Question

Rearden Metal imports ore from South America. Rearden Metal is worried that the South American mines may enter into a long-term contract with the Chinese to sell all of their ore output to China, hence cutting off Rearden Metal’s supply. In the event of such a contract with the Chinese, Rearden Metal will face much higher costs for its raw materials causing its operating profits to decline substantially and its marginal tax rate to fall from its current level of 35% down to 10%. An insurance firm has agreed to write a trade insurance policy that will pay Rearden Metal $1,500,000 in the event of the South American supply of ore being cut off. The chance of the South American supply being cut off is estimated to be 16%, with a beta of -2.0. The risk-free rate of interest is 4% and the return on the market is estimated to be 12%.

(a). Compute the actuarially fair premium for this insurance policy.

The fair premium for this insurance policy is_______ $ (round to the nearest number).

(b) Calculate Rearden’s NPV for purchasing this policy.

The NPV for purchasing this policy is _______$ (round to the nearest number).

Answer 1

Calculate Insurance Premium -

rL= = rf+ βL(rm- rf)

rL= 4% + (-2.0)(12%-4%)

rL= -12%.

Insurance Premium = 16%*$15,00,000/(1-0.12)

Insurance Premium = $272,727

Calculate NPV = -Premium (1-Thigh) + 1/ (1-rL) * pr(Loss) * payment * (1-Tlow)

Calculate NPV = -$272727 (1-0.35)+1/0.88 *(0.16)($15,00,000)(1-0.10)

Calculate NPV = -$177272.55+$245441

Calculate NPV = $68,169

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