Question

2. A) What is the present value of a cash flow stream of $10,000 per year at an interest rate of 6% starting one year from today and goes on forever? B) What is the present value of a cash flow stream of $10,000 per year starting one year from today that grows at 3% at an interest rate of 6% starting one year from today and goes on forever? C) What is the present value of a cash flow stream of $10,000 per year starting one year from today at an interest rate of 6% for ten years? C-2) What is the future value of the cash flow stream in part C? D) What is the present value of a cash flow stream of $10,000 per year starting one year from today that grows at 3% at an interest rate of 6% for ten years? This problem is good practice of A) PV of a perpetuity, B) PV of a growing perpetuity, C) PV of an annuity, C-2) FV of an annuity, D) PV of a growing annuity.

Answer 1

A)

PV of perpetuity = Cash flow / interest rate

PV of perpetuity = 10,000 / 0.06

PV of perpetuity = $166,666.67

B)

PV of growing perpetuity = Cash flow / interest rate - growth rate

PV of growing perpetuity = 10,000 / 0.06 - 0.03

PV of growing perpetuity = 10,000 / 0.03

PV of growing perpetuity = $333,333.33

C)

PV of an annuity = Annuity * [ 1 - 1 / ( 1 + r)ⁿ] / r

PV of an annuity = 10,000 * [ 1 - 1 / ( 1 + 0.06)¹⁰] / 0.06

PV of an annuity = 10,000 * 7.360087

PV of an annuity = $73,600.87

C - 2)

FV of an annuity = Annuity * [ ( 1 + r)ⁿ - 1] / r

FV of an annuity = 10,000 * [ ( 1 + 0.06)¹⁰ - 1] / 0.06

FV of an annuity = 10,000 * 13.180795

FV of an annuity = $131,807.95

D)

PV of a growing annuity = (P / r - g) [ 1 - ( 1 + g / 1 + r)ⁿ]

PV of a growing annuity = ( 10,000 / 0.06 - 0.03)[ 1 - ( 1 + 0.03 / 1 + 0.06)¹⁰]

PV of a growing annuity = ( 333,333.33) [ 1 - 0.750436]

PV of a growing annuity = $83,187.99