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Suppose you invest today and receive in five years. a. What is the internal rate of return​ (IRR) of this​ opportunity? b. Suppose another investment opportunity also requires ​upfront, but pays an equal amount at the end of each year for the next five years. If this investment has the same IRR as the first​ one, what is the amount you will receive each​ year? a. What is the internal rate of return​ (IRR) of this​ opportunity? The IRR of this opportunity is 30.60​%. ​ (Round to two decimal​ places.) b. Suppose another investment opportunity also requires ​upfront, but pays an equal amount at the end of each year for the next five years. If this investment has the same IRR as the first​ one, what is the amount you will receive each​ year? The periodic payment that gives the same IRR is ​$ nothing. ​(Round to the nearest​ cent.)

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jepessoa

Answer:

the numbers are missing, so I looked for a similar question:

  • investment today = $3,000
  • receive $10,250 in 5 years

a) I will use the future value formula to determine the internal rate of return:

future value = present value x (1 + r)ⁿ

  • future value = 10,250
  • present value = 3,000
  • n = 5

10,250 = 3,000 x (1 + r)⁵

(1 + r)⁵ = 10,250 / 3,000 = 3.4166667

⁵√(1 + r)⁵ = ⁵√3.4166667

1 + r = 1.27855826

r = 0.27855826 = 27.86%

b) assuming a $3,000, 27.86%, 5 year annuity, the annual payment will be:

annual payment = principal / FV annuity factor, 27.86%, 5 periods

  • principal = $10,250
  • PV annuity factor, 27.86%, 5 periods = 8.67633

annual payment = $10,250 / 8.67633 = $1,181.38

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