Samsung SDI’s primary semiconductor fabrication plant is located in Gyeonggi Province, South Korea. Suppose Samsung SDI is considering purchasing an insurance policy that pays $400 million if a major wildfire disrupts its chip production operations. The probability of such an event is 2% per year, with a beta of zero. Because of the avoidance of financial distress and issuance costs, each $1 received in the event of loss is worth $1.50 to the firm. The risk-free rate is 4% per annum. The insurance company charges 16% more than the actuarially fair premium to cover administrative expenses. The NPV of purchasing the insurance for Samsung SDI is closest to:[Fill in the blank]单项选择题
A
a. -$1.23 million
B
b. $2.62 million
C
c. $0 million
D
d. $3.85 million

Question

Samsung SDI’s primary semiconductor fabrication plant is located in Gyeonggi Province, South Korea. Suppose Samsung SDI is considering purchasing an insurance policy that pays $400 million if a major wildfire disrupts its chip production operations. The probability of such an event is 2% per year, with a beta of zero. Because of the avoidance of financial distress and issuance costs, each $1 received in the event of loss is worth $1.50 to the firm. The risk-free rate is 4% per annum. The insurance company charges 16% more than the actuarially fair premium to cover administrative expenses. The NPV of purchasing the insurance for Samsung SDI is closest to:[Fill in the blank]单项选择题

A

a. -$1.23 million

B

b. $2.62 million

C

c. $0 million

D

d. $3.85 million

BlackTom AI · Accepted Answer

Actuarially fair premium = expected payout discounted at the risk-free rate: (0.02 × $400M) / 1.04 = $7.692307692M.

1) Relevant concepts
- Actuarially fair premium = risk-neutral (risk-free) present value of expected claim when the insured risk has beta = 0.
- Insurance company loads the fair premium by 16% to cover costs, so charged premium = 1.16 × fair premium.
- The firm’s benefit from an insurance payout is larger than the dollar payout because insurance avoids financial distress/issuance costs: each $1 received in the loss state is worth $1.50 to the firm.
- NPV to the firm = present value (PV) of the firm’s expected benefit from the policy minus the premium paid.

2) Complete reasoning and step-by-step calculation
- Expected payout in the loss state (one year ahead) = p × payout = 0.02 × $400M = $8.0M.
- Discount that expected payout at the risk-free rate to get the actuarial fair premium:
  Fair premium = $8.0M / 1.04 = $7.692307692M.
- Insurer charges 16% more:
  Charged premium = 1.16 × $7.692307692M = $8.923076923M.
- The firm values each $1 of a payout at $1.50, so the PV of the firm’s expected benefit from the policy is 1.5 times the PV of the expected payout:
  PV of firm benefit = 1.5 × ($8.0M / 1.04) = 1.5 × $7.692307692M = $11.538461538M.
- NPV to the firm = PV of firm benefit − premium paid:
  NPV = $11.538461538M − $8.923076923M = $2.615384615M ≈ $2.62M.

3) Intermediate steps shown above (numbers repeated):
- 0.02 × 400 = 8.0 (million)
- 8.0 / 1.04 = 7.692307692
- 7.692307692 × 1.16 = 8.923076923
- 7.692307692 × 1.5 = 11.538461538
- 11.538461538 − 8.923076923 = 2.615384615

4) Why the correct answer is correct
Because we correctly account for discounting at the risk-free rate (beta = 0) when computing the actuarially fair premium, apply the insurer’s 16% loading to get the charged premium, and scale the firm’s benefit by 1.5 to reflect avoided distress costs. The resulting positive NPV ($2.62M) reflects that the value of avoiding distress exceeds the loaded premium.

5) Why the other options are incorrect
- (a) −$1.23M corresponds to ignoring the 1.5 distress-avoidance multiplier (7.692 − 8.923 ≈ −1.231), so it underestimates the benefit.
- (c) $0M would imply exact break-even (not the case once the 1.5 multiplier is applied).
- (d) $3.85M is inconsistent with correct discounting and multiplier calculations; it does not match the precise arithmetic above.