Pearson Corporation makes an investment today (January 1, 2012). They will receive $6,000 every December 31st for the next six years (2012 – 2017). If Pearson wants to earn 12% on the investment, what is the most they should invest on January 1, 2012?
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To find out the most Pearson Corporation should invest on January 1, 2012, we need to calculate the present value of the cash flows they will receive over the next six years.
To calculate the present value, we can use the formula:
PV = CF1 / (1+r)^1 + CF2 / (1+r)^2 + ... + CFn / (1+r)^n
Where:
PV = Present Value
CF = Cash Flow
r = Discount rate
In this case, the cash flows are $6,000, and the discount rate is 12% or 0.12. The cash flows occur at the end of each year for six years, so n = 6.
Now let's calculate the present value:
PV = $6,000 / (1+0.12)^1 + $6,000 / (1+0.12)^2 + ... + $6,000 / (1+0.12)^6
Calculating this equation will give us the present value of the investment. The most Pearson Corporation should invest on January 1, 2012, is equal to the present value of the cash flows.
Note: This calculation assumes that the cash flows are received annually and that the discount rate remains constant throughout the investment period.