Residual Income Valuation

CFA Level II
#1

Page 407 in CFA curric:

Q: SWI acheieved an Operating Profit after taxes of 10mm on Total Assets of 100mm. Half of its assets were financed with debt with a pre-tax cost of 9%. Its cost of equity capital is 12%, and its tax rate is 40%. Did SWI achieve a positive RI?

I have the answer as yes, 10mm - equity charge of [50mm x. 12] = 4mm.

However, the book has as follows:

To acheieve a positive RI, a company’s net operating profit after taxes as a % of TA can be compared to WACC. The book does the calc to get WACC at 8.7%.

Then takes NOPAT / TA [10 / 100] = 10%

10% - 8.7% x 100mm (Total Capital)

Can anyone help explain to me why my answer is wrong? How the question steers you to solve it the way the book did? How would I be keyed into this on the test? Totally lost

#2

Hi,

My way to solve this is : NOPAT - (cost of equity x equity capital + after-tax cost of debt x debt capital)

So : 10(0.6) - (0.12 x 0.5 x 100 + 0.09 x .6 x .5 x 100) = 1.3

Is that formula somewhere in the readings? Cause I’m studying with Elan and they provided that formula.

#3

Oh and looking at your answer again, I noticed that you only considered the equity charge. You should deduct only the equity charge you’re starting at Net Income.

That is, Residual Income = Net Income - Equity Charge

#4

Tahi,

You are right. I did not take into consideration the after tax costs of debt charge. I read “Operating profit after tax” and didn’t even think twice. ahh! Thanks for typing this out.