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An asset is projected to generate 12 annual cash flows of $13,000 starting 4 years from...

An asset is projected to generate 12 annual cash flows of $13,000 starting 4 years from today. If the discount rate is 4.8%, how much is this asset worth today? Round to the nearest cent.

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Expert Solution

PV of Annuity:

Annuity is series of cash flows that are deposited at regular intervals for specific period of time. Here cash flows are happened at the end of the period. PV of annuity is current value of cash flows to be received at regular intervals discounted at specified int rate or discount rate to current date.

PV of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r
r - Int rate per period
n - No. of periods

PV of Annuity after 3 Years:

CFs from Year 4 discounted will become PV of Annuity at Year 3.

Particulars Amount
Cash Flow $          13,000.00
Int Rate 4.8000%
Periods 12

PV of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r
= $ 13000 * [ 1 - [(1+0.048)^-12]] /0.048
= $ 13000 * [ 1 - [(1.048)^-12]] /0.048
= $ 13000 * [ 1 - [0.5697]] /0.048
= $ 13000 * [0.4303]] /0.048
= $ 116533.05

PV Today:

Particulars Amount
Future Value $          116,533.05
Int Rate 4.8000%
Periods 3

Present Value = Future Value / ( 1 + r )^n
= $ 116533.05 / ( 1 + 0.048 ) ^ 3
= $ 116533.05 / ( 1.048 ) ^ 3
= $ 116533.05 / 1.151
= $ 101243.06

jeff jeffy answered 1 year ago
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