It is shown that if the monopoly firms supply the same products, the price of first stage is larger than the discount value of the second's;

研究表明，若垄断厂商在不同阶段提供同质产品，则第一时段的价格要高于第二时段价格的贴现值；

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When the market is complete, the present value of any derivative security is equivalent to mathematical expectation of its underlying profit discount value under equivalent martingale measurement.

当市场是完备时，任意衍生证券的现值等于该证券未来收益折现值在等价鞅测度下的数学期望。

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One such is factoring, in which a company sells its invoices to a specialist lender at a discount to face value.

其中一个就是保理，是指公司将其应收款额相对市面价值的以一定折扣价出售给保理商。

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If you had a perpetuity, which paid C/2 forever, you already know from the perpetuity formula that the value of that would be C/2 divided by r/2 if r/2 is the discount rate.

如果你有一只永续债券,每半年付息C/2,没有到期日,从永续债券的公式可以知道,债券价格等于C/2除以r/2,r/2为贴现率

耶鲁公开课 - 金融市场课程节选

Taking this mantra on face value, many discount the value of formal training, and end up under investing in it.

FORBES: Choosing the Right Training?

If passed by Congress, pending legislation will eliminate the ability to discount the value of FLP gifts.

FORBES

Now, if you give a family member a minority share in your business, an appraiser legally can discount its value.

WSJ: Family Value: New Hazards for Estate Plans