Question

In: Finance

What is the present value​ (PV) of an investment that pays $90,000 every year for four...

What is the present value​ (PV) of an investment that pays $90,000 every year for four years if the interest rate is 9​% ​APR, compounded​ quarterly?

Solutions

Expert Solution

Effective Annual Rate = ( 1 + r ) ^ n - 1
r = Int Rate per period
n = No.of periods per anum

Particulars Amount
Ret period 2.2500%
No. of periods       4.0000

EAR = [ ( 1 + r ) ^ n ] - 1
= [ ( 1 + 0.0225 ) ^ 4 ] - 1
= [ ( 1.0225 ) ^ 4 ] - 1
= [ 1.0931 ] - 1
= 0.093083
I.e EAR is 9.308332 %

As the CFs are yearly CFs, Effective rate per anum is calculated.

Present value of Investment:

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

Particulars Amount
Cash Flow $          90,000.00
Int Rate 9.3083%
Periods 4

PV of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r
= $ 90000 * [ 1 - [(1+0.0931)^-4]] /0.0931
= $ 90000 * [ 1 - [(1.0931)^-4]] /0.0931
= $ 90000 * [ 1 - [0.7005]] /0.0931
= $ 90000 * [0.2995]] /0.0931
= $ 289612.35
PV of Investment is $ 289612.35


Related Solutions

What is the present value​ (PV) of an investment that pays $90,000 every year for four...
What is the present value​ (PV) of an investment that pays $90,000 every year for four years if the interest rate is 9​% ​APR, compounded​ quarterly?
What is the present value​ (PV) of an investment that pays $90,000every year for four...
What is the present value (PV) of an investment that pays $90,000 every year for four years if the interest rate is 9% APR, compounded quarterly?
What is the present value of an investment that pays $200 every other year forever if...
What is the present value of an investment that pays $200 every other year forever if the first cash flow occurs in two years? What is the value when the first cash flow occurs in one year? The opportunity cost of capital is 12% per year.
Urgently required. What is the present value (PV) today of a stable perpetuity that pays $11,000...
Urgently required. What is the present value (PV) today of a stable perpetuity that pays $11,000 every 3 years, starting 7 years from today? The appropriate annual discount rate is 12% p.a. Round your answer to the nearest dollar. Do not include the $ symbol nor the separating comma, if any Thus, for example, if the PV is $24,323 55 write 24324 in the answer box. IMPORTANT. Use at least 4 decimals in all your intermediate calculations In the case...
What is the present value of an ordinary annuity that pays $300 every six months for...
What is the present value of an ordinary annuity that pays $300 every six months for four years if the discount rate is 5.6% per year? Question 5 options: A) $1,994.34 B) $2,109.56 C) $2,123.79 D) $2,098.25 E) $2,281.41
An investment costs $200,000. If the present value (PV) of all the future cash flows is...
An investment costs $200,000. If the present value (PV) of all the future cash flows is $175,000, which of the following statements is correct? a. The project should be rejected since the Profitability Index is less than 1. b. The project should be rejected since the NPV is $25,000. c. The project should be accepted since the Profitability Index is greater than 0 d. The project should be rejected since the NPV is -$175,000.
What is the value today of an investment that pays $2,200 every two years forever starting...
What is the value today of an investment that pays $2,200 every two years forever starting one year from today and $4,400 every two years forever starting two years from today if the APR is 8.50% compounded quarterly? That is, a $2,200 payment occurs 1 year from today, a $4,400 payment 2 years from today, a $2,200 payment 3 years from today, and so on. Question 21 options: $37,081 $38,008 $38,935 $39,862 $40,789
Consider an investment that pays $39.66 in year 1, and then stabilizes and pays $4.73 every...
Consider an investment that pays $39.66 in year 1, and then stabilizes and pays $4.73 every year forever after that (the first cash flow is in year 2) This firm does not intend to grow and has an interest rate (required rate of return) of 7%.  What is the present value of this investment opportunity? Give your answer to two decimals.
what is the present value of a perpetuity that pays $8.50 per year forever (at the...
what is the present value of a perpetuity that pays $8.50 per year forever (at the end of every year) if the appropriate discount rate is 7%
What does change in (PV) present value mean to a company?
What does change in (PV) present value mean to a company?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT