Question

An investor is considering an investment that pays a cash flow of $200 annually in perpetuity. The first cash flow is in the 4th year. If the interest rate is 12%, what is the present value of this investment? (round your final answer to the nearest dollar)

What is the present value of a security that will pay $30,000 in 20 years if securities of equal risk pay 5% annually? Assume annual compounding. (round to the nearest dollar and do not include the $ in your answer, e.g., 30,000)

Answer 1

Part A:

PV of perpectual ANnuity = CF / Int rate

PV of ANnuity after 3 Years = $ 200 / 12%

= $ 1666.67

PV of annuity Today = PV of PV of annuity after 3 Years

Present Value:

Present value is current value of Future cash flows discounted at specified discount Rate.

PV = FV / (1+r)^n
Where r is Int rate per period
n - No. of periods

Particulars	Amount
Future Value	$              1,666.67
Int Rate	12.0000%
Periods	3

Present Value = Future Value / ( 1 + r )^n
= $ 1666.67 / ( 1 + 0.12 ) ^ 3
= $ 1666.67 / ( 1.12 ) ^ 3
= $ 1666.67 / 1.4049
= $ 1186.3

PV of perpectual annuity is $ 1186.30

Part B:

Particulars	Amount
Future Value	$            30,000.00
Int Rate	5.0000%
Periods	20

Present Value = Future Value / ( 1 + r )^n
= $ 30000 / ( 1 + 0.05 ) ^ 20
= $ 30000 / ( 1.05 ) ^ 20
= $ 30000 / 2.6533
= $ 11306.68

Present Value of $ 20000 today is $ 11306.68