Two-Stage Investment Model With Loan Guarantees and Share Buybacks

We consider an entrepreneur who has an option to invest in an irreversible but delayable project. If the project is sufficiently profitable, the firm has an option to make a growth investment, which makes the project cash flow increase by a constant factor. The entrepreneur has no money to invest. All the two-stage investment costs must be financed by a bank loan guaranteed by an insurer in the first-stage investment or directly by the insurer in the second-stage investment. In return for the insurer, the entrepreneur pays the insurer a fraction of the loan at the first-stage investment and grants her/him a part of equity when the second-stage investment is exercised. The insurer has a higher discount rate than the entrepreneur and thus share buyback is profitable. To control the insurer's risk exposure, a mandatory buyback would be initiated. We develop an explicit model to describe guarantee costs, the timing and pricing of the two-stage investment options and share buyback option. We find that there exists an optimal guarantee cost combination that maximizes the firm value, where the fixed guarantee fee rate is about 1% or 2%, quite in agreement with the one suggested for some industries by the Chinese government. The firm value is higher and the negotiated buyback happens much earlier if the buyback is initiated by the entrepreneur rather than the insurer. The later the mandatory buyback, or the earlier the negotiated share buyback, the higher the firm value