Exercise 1 Solution.docx

# Exercise 1 Solution.docx - Exercise 1 Solution Question 1 a...

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Exercise 1 - Solution Question 1: a. The cash flows of the perpetuities are: Time Cash flow of time 1 perpetuity Cash flow of time 0 perpetuity 0 (today) 0 C 1 C C(1+g) 2 C(1+g) C(1+g) 2 3 C(1+g) 2 C(1+g) 3 4 C(1+g) 3 C(1+g) 4 …(continues to grow at rate g forever) …(continues to grow at rate g forever) b. The present value (PV) of perpetuity 1 is given by: ... ) 1 ( ) 1 ( ) 1 ( ) 1 ( ) 1 ( ) 1 ( 1 ) 1 ( 4 3 3 2 2 r g C r g C r g C r C perpetuity PV We can multiply both sides of the equation above by (1+g): ... ) 1 ( ) 1 ( ) 1 ( ) 1 ( ) 1 ( ) 1 ( 1 ) 1 ( ) 1 ( ) 1 ( 4 4 3 3 2 2 r g C r g C r g C r g C g perpetuity PV 1

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1 1 1 1 ) 1 ( ) 1 ( ) 1 ( ) 1 ( so, t t t t t r g C r g C g perpetuity PV Now, a well known formula in mathematics is: 0 1 0 if 1 1 t t x x x Notice that the summation in this formula starts from t=0 and not from t=1. We can apply this formula to compute the PV of perpetuity 1. In order to be able to apply the formula, we must assume that r>g, in which case 1 1 1 0 r g 2
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ) 1 ( ) 1 ( ) 1 ( ) 1 ( then, 0 0 0 0 0 0 1 1 1 t t t t t t t t t t t t t r g C C r g C r g C r g C r g C r g C r g C r g C r g C g perpetuity PV we can now apply the formula:

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