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Dear John, Thanks for your fantastic lectures and great website. Can you help to show the workings for the following question, which are in opentuition’s MCQ bank. Thank you very much.
Q: A company has sales of $200m per year. Currently customers take on average 40 days to pay. The company is considering offering a discount of 1% for payment within 15 days and expects that 60% of customers will take advantage of the discount. What is the effective annual cost of offering the discount?
A: 15.8%
Q: The share price of CP plc is $4 per share. They announce a 1 for 5 rights issue at $3.10 per share. What % of the rights offered to a shareholder does the shareholder need to take up so as to have no net cash flow resulting from the issue?
A: 19.48%
Best regards,
Ning
Q1:
The effective cost is 1/99 = 1.010101% over a period of 25 days (40 – 15).
To turn this into an annual rate, R, (1+R) = 1.010101^(365/25)
Q2:
The TERP is ((5 x $4.00) + 3.10) / 6 = $3.85
If someone currently owns 10000 shares (using any number will work) then their current wealth is 10,000 x $4 = $40,000.
In theory their total wealth will not change after the rights issue, and so if there is to be no net cash flow, their new shareholding must be worth $40,000 in total.
Since the new share price is $3.85 it must mean that they end up owning 40,000/3.85 = 10389.6 shares.
They were entitled to rights of 1/5 x 10,000 = 2000.
So if they take up 389.6 then they are taking 389.6/2,000 = 19.48%Dear Sir,
Thanks a lot for your prompt reply and clear explanation.
For Q1 I can only get the final answer as 14.74%, different from the std answer given. But I understand the working now.
Many thanks again.
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