A company has identified the following investments as looking promising. Each requires an initial investment of $1.2 million. Which is the best investment?
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 $80,000, 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%
To determine which investment is the best, we need to calculate the present value of each investment and compare them. We can use the present value formula, which takes into account the cash flows, growth rates, and cost of capital.
For option a, we have a perpetuity with a cash flow of $100,000 at the end of year 1, a growth rate of 1.25%, and a cost of capital of 10%. To calculate the present value, we can use the formula:
PV = CF / (r - g)
where PV is the present value, CF is the cash flow, r is the cost of capital, and g is the growth rate. Plugging in the values, we get:
PV = $100,000 / (0.10 - 0.0125)
PV = $100,000 / 0.0875
PV = $1,142,857.14
For option b, we have a perpetuity with a cash flow of $80,000 at the end of year 1, a growth rate of 2.25%, and a cost of capital of 12%. Using the same formula, we can calculate the present value:
PV = $80,000 / (0.12 - 0.0225)
PV = $80,000 / 0.0975
PV = $820,512.82
For option c, we have an investment with cash flows of $400,000 at the end of each of the next five years and a cost of capital of 6%. To calculate the present value, we can use the formula for the present value of an annuity:
PV = CF * (1 - (1 + r)^-n) / r
where CF is the cash flow, r is the cost of capital, and n is the number of periods. Plugging in the values, we get:
PV = $400,000 * (1 - (1 + 0.06)^-5) / 0.06
PV = $400,000 * (1 - 0.7473) / 0.06
PV = $400,000 * 0.2527 / 0.06
PV = $1,680,666.67
For option d, we have an investment with cash flows of $200,000 at the end of each of the next ten years and a cost of capital of 6%. Using the same formula for the present value of an annuity:
PV = $200,000 * (1 - (1 + 0.06)^-10) / 0.06
PV = $200,000 * (1 - 0.5584) / 0.06
PV = $200,000 * 0.4416 / 0.06
PV = $1,323,200
Comparing the present values, we can see that the highest present value is for option c, which has a present value of $1,680,666.67. Therefore, option c is the best investment among the given options.