2. A) What is the present value of a cash flow stream of $10,000 per year at an
ID: 2818744 • Letter: 2
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.
Explanation / Answer
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
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