Equity Residual income valuation. CFAI practice problem 2 Page 517

CFA Level II Equities
#1

I am bit confused in the problem. The problem mentions book value per share is $20

Its going to earn constant EBIT of 300,000 forever and based on that number, first year’s Residual income is 8000 or $0.16 per share.

So this 0.16 per share is considered perpetuity and is valued accordingly. (0.16/0.1)

However, my question is, this number of 0.16 is not going to stay constant. Because there are no dividends paid, the net income will keep increasing book value of Equity each year through retained earning. So cost of equity will keep increasing and hence, the residual income will keep decreesing… So its not a perpetuity…

Am I missing something here?

Thanks in advance.

#2

It’s a perpetuity because the timeline is indefinite, not because RI is descreasing.

#3

Well, perpetuity should be constant amount for indefinite time.

If it keeps decreasing, its not perpetuity… right?

#4

I agree, this is a poorly written question. I’m stumped, only thing i can think of is they are trying to tie back to the text in section 3.4 of Reading 38.

#5

ok thanks… Good to know that I am not totally off the track…

#6

I guess you could argue the residual income declines to zero over time in this example and valuing a perpetuity (sort of) assumes the same thing since the PV of long dated cash flows is minimal

#7

but formula for perpetuity shouldn’t be applied here… right? instead I’d use retention rate =1 and growth to be equal to ROE… and then use the formula with growth here…

#8

That is conceptually the same as valuing a perpetuity.