Question

Questions 4 and 5 please. Is M 30 or 36 for Q4? Is it $5.63 for Q5?

1. A black box spews out $100 today and then every year, forever. The risk-free rate is currently 7% per year, and is not expected to change. What is the value of the black box today, before the first $100 are spewed out? 2. What is the value of the box from Q1, if the amount it spews out grows by 5% every year (i.e., it'll be $105 in 1 year, $110.25 in two years, ...)? 3. What is the value of the box from Q2, if we now learn that it'll stop spewing money in 10 years (after spewing out its 11th payment)? 4. You are now told that the box from Q2 will stop spewing money in M years. You are also told this box is traded for $3000 today. What is the market's estimate of M (round to nearest year? 5. The box from Q3 was upgraded to spew out $A today, still grows by 5% per year and stops in 10 years. You are given that it is worth $4000. What is A?

Answer 1

4. 100+ 100 (1.05 1007 => 1oo + 100 (1.052 t unt loo(105) = 3000 (1072) (1107)m 1-(1.05 m = 3000 (107) X-1.05 1007/ - > 100 x 107 fl-(1.05)) = 3000 6.02 (107) J => I-11-05 - 3000 X 0.02=0.5607 (oo x1007 -07 => loosim = (1-0,5607) = 4393 - => m= = 43.59 en(0.4393) en (05/1-07) > m=44 years

5. A A (-5)= е дъ5) E A (co5 ) = 4воо - А - (s)" - Чово Ах 9-14946 — Чооо 27 4 = Чооо е. 3ч. &| 4-1946 :. (A = $ чзч•3]

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