400 - 15052.57 = $ 15347.43
Investment B has a future cash flow of $ 22374 which when discounted at the expected return rate of 4.74 % over the investment tenure of T years should give a value equal to the PV of Investment B's Future Cash Flows.
Therefore, 15347.43 = 22374 / (1.0474)^(T)
(22374 / 15347.43) = (1.0474)^(T)
Using the logarith function to solve the above equation, we get:
T = 8.139 or 8.14 years approximately.
(2)
All three facilities have equal sale cash flow of $ W. The value of each facility is given by the following relationship:
Value(facility) = W / (1+R)^(t) where R is the cost of capital and t is the time of sale for each facility. As is observable a low value of t and R would lead to a higher facility value.
The Memphis facility has the lowest cost of capital of P as Q>P. Further, Columbus facility and Memphis facility are both sold after Z years, thereby implying t = Z years. However, as R = Q for Columbus is greater than R =P for Memphis, the latter has the higher value of the two. The Detroit facility will have a lower value than the Memphis facility because its cost of capital Q and time T are both greater than the corresponding values for Memphis. Hence, the Memphis facility has the highest value.
Moreover, the statements 1 and 4 are both false as statement 2 is true. Additionally, none of the three facilities has equal value as they have different (t,R) combination. Hence, statement 5 is false. The last remaining statement 3 is meaningless as statement 2 has already proven to be true.
Therefore, the only true statement is statement 2.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.