assuming that the firm's goal is to maximize present value of the profits in the subsequent 5 years, which of the following flows of profit would achieve that goal? Justify your answer. Note that the flows are represented by 5-tuples, i.e. five number each of which represents profit in the respective year. Assume that the numbers represent profits in $. Use r=5% for discounting the value of future profits.

Question

assuming that the firm's goal is to maximize present value of the profits in the subsequent 5 years, which of the following flows of profit would achieve that goal? Justify your answer. Note that the flows are represented by 5-tuples, i.e. five number each of which represents profit in the respective year. Assume that the numbers represent profits in $. Use r=5% for discounting the value of future profits.

a: (1000, 1000, 1000, 1000, 1000)
b: (800, 900, 1000, 1100, 1200)
c: (1200, 1100, 1000, 900, 800)

Answer 1

I believe the answer is C.

Answer 2

To determine which flow of profit would maximize the present value of the profits over the subsequent 5 years, we need to calculate the present value (PV) of each flow and choose the one with the highest value.

The present value of an amount of money received in the future can be calculated using the following formula: PV = FV / (1 + r)^n, where PV is the present value, FV is the future value, r is the discount rate, and n is the number of periods.

Let's calculate the present value for each option:

a: (1000, 1000, 1000, 1000, 1000)
PV(a) = 1000 / (1 + 0.05)^1 + 1000 / (1 + 0.05)^2 + 1000 / (1 + 0.05)^3 + 1000 / (1 + 0.05)^4 + 1000 / (1 + 0.05)^5
= 1000 / 1.05 + 1000 / 1.1025 + 1000 / 1.1576 + 1000 / 1.2155 + 1000 / 1.2763
= 952.38 + 907.03 + 864.20 + 823.05 + 783.53
= 4330.19

b: (800, 900, 1000, 1100, 1200)
PV(b) = 800 / (1 + 0.05)^1 + 900 / (1 + 0.05)^2 + 1000 / (1 + 0.05)^3 + 1100 / (1 + 0.05)^4 + 1200 / (1 + 0.05)^5
= 800 / 1.05 + 900 / 1.1025 + 1000 / 1.1576 + 1100 / 1.2155 + 1200 / 1.2763
= 761.90 + 816.33 + 866.03 + 910.68 + 950.00
= 5304.94

c: (1200, 1100, 1000, 900, 800)
PV(c) = 1200 / (1 + 0.05)^1 + 1100 / (1 + 0.05)^2 + 1000 / (1 + 0.05)^3 + 900 / (1 + 0.05)^4 + 800 / (1 + 0.05)^5
= 1200 / 1.05 + 1100 / 1.1025 + 1000 / 1.1576 + 900 / 1.2155 + 800 / 1.2763
= 1142.86 + 997.73 + 865.80 + 744.53 + 632.16
= 5383.08

By calculating the present value of each option, we can see that option c, (1200, 1100, 1000, 900, 800), achieves the highest present value of $5383.08. Therefore, option c would maximize the present value of the profits over the subsequent 5 years, assuming the goal is to maximize the present value of profits.