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,
OmnivorousGA 
Clarification of Answer by
omnivorousga
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,
OmnivorousGA
