$\backslash$table$[[,$Aspen Inc.,Birch Inc.,Cherry Inc.$],[$Common stock capital $($$M$),$$$1500,2400,960],[$Retained earnings $($$M$),$$$1200,3400,920],[3\mathrm{.}8\%15-$year Bank loan $ M$,$$$9600,-,-],[3\mathrm{.}25-$year zero$-$coupon, semi$-$annual Po: Current stock price$=$EPS$*$P$/$E ratio

COGS: Cost of goods sold

TVC: Total variable costs

FC: Total fixed costs

EBIT: Earnings before interest and taxes

EBITDA: Earnings before interest, taxes, Depreciation and Amortization

NI: Net income

OCF: Operating Cash flows

Dep: Depreciation

FCF: Free cash Flow

WC: Working capital

Rf: Risk Free rate

Bel: Beta of equity of a levered firm

Beu: Beta of equity of unlevered firm

ERm: Expected or average return of the market portfolio

Ke$=$Rf$+$Bel$($Erm$-$Rf$)$

E or MVE: Market value of equity

D or MVD$=$market value of debt

EV$=$E$+$D: Enterprise value

Kd$(1-$T$)=$ After$-$tax cost of debt or after$-$tax yield to maturity $($YTM$)$

D: E or MVD: MVE: Debt: Equity ratio

B$\_$eu$=$B$\_$el$*\backslash$geoquad $($E$/($E$+$D$(1-$T$)))$

B$\_$el$=$B$\_$eu$*\backslash$geoquad $([1+($D$(1-$T$))/($E$+$D$(1-$T$))])$

Fisher equation: $(1+$NWACC$)=($I$+$RWACC$)*(1+$INF$)$ where INF$=$inflation rate.

WACC$=$Ke E$/$EV$+$Kd$(1-$T$)$D$/$EV $($When we have only debt and equity capital$)$

FCFF$=$EBIT$-$ Taxes $+$ Depreciation $\backslash$Delta WC $-$ CAPEX

Question $1$

Jaca Inc., a private company, specializes in the manufacture of household goods $($consumer durables$)$ targeting high$-$income households. The company will undertake a $5-$year project to manufacture high$-$end hardwood dining room tables. One of the biggest challenges in identifying the discounting rate to be used to compute the NPV of the project. The company has gathered the following balance sheet information of the three listed peers who also specialize in household goods.

Aspen Inc. Birch Inc. Cherry Inc.

Common stock capital $($$M$)$ $$15002400960$

Retained earnings $($$M$)$ $$12003400920$

$3\mathrm{.}8\%15-$year Bank loan $M $$9600--$

$3\mathrm{.}25-$year zero$-$coupon, semi$-$annual $M $-$ $$8000-$

$5\mathrm{.}4\%,5-$year coupon $($Semi$-$annual$)$ $M $--$ $$7,200$

Per share information

Par value $$5$ $$10$ $$3$

Current stock price, Po $$48$ $$60$ $$50$

Beta $1\mathrm{.}51\mathrm{.}31\mathrm{.}1$

Bond price $(\%$ of par value$)-90\mathrm{.}77593\mathrm{.}35$

Jaca Inc. has decided to use the average weighted average cost of capital $($WACC$)$of each of the three firms as the discounting rate. Long term interest rate on treasuries is $3\%$ while the market risk premium is $7\%.$ Jaca Inc. evaluates all projects using real prices and expenses $($current purchasing power$).$ The long$-$term general inflation rate in the US is $2\mathrm{.}87\%.$ The marginal corporate tax rate is $25\%$

The company needs to decide on whether to introduce a new oak dining room table $($ODRT$)$ set. The ODRT set will sell for $$6,600,$ including a set of eight chairs each with a detachable velvet headrest. The company projects to sell the following sets per year for the next $5$ years.

Year $12345$

Sets $23,00024,50030,00028,500026,000$

Variable production costs will amount to $45$ percent of sales and fixed costs are $$18\mathrm{.}4$ million per year. Hint: revenue in $M$=($price$*$units$)/1000,000$

The new ODRT sets will require inventory amounting to $10$ percent of sales revenue, produced, and stockpiled in the year prior to sales.

The company projects that the introduction of the ODRT set will result in a loss of sales of $4,000$ dining room table sets per year of the maple tables the company currently produces. These tables sell for $$3,900$ and have variable costs of $40$ percent of sales. The inventory for this maple table is also $10$ percent of sales. The company believes that sales of the maple oak table will be discontinued after three years.

Jaca Inc. currently has excess production capacity. If the company buys the necessary equipment today, it will cost $$190$ million. However, the excess production capacity means the company can produce the new ODRT sets without buying the new equipment. The company$$s finance manager has said that the current excess capacity will end in two years with current production. This implies that if the company uses the current excess capacity for the new ODRT sets, it will be forced to spend the $$190$ million in two years to accommodate the increased sales of its current products.

In five years from today, the new equipment will have a market value of $$36$ million if purchased today, and $$80$ million if purchased in two years. The equipment is depreciated on a seven$-$year MACRS schedule. The respective depreciation rates are as follows:

Year $12345678$

Depreciation rate $14\mathrm{.}29\%24\mathrm{.}49\%17\mathrm{.}49\%12\mathrm{.}49\%8\mathrm{.}93\%8\mathrm{.}92\%8\mathrm{.}93\%4\mathrm{.}46\%$

The company tax rate is $25$ percent. b$)$ Derive the free cash flow $($FCF$)$ of the new project and compute the NPV$.$ Be sure to show.

$-$Depreciation charge per year

$-$After$-$tax salvage value

$-$Working capital and change in working capital

$-$Recouped working capital

$-$Schedule of free cash flow derivation

$-$The project$$s NPV$?(23$ points$)$