Question

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

Answer 1

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

Answer 2

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