An investment offers $100 per year forever. If Peter Wallace’s required rate of return on this investment is 10%, how much is this investment worth to him?
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For a perpetuity, PV = PMT ÷ I = 100 ÷ 0.10 = 1,000.
Compute the present value of a perpetuity with $100 payments beginning four years from now. Assume the appropriate annual interest rate is 10%.
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Compute the present value of the perpetuity at (t = 3). Recall, the present value of a perpetuity or annuity is valued one period before the first payment. So, the present value at t = 3 is 100 / 0.10 = 1,000. Now it is necessary to discount this lump sum to t = 0. Therefore, present value at t = 0 is 1,000 / (1.10)3 = 751.
Nortel Industries has a preferred stock outstanding that pays (fixed) annual dividends of $3.75 a share. If an investor wants to earn a rate of return of 8.5%, how much should he be willing to pay for a share of Nortel preferred stock?
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PV = 3.75 ÷ 0.085 = $44.12.
Given investors require an annual return of 12.5%, a perpetual bond (i.e., a bond with no maturity/due date) that pays $87.50 a year in interest should be valued at:
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87.50 ÷ 0.125 = $700.
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