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 Subject: Time Value of Money Category: Business and Money > Finance Asked by: altheg-ga List Price: \$10.00 Posted: 03 Aug 2005 16:32 PDT Expires: 02 Sep 2005 16:32 PDT Question ID: 551418
 ```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``` 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``` Clarification of Answer by omnivorous-ga on 04 Aug 2005 03:59 PDT `\$3,855.50 is the answer to (C) here.`
 altheg-ga rated this answer: `Thank you very much for the fast and well explained answer!`