Question

5. (5 pts) Change the following geometric gradient series into a linear gradient series by determining the unknown CFs if,-5%/year. S1000 S?? $700 $490 $343 4 6. (3 pts) Given the following cash flow on the left, identify if any of the following equations are incorrect in describing the equivalent value in year four. 200 200 200 200 200 123456 0 23 4 56 (a) V4-V00(FA, İ, 3)(F/P, İ, 1) + $200(PA, i, 2)(P/F, i, 1) (b) V4-s200(F/A, i, 3) + $200(P/A, 1,2) (c) V4- S200(F/A, i, 4) $200$200(P/A, i, 2) (d) V4 [S200(PA, i, б)-$200(P/F, i, 4)(F/P, i, 4) (e) V4-[$200(FA, i, 6)-$200(F/P, i, 2)](P/E, i, 2)

Answer 1

(5)

NPV of geometric gradient series = 1000/1.05 + 700/1.05² + 490/1.05³ + 343/1.04⁴ = $2303.78

Let the linear gradient series start with x and reduce by a

Hence, CF0 = a
CF1 = a-x
CF2 = a-2x
CF3 = a-3x

Hence, NPV of linear series = a + (a-x)/1.05 + (a-2x)/1.05² + (a-3x)/1.05³ = 3.72a - 5.36x

This is equal to NPV calculated earlier

=> 3.72a - 5.36x = 2303.78

Also, CF4 = 0 => a-4x = 0 => a = 4x.. putting this is equation above,

3.72*4x - 5.36x = 2303.78 => x = 242

=> a = 968

Hence,

CF0 = $968
CF1 = 968 - 242 = $726
CF2 = 968 - 2*242 = $484
CF3 = 968 - 3*242 = $242