$($End$-$of$-$chapter numerical problem $9\mathrm{.}7)$ Upton Computers makes bulk purchases of small computers, stocks them in conveniently located warehouses, ships them to its chain of retail stores, and has a

staff to advise customers and help them set up their new computers. Upton's balance sheet as of

December $31,2018,$ is shown here $($millions of dollars$)$:

Sales for $2018$ were $$350$ million, and net income for the year was $$10\mathrm{.}5$ million, so the firm's profit

margin was $3\mathrm{.}0\%.$ Upton paid dividends of $$4\mathrm{.}2$ million to common stockholders, so its payout ratio

was $40\%.$ Its tax rate was $40\%,$ and it operated at full capacity. Assume that all assets$/$sales ratios,

$($spontaneous liabilities$)/$sales ratios, the profit margin, and the payout ratio remain constant in $2019.$

a$.$ If sales are projected to increase by $$70$ million, or $20\%,$ during $2019,$ use the AFN equation to

determine Upton's projected external capital requirements.

b$.$ Using the AFN equation, determine Upton's self$-$supporting growth rate. That is$,$ what is the

maximum growth rate the firm can achieve without having to employ nonspontaneous external

funds?

c$.$ Use the forecasted financial statement method to forecast Upton's balance sheet for December

$31,2019.$ Assume that all additional external capital is raised as a line of credit at the end of the

year and is reflected $($because the debt is added at the end of the year, there will be no additional

interest expense due to the new debt$).$ Assume Upton's profit margin and dividend payout ratio

will be the same in $2019$ as they were in $2018.$ What is the amount of the line of credit reported

on the $2019$ forecasted balance sheets? $($Hint: You don't need to forecast the income statements

because the line of credit is taken out on the last day of the year and you are given the projected

sales, profit margin, and dividend payout ratio; these figures allow you to calculate the $2019$

addition to retained earnings for the balance sheet without actually constructing a full income

statement.$)$