A firm has issued a perpetuity with a total face value of 100 million dollars and a coupon rate of 5.8%. If the risk free rate equals 5.8% and investors require a rate of return of 10.6% from the perpetuity, what's the amount the firm raised through the issue?
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A. B. C. D.D
The price of a perpetuity that pays C per year, at a discount rate of R, equals C/R. Hence, the price of the perpetuity issue = $(100*5.8%/10.6% ) million = $54.72 million.
To calculate the amount the firm raised through the perpetuity issue, we need to use the formula for the present value of a perpetuity:
PV = C / r
where PV is the present value, C is the coupon payment, and r is the required rate of return.
In this case, the face value of the perpetuity is $100 million, and the coupon rate is 5.8%. The coupon payment is calculated as a percentage of the face value, so the coupon payment would be (5.8% * $100 million) / 100 = $5.8 million.
The required rate of return is given as 10.6%. To convert it into a decimal, we divide by 100, so r = 10.6% / 100 = 0.106.
Now, we can substitute the values into the formula:
PV = $5.8 million / 0.106 = $54.72 million
Therefore, the amount the firm raised through the perpetuity issue is $54.72 million.
The correct answer is D. $54.72 million.