contestada

The fair rate is 8%. What is 100 per year, forever, worth now?



2.What is the same 100 per year worth if it only lasts for 15 years?



3.What if the 100 was the past cash flow and we expect it to grow at 5% forever?



4.What if we only get the 100 once at the end of this year?



5.What if it we get it once, at the end of ten years?



6.If we get the 100 each year for ten years and invest each payment in an account that earns 8% how much will be there at the end?

Respuesta :

hyderali230

Answer:

1. $1,250

2. $855.95

3. $3,333.33

4. $92.59

5. $46.32

6. $671.01

Explanation:

1.

$100 per year forever

Constant Cash flow every year forever is actually a perpetuity its present value is

PV of Perpetuity = Cash flow / rate of return

PV of $100 Perpetuity = $100 / 0.08 = $1,250

2.

$100 per year for 15 years

Constant Cash flow every year for specific time period is actually a Annuity  its present value is

PV of annuity = P + P [ ( 1 - ( 1 + r )^-n ) / r ] = $100 + $100 [ ( 1 - ( 1 + 0.08 )^-15 ) / 0.08 ] = $855.95

3.

$100 per year grow at 5% forever

It is a growing perpetuity and its present value will be calculated as follow

Present value of growing perpetuity = Cash flow / Rate of return - growth rate

Present value of growing perpetuity = $100 / 0.08 - 0.05 = $3,333.33

4.

$100 once at the end of this year

Present value = P ( 1 + r)^-n = $100 ( 1 + 0.08 )^-1 = $92.59

5.

$100 once after 10 years

Present value = P ( 1 + r)^-n = $100 ( 1 + 0.08 )^-10 = $46.32

6.

$100 each year for 10 years @ 8%

PV of annuity = P + P [ ( 1 - ( 1 + r )^-n ) / r ] = $100 + $100 [ ( 1 - ( 1 + 0.08 )^-10 ) / 0.08 ] = $671.01

Answer: Please refer to the explanation section

Explanation:

Investment = 100

Interest rate = r = 8%

1. Value of a Perpetual (forever) investment  

Present Value =  Investment/r = 100/0.08 = 1250

Present Value = $ 1250

2. Present Value with a period of 15 years

Present Value = Investment/(1+r)^n

Present Value = 100/(1+0.08)^15 = 31.524170497

Present Value = $ 31.52

3. Present Value of a Perpetual (forever) investment with Growth rate of 5%

Present Value =  Investment/r = 100/0.08 – 0.05 = 3333.333333

Present Value =  $ 3333.33  

4. Future Value if we get 100 at the end of the year

Future Value = investment(1+r) = 100(1+0.08) = 108

Future Value = $ 108

5. Future Value if we get 100 at the end of 10 years

Future Value = investment(1+r) = 100(1+0.08)^10 = 251.524170497

Future Value = $ 251.52

6. Future Value if 100 is reinvested every year for 10 years

Future Value = Payment x [(1+r)^n – 1)/ r]

Future Value = 100 x [(1+0.08)^10 – 1)/ 0.08)

Future Value = 1448.6562466 = $ 1448.66

ACCESS MORE

Otras preguntas