Question

Question 3 (12 marks) Consider the following infinite series of cash flows, of which alternate cash flows of $9 and $5 take place between t=2 and t=26. All other cash flows, including those at t=0, t=1 and from t=27 onwards are $5 per year (with the only except of Year 47, at which the cash flow is $1).

Time(yr.) 0 1 2 3 4 5 … 25 26 27 28 … 45 46 47 48 49 . . . CF $5 $5 $9 $5 $9 $5 … $5 $9 $5 $5 … $5 $5 $1 $5 $5 . . . Suppose the effective annual rate is 5%.   
a) Calculate the present value (at t=0) of this cash flow series. (10 marks)

[Hints: (1) What is the (effective) 2-year rate (E2YR)? (2) Can assume the “basic” cash flows are $5 each year.]

b) Is it possible to find the future of this cash flow series? Explain. (2 marks)   
3

Answer 1

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Answer:

hower of cash flow $9 and 85 take place Altunate between t=2 and t= 26. those at onwards t=0, spa year. call flows including tel and from t= 27 All other - in year 47., rosy. a cash flows can be split as spee petual effective rate a year = (1+ 5%, 2-1 1. = 10.254. pro s po peteret = 5(Hr) = 105 prof 13 Installment 884 discounted at syear Effective annual rate. (10.25%) =p1 ( 10.25% 4,13). 28.05. prof x4 in year 47 = 34/(1:05) "? = 0.40, 0 .". Total present Series = 105 +8.05 -0.40

1. As this as an infinite Series e It is not possible to and future value. Future value for an infinite Series es infinite. the duture for this series es infinitely distant