Question

An investment offers $5,100 per year for 10 years, with the first payment occurring one year from now.

a.	If the required return is 5 percent, what is the value of the investment today? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
b.	What would the value today be if the payments occurred for 35 years? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
c.	What would the value today be if the payments occurred for 65 years? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
d.	What would the value today be if the payments occurred forever? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

a)

Value today = Annuity * [1 - 1 / (1 + r)^n] / r

Value today = 5100 * [1 - 1 / (1 + 0.05)^10] / 0.05

Value today = 5100 * [1 - 0.613913] / 0.05

Value today = 5100 * 7.721735

Value today = $39,380.85

b)

Value today = Annuity * [1 - 1 / (1 + r)^n] / r

Value today = 5100 * [1 - 1 / (1 + 0.05)^35] / 0.05

Value today = 5100 * [1 - 0.18129] / 0.05

Value today = 5100 * 16.374194

Value today = $83,508.39

c)

Value today = Annuity * [1 - 1 / (1 + r)^n] / r

Value today = 5100 * [1 - 1 / (1 + 0.05)^65] / 0.05

Value today = 5100 * [1 - 0.041946] / 0.05

Value today = 5100 * 19.16107

Value today = $97,721.46

d)

Value today = Next year cash flow / discount rate

Value today = 5100 / 0.05

Value today = $102,000.00