Question

Calculate the discount factors (present value factors) at 8% for years 1, 2, 3, and 4 (show all work, including equations). What if the discount factor for year 3 above is equal to .900. Would that provide arbitrage opportunities? Explain fully.

Answer 1

Present Value Factor = 1/(1+r)t

r = interest rate

t = time period

PV factor for year 1 = 1/1.08 = 0.9259

PV factor for year 2 = 1/(1.08)² = 0.8573

PV factor for year 3 = 1/(1.08)³ = 0.7938

PV factor for year 4 = 1/(1.08)⁴ = 0.7349

If discount factor for year 3 is equal to 0.900

0.900 = 1/(1+r)³

r = 3.57%

So, this provides arbitrage opportunity as then one can borrow at 3.57% and invest at 8% interest rate.