I need the answers to these 3 simple questions ASAP!
Please show working out so I can follow your steps. Thanks!

a.) What is the present value of a $1000 perpetuity discounted back to
the present at 8 percent?

b.) What is the present value of a $1000 annuity for 10 years, with
the first payment occuring at the end of year 10 (that is, ten $1000
payments occuring at the end of year 10 through year 19), given an
appropriate discount rate of 10 percent?

c.) Given a 10-percent discount rate, what is the present value of a
perpetuity of $1000 per year if the first payment does not begin until
the end of year 10?

Altheg ?

Each of these is a little different case of annuity calculations, with
only (b) being more complex than normal.

Perpetuities are figured as:

P0 = D1 / r

Where,
P0 = today's price
D1 = dividends in period 1
r = required rate of return (in decimals)

A.	P = $1,000/0.08 = $12,500

C.  This also helps us arrive at an answer to (C) because THAT annuity
will be worth $12,500 ? but must be discounted back to the present by
10 years:

NPV = $12,500 / (1.10)^10 = $12,500 / 2.5937 = $4,819.37

B.	Now let?s go to $1,000 for years 10, 11, 12, 13 . . . 19.  This can
be done quickly in a spreadsheet but it looks like this:

NPV = Di / (1 + r)*i

Where,
Di = payment in year i
r = discount rate or required rate of return (in decimals)
i = complete years at point payment is received

Year 10: $1,000 / (2.5937) = $385.55
Year 11: $1,000 / (1.10)^11 = $1,000/2.8531 = $350.50
Year 12: $1,000 / (1.10)^12 = $1,000/3.1384 = $318.63
Year 13: $1,000 / 3.4523 = $289.66
Year 14: $1,000 / 3.7972 = $263.35
Year 15: $1,000 / 4.1772 = $239.39
Year 16: $1,000 / 4.5950 = $217.63
Year 17: $1,000 / 5.0545 = $197.84
Year 18: $1,000 / 5.5599 = $179.86
Year 1: $1,000 / (1.10)^19 = $1,000/ 6.1159 = $163.51

TOTAL NPV = $2,605.92


Best regards,

Omnivorous-GA

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Clarification of Answer by omnivorous-ga on 04 Aug 2005 03:50 PDT

Altheg --

I realized after submitting this that the answer to (B) is incorrect:

1.  it's value in year 10 is P = $1,000/0.1- = $10,000

2.  now, discounting it back to the present it's 

NPV = $10,000 / (1.10)^10 = $10,000 / 2.5937 = $3,855.50

Best regards,

Omnivorous-GA

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Clarification of Answer by omnivorous-ga on 04 Aug 2005 03:59 PDT

$3,855.50 is the answer to (C) here.

Thank you very much for the fast and well explained answer!