$($Divisional costs of capital and investment decisions$)$ In May of this$$ year, Newcastle Mfg$.$ Company's capital investment review committee received two major investment proposals. One of the proposals was put forth by the$$ firm's domestic manufacturing$$ division, and the other came from the$$ firm's distribution company. Both proposals promise a return on invested capital to approximately $13$ percent. In the$$ past, Newcastle has used a single$$ firm$-$wide cost of capital to evaluate new investments.$$

$$However$,$ managers have long recognized that the manufacturing division is significantly more risky than the distribution division. In$$ fact, comparable firms in the manufacturing division have equity betas of about $1\mathrm{.}6,$ whereas distribution companies typically have equity betas of only $1\mathrm{.}2.$ Given the size of the two$$ proposals, Newcastle's management feels it can undertake only$$ one, so it wants to be sure that it is taking on the more promising investment. Given the importance of getting the cost of capital estimate as close to correct as$$ possible, the$$ firm's chief financial officer has asked you to prepare cost of capital estimates for each of the two divisions. The requisite information needed to accomplish your task$$ follows:

bullet The cost of debt financing is $11$ percent before a marginal tax rate of $27$ percent. You may assume this cost of debt is after any flotation costs the firm might incur.

bullet The$$ risk$-$free rate of interest on$$ long$-$term U$.$S$.$ Treasury bonds is currently $7\mathrm{.}4$percent$,$ and the$$ market$-$risk premium has averaged $3\mathrm{.}2$ percent over the past several years.

bullet Both divisions adhere to target debt ratios of $40$ percent.

bullet The firm has sufficient internally generated funds such that no new stock will have to be sold to raise equity financing.

a$.$ Estimate the divisional costs of capital for the manufacturing and distribution divisions.

b$.$ Which of the two projects should the firm undertake$($assuming it cannot do both due to labor and other nonfinancial$$ restraints$)?$ Discuss.