Market value = Book value + PV of residuals, why?

CFA Level II
#1

Market value = Book value + PV of residuals

Can some one please explain this to me as of why it is the case? why market value equals book and pv of residuals?

#2

Residual income is the amount of earnings above the required amount of earnings.

If RI is positive, then the asset is providing a value above its book value. Therefore you have the book value of asset and the present value of the RI as total value.

#3

This is something that u have to apply reasoning rather than looking at formulas

We are thinking in terms of the Market value that is created which will be priced based on the amount of residuals.

Remember, residuals is the excess after the equity charge.

Total market value hence, wlll be initial iinvestment (book value) + PV of residuals

#4

simplifying a lot; imagine residual as retained earnings.

#5

A simple analogy is to think of the price of a bond, where book value is par:

  • If the coupon payments equal the required rate of return (YTM), then residual income is zero (the bond is paying exactly the required rate of return), and the value today is par: book value plus zero.
  • If the coupon payments are above the required rate of return (YTM), then residual income is positive (the bond is paying more than the required rate of return), and the value today is above par: book value plus (positive) residual value.
  • If the coupon payments are below the required rate of return (YTM), then residual income is negative (the bond is paying less than the required rate of return), and the value today is below par: book value plus (negative) residual value.
#6

If i recall correctly this relationship is similar to one of the Residual Income formulas given by deriving the Vo with the Po/Bo ratio.

Thanks for putting this here.

#7

You’re welcome.