A company has a current tax rate of 30 and faces a 15 chance

A company has a current tax rate of 30% and faces a 15% chance that the its output prices will drop, and it will lose $100,000 over the next year. The firm would then be in a 10% tax bracket if it faces a loss. Compute the net present value (NPV) from purchasing insurance if the rate of interest is 5% and the beta of the output prices is 0.

Solution

NPV= Insurance premium * (1-current tax) + ((profitability of loss * expected payment in case of a loss) /(1 + risk free rate ))* (1- tax rate if there is a loss)

Expected loss = $100,000*.15

= $15,000

acturially fair premium = $15,000/1.05 = 14,285.71

NPV = -14285.71 * (1-0.30)+0.15*100,000 * (1-0.10)/1.05

= 4285.723