A company has identified the following investments as looking promising. Each requires an initial investment of $1.2 million. Which is the best investment?Question 4 options:
A) a perpetuity that generates a cash flow at the end of year 1 of $100,000, has a growth rate of 1.25%, and a cost of capital of 10%
B) a perpetuity that generates a cash flow at the end of year 1 of $800,000, has a growth rate of 2.25%, and a cost of capital of 12%
C) an investment that generates a cash flow of $400,000 at the end of each of the next five years, when the cost of capital is 6%
D) an investment that generates a cash flow of $200,000 at the end of each of the next ten years, when the cost of capital is 6%
Maybe....?
To determine the best investment out of the options provided, we need to calculate the present value of each investment and compare them.
For option A, we have a perpetuity that generates a cash flow of $100,000 at the end of year 1, with a growth rate of 1.25% and a cost of capital of 10%. To calculate the present value of this perpetuity, we can use the formula:
PV = CF / (r - g),
where PV is the present value, CF is the cash flow, r is the discount rate, and g is the growth rate. Plugging in the values, we get:
PV_A = $100,000 / (0.10 - 0.0125) = $1,428,571.
For option B, we have a perpetuity that generates a cash flow of $800,000 at the end of year 1, with a growth rate of 2.25% and a cost of capital of 12%. Using the same formula:
PV_B = $800,000 / (0.12 - 0.0225) = $8,000,000.
For option C, we have an investment that generates a cash flow of $400,000 at the end of each of the next five years, with a cost of capital of 6%. To calculate the present value of these cash flows, we can use the formula for the present value of an ordinary annuity:
PV = CF * (1 - (1 + r)^(-n)) / r,
where n is the number of years. Plugging in the values, we get:
PV_C = $400,000 * (1 - (1 + 0.06)^(-5)) / 0.06 = $1,848,932.
For option D, we have an investment that generates a cash flow of $200,000 at the end of each of the next ten years, with a cost of capital of 6%. Again, using the formula for the present value of an ordinary annuity:
PV_D = $200,000 * (1 - (1 + 0.06)^(-10)) / 0.06 = $1,510,823.
Comparing the present values, we can see that option B has the highest present value of $8,000,000. Therefore, option B is the best investment out of the options provided.