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A company receives a perpetuity of $20000 per year in arrears and pays 30% corporation tax 12 months after the end of the year to which cash flows relate. At cost of capital of 10% what is the after tax present value of the perpetuity?
My question is why does the answer scheme not include the after tax cost of capital of 7% and why is one year in arrears of $20000 not in T2 instead of T1?
I have no idea what answer scheme you are referring to.
The 20,000 is a normal perpetuity starting in 1 years time.
The tax on the 20,000 is 1 year in arrears and is therefore a perpetuity starting in 2 years time. As always (and as revision from Paper MA) if a perpetuity starts 1 year laters (at time 2 instead of at time 1, then we need to discount by one more year to get back to the present value now.)
According to what you have written the cost of capital is 10%, so why on earth do you want to use 7%? The WACC is calculated always using the cost of equity (for which tax is irrelevant) and the after tax cost of debt.
But in the free lectures specifically example 7, we took T1-infinity minus T1-T4, meaning the perpetuity usually starts in 1 year hence when they say arrears doesn’t it mean T2?
No. In arrears means the end of the year.
The end of the first year (and start of the second year) is one year from now and is therefore time 1.
So if say the question states the company receives $20000 now(or in advance) in perpetuity, does that mean its T0-infinity ?
Yes – it would be time 0 to infinity.