Question

Your company has a customer who wants to purchase $5,000 of goods on credit. Assume an investment of 90% of the amount of the sale and a required return of 20% APY. The customer has a 95% probability of paying the $5,000 in 3 months and a 5% probability of not paying at all. Estimate the probability of payment required for your company to break even. (Enter your answer as a decimal accurate to four decimal places)

Answer 1

Investment to sell $5000 of goods = $5000 *90% = $4500

Return required in 3 months on cost = 20%*3/12 = 5%

Amount required after 3 months = $4500 * (1+5%) = $4725

let p be the probability of payment required for breakeven, then

p*$5000+ (1-p) *0 = $4725

p = 4725/5000 = 0.9450 or 94.50%

So, the probability of payment required for your company to break even is 94.50%