Question

Sharak and Ruh each offer Dar an investment opportunity. In exchange for an initial investment of X, Sharak will give Dar 200 in six years and 600 in twelve years. In exchange for an initial investment of X, Ruh will give Dar 100 in three years and Y in six years.

Assuming that both investments are valued at the same annual effective rate i = 0.10, find Y .

Answer 1

Initial Investment X is the Present Value of Future Cashflows.

Sharak - 200 in 6 years & 600 in 12 years

Ruh - 100 in 3 years & Y in 6 years

annual effective rate i = 0.10 or 10%

PV of investment opportunity provided by Sharak = PV of investment opportunity provided by Ruh

We know that, PV = CF / (1 + r)^t

200 / (1+0.1)⁶ + 600 / (1+0.1)¹²  = 100 / (1+0.1)³ + Y / (1+0.1)⁶

200 / 1.7716+ 600 / 3.1384 = 100 / 1.331 + Y / 1.7716

112.8923 + 191.1802 = 75.1315 + Y / 1.7716

Y / 1.7716 = 112.8923 + 191.1802 - 75.1315

Y / 1.7716 = 228.9418

Y = 228.9418 * 1.7716 = 405.5933 = 405.60