Answer:
PV at time zero=$12621.48
Step-by-step explanation:
Looking at the given data we can see that perpetuity is increasing arithmetically with payment after ever 4 years
Starting payment is $300 at time 6
payment reaches to $900 at time 14
Present value of the 3rd payment = $535.35
Note:
Considering the 4 year interval starting time will be at 2 which is half i.e 0.5 of 4 year that is why we are going to use 3.5 years for any time and 0.5 years for time zero
Present value of time 14 at $900 is discounted back to $535.35 for 3.5 years period
PV=P/(1+i)^n
where:
P is the given value at the time
n is the number of years
i is the interest rate
PV is the present value in given time
Solving above equation for time 4:
535.35*(1+i)^3.5=900
i=0.1599≅0.16
So interest i is 16%
Perpetuity immediate at present time:
P/i +Q/i^2
where:
P is $300 which is amount of first period
Q is $300 which is the increment after each interval
300/0.16 +300/0.16^2 =13593.75
The above value is discount for 2 years not for 4 years
So in order to find present value at time zero we must discount it back
Now:
PV=P/(1+i)^n
where:
P is the given value at the time
n is the number of years
i is the interest rate
PV is the present value in given time
PV=$13593.75/(1=0.16)^0.5
PV at time zero=$12621.48
