I am having problems with this problem from my Econcoursework. I understand how

Question

I am having problems with this problem from my Econcoursework. I understand how to do parts 1 and 2, but amhaving trouble with parts 3 and 4. For part 3, how do I dothe calculation for an infinite period? As the time becomeslonger the present value goes to zero, so do i assume a period, oris there an actual method for infinite periods? For part 4,do I simply do the sum for the future value and plug it into thePresent value equation? Not really looking for the solutionhere, but I need some help getting the third and fourth partssolved.

Congratulations! You just won the lottery! You can elect to receiveyour prize in one of four
payment streams:
(i) $1,000,000 now
(ii) $1,500,000 at the end of five years
(iii) $60,000 per year in perpetuity (for ever), with payments madeat the end of each year (so your
first payment comes one year from today)
(iv) $150,000 per year for the next ten years, with payments madeat the end of each year (so your
first payment comes one year from today)

Suppose the annual interest rate is 5% with certainty and inperpetuity. Calculate the present value of
each of the four payment options (i.e., in today’s dollars).Rank for four options from most to least
valuable. You can use Excel or a calculator to solve this, but youmust show the formulas you use.

Explanation / Answer

Answer:

Part (3):

Yes for part 3, which is the case of perpetuity, there is anactual method for calculating present value, as you only want thehints, so here is the formula of perpetuity, and no you don’thave to assume a period of high lenth,

PV = C / r (Payments made at the end, this is your example)

PV = (C / r) * (1+r) (Payment made at the beginning, extraknowledge)

Here,

PV = Present Value of Perpetuity

C = Cash Flow

r = Interest Rate or Discount Rate

Perpetuity is another form of annuity. Annuity means the streamof same cash flows, and these same cash flows are also present inperpetuity, so what makes the difference between them? Answer: Inperpetuity there is no limit of time period, the investor willinvest PV in a bank and will enjoy yearly cash flows forever untilhe/she dies, this is perpetuity while in annuity there are numberof time periods, up to which an investor can get cash flows.

Summary:

Cash flows are constant in both annuity and perpetuity.

While time period is limited in annuity and infinite orunlimited in perpetuity.

Part (4):

Yes, you can simply get the individual future values of $150,000for ten years, 10 times, and then you will have to sum theindividual FVs to get the final answer. But just imagine, if thepayment of $150,000 is made for 50 years and not for 10 years, thenwhat will you do, as then in that case this process will be toolong and too time consuming, so for your example, there is aformula of annuity, or future value annuity. Here it is,

Present Value Ordinary Annuity:

FV = P * [{1 – (1 / (1+r) t)}] /r           (Whenpayment made at the end of period)

Present Value Annuity Due:

FV = P * [{1 – (1 / (1+r) t)}] / r * (1+r)t         (Whenpayment made at the beginning of period)

Future Value Ordinary Annuity: (This isfor your example)

FV = P * [(1+r) t – 1] /r          (Whenpayment made at the end of period)

Future Value Annuity Due:

FV = P * [(1+r) t – 1] / r * (1+r)t        (Whenpayment made at the beginning of period)

Here,

P = Payment per period, $150,000 in your example

r = Interest Rate or Discount Rate = 5% or 0.05 in yourexample

t = (Time) = 10 years in your example

Note: If you want the exact answer, then I canhelp you, you may also first try by yourself, no problem, but I canstill help with this example! I love Finance!

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