A company reported core operating income of $30$ on sales revenue of $250$ in $2017.$ The book

value of net operating assets in the beginning of $2017$ was $125.$ Sales revenue is expected to

grow at $6\%$ in $2018$ and $2019,$ at $5\%$ in $2020$ and at $4\%$ thereafter.

a$)$ Forecast sales, operating income, net operating assets and residual operating income

for $2018$ to $2022.$ Use a firm cost of capital of $8\%.$ State your assumptions.

b$)$ Use the residual operating income model to compute the firm value.

c$)$ Forecast free cash flows and repeat the valuation using the discounted cash flow

model.

d$)$ The total book value of the net debt is $200.$ However, a bank loan with a book value of

$80$ has a fair value of only $60.$ Estimate the intrinsic equity value of the firm.

e$)$ Prove $($mathematically$)$ that the Residual Operating Income Model and the Discounted

Cash Flow Model are equivalent.