Privateer Equity Partners Limited is putting out a new financial product. The product will start to pay out 1600 dollars from the end of the third year, and after that the payouts will grow by an annual rate of 3 percent forever. If you are able to invest the cash flows at 7.5 percent per annum, what is the present value of this product?a.33075b.123072c.35556d.30767
Question
Privateer Equity Partners Limited is putting out a new financial product. The product will start to pay out 1600 dollars from the end of the third year, and after that the payouts will grow by an annual rate of 3 percent forever. If you are able to invest the cash flows at 7.5 percent per annum, what is the present value of this product?a.33075b.123072c.35556d.30767
Solution
To solve this problem, we need to use the formula for the present value of a growing perpetuity. The formula is:
PV = D / (r - g)
where:
- PV is the present value we are trying to find
- D is the cash flow in the first period
- r is the discount rate
- g is the growth rate
In this case, the cash flow (D) is $1600, the discount rate (r) is 7.5% or 0.075, and the growth rate (g) is 3% or 0.03. However, the cash flow doesn't start until the end of the third year, so we need to discount the value of the perpetuity back to the present.
First, calculate the value of the perpetuity at the end of the second year:
PV = 1600 / (0.075 - 0.03) = $32,000
Then, discount this value back to the present (i.e., to time 0). The formula for the present value of a future amount is:
PV = FV / (1 + r)^n
where:
- FV is the future value
- r is the discount rate
- n is the number of periods
In this case, FV is $32,000, r is 0.075, and n is 2:
PV = 32000 / (1 + 0.075)^2 = $27,675.32
So, the present value of the product is approximately $27,675.32. This is not one of the options given, so there may be a mistake in the problem or the answer choices.
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