An investment offers $6,500 per year for 20 years, with the first payment occurr
ID: 2615374 • Letter: A
Question
An investment offers $6,500 per year for 20 years, with the first payment occurring one year from now. If the required return is 7 percent, what is the value of the investment? (Do not round intermediate calculations and round your final answer to 2 decimal places, e.g., 32.16.) Present value What would the value be if the payments occurred for 45 years? (Do not round intermediate calculations and round your final answer to 2 decimal places, e.g., 32.16.) Present value What would the value be if the payments occurred for 70 years? (Do not round intermediate calculations and round your final answer to 2 decimal places, e.g., 32.16.) Present value What would the value be if the payments occurred forever? (Do not round intermediate calculations and round your final answer to 2 decimal places, e.g., 32.16.) Present valueExplanation / Answer
Formula for PV of annuity is:
PV = P x [1-(1+r)-n/r]
P = Periodic cash flow = $ 6,500
r = Rate per period = 7 % or 0.07 p.a.
n = Numbers of periods
Requirement 1:
n = 20
PV = $ 6,500 x [1-(1+0.07)-20/0.07]
= $ 6,500 x [1-(1.07)-20/0.07]
= $ 6,500 x [1-(1.07)-20/0.07]
= $ 6,500 x [(1-0.258419)/0.07]
= $ 6,500 x (0.741581/0.07)
= $ 6,500 x 10.59401
= $ 68,861.09
Requirement 2:
n = 45
PV = $ 6,500 x [1-(1+0.07)-45/0.07]
= $ 6,500 x [1-(1.07)-45/0.07]
= $ 6,500 x [1-(1.07)-45/0.07]
= $ 6,500 x [(1- 0.04761349)/0.07]
= $ 6,500 x (0.95238651/0.07)
= $ 6,500 x 13.6055216
= $ 88,435.89
Requirement 3:
n = 70
PV = $ 6,500 x [1-(1+0.07)-70/0.07]
= $ 6,500 x [1-(1.07)-70/0.07]
= $ 6,500 x [1-(1.07)-70/0.07]
= $ 6,500 x [(1- 0.00877275)/0.07]
= $ 6,500 x (0.99122725/0.07)
= $ 6,500 x 14.1603893
= $ 92,042.53
Requirement 4:
Formula for PV of perpetuity is:
PV = Periodic cash flow/Rate of interest
= $ 6,500/0.07 = $ 92,857.14
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