金融数学 Investments and Portfolio Management  BUSI97631

这是一份 Imperial帝国理工大学  BUSI97631作业代写的成功案例

金融数学 Maths for Finance FINANCE 2110 
问题 1.

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.

证明 .

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:
$$
\text { average day’s purchases }=\frac{\text { annual purchases }}{365}
$$


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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 $=\sqrt[3]{1+\mathrm{HPR}}-1=\sqrt[3]{1.08192}-1=2.66 \%$








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