Question

An unusual security promises to pay the amount of $1,000 at the end of 12 years (nothing between now and year 12), and then grows that amount by 5% per year forever. Which of the following comes closest to an estimate of the price of this unusual security if the discount rate is 19%?

		$1,054
		$20,000
		$2,951
		$6,000
		$45,667

Answer 1

Answer is $1,054

Expected Payment in Year 12 = $1,000
Discount Rate = 19%
Growth Rate = 5%

Value of Security at the end of Year 11 = Expected Payment in Year 12 / (Discount Rate - Growth Rate)
Value of Security at the end of Year 11 = $1,000 / (0.19 - 0.05)
Value of Security at the end of Year 11 = $1,000 / 0.14
Value of Security at the end of Year 11 = $7,142.857

Current Value of Security = Value of Security at the end of Year 11 / (1 + Discount Rate)^11
Current Value of Security = $7,142.857 / 1.19^5
Current Value of Security = $1,054