# 金融数学 Investments and Portfolio Management  BUSI97631

The discount is $2 \%$. The annualized cost of not taking the discount can be calculated when the invoice is paid on:
Day 40: $\left(1+\frac{0.02}{1-0.02}\right)^{\frac{365}{40-10}}-1=27.9 \%$
Day $50:\left(1+\frac{0.02}{1-0.02}\right)^{\frac{365}{50-10}}-1=20.2 \%$
Day 60: $\left(1+\frac{0.02}{1-0.02}\right)^{\frac{365}{60-10}}-1=15.9 \%$
The annualized cost of trade credit decrea ses as the payment period increases. If the company does not take the $2 \%$ discount within the first ten days, it should wait until the due date (day 60 ) to pay the invoice.

Our primary quantitative measure of payables management is average days of payables outstanding, which can also be calculated as:
$$\text { number of days of payables }=\frac{\text { accounts payable }}{\text { average day’s purchases }}$$
where:
$$\text { average day’s purchases }=\frac{\text { annual purchases }}{365}$$

## BUSI97631  COURSE NOTES ：

Ending value $=(1,000)(1.05)(0.92)(1.12)=\$ 1,081.92$Holding period return$=(1.05)(0.92)(1.12)-1=0.08192=8.192 \%$, which can also be calculated as$1,081.92 / 1,000-1=8.192 \%$. Arithmetic mean return$=(5 \%-8 \%+12 \%) / 3=3 \%$. Geometric mean return$=\sqrt[3]{(1.05)(0.92)(1.12)}-1=0.02659=2.66 \%$, which can also be calculated as geometric mean return$=\sqrt[3]{1+\mathrm{HPR}}-1=\sqrt[3]{1.08192}-1=2.66 \%\$