Question

Singer inc. is about to start a 4-year project. A new plant will be built. The plant will require an amount of $40 million to acquire new fixed assets that will be depreciated straight-line through the life of the project. The company also possesses a building that it bought for $5 million and has a net book value of 0. Today's market value for the building is $4.1 million, while it can be rented for $220,000 yearly. The company wants to situate its new plant in this building. The following are today's market data for Singer (that is before the project starts):

?Debt: $240,000,000. Interest rate: 7.5%. The debt amount is kept constant.

?Common stocks: 9,500,000 shares outstanding. Stock price: $63.

?The levered equity Beta is 1.2. Market: 8% expected market risk premium, 5% risk free rate. JP Simon Bank charges Singer $1,040,000 as an underwriter fee on new common stock issues (i.e. the cost of helping Singer issue stocks). Singer will raise the funds needed for the project by only issuing stocks. The corporate tax rate is 35%. The project will be managed in total separation from the other operations of the ?firms.

(a) Calculate the new project's initial (time 0) cash ?flow.

(b) The new project has a risk pro?le comparable with the riskiness of its assets in place. What is the appropriate opportunity cost of capital for the project? The company will incur $4,000,000 in annual administrative costs. The plant will manufacture 20,000 widgets per year and sell them for $6,900 each. The unit production cost is $5,400.

(c) What is the annual after-tax cash ?ow from the new project at the end of each of the four years of its life?

(d) Assuming that the depreciation tax shield is as risky as the company's debt, what is the project's NPV?

Answer 1

a. As it is given that

the company wants to situate its new plant in this building,

the market value $ 4.1 mln. is irrelevant to the project decision

Only the loss of after-tax annual rental income of 220,000 counts while calculting relevant cash flows of the project--- t=0 CF= $ 40 mlns.

b & d.Appropriate opportunity cost of capital / WACC

After-tax cost of debt=7.5%*(1-35%)=

4.875%

Cost of equity

Given that

The debt amount is kept constant.

so, we will have the funding of $ 40 mln..fully by equity

whose issue costs are 1.040 mln.

ie. 1.040/40=

2.60%

Additional cost of equity

Cost of equity as per CAPM,

ke=RFR+(Beta*MRP)

ie. 5%+(1.2*8%)=

14.60%

PLUs the above issue costs,

14.60%+2.6%=

17.20%

so, now the WACC=

(Wtd*kd)+Wt.e*ke)

MV of debt= $ 240 mln.

MV of Equity=9.5 mln.*63= $ 598.5 mlns+ new 40 mlns.=638.5 mlns.

So, WACC= (240/(240+638.5)*4.875%)+(638.5/(240+638.75)*17.20%)=

13.83%

so, the Appropriate opportunity cost of capital. Will be the cost of equity 17.20%

but , given in d. that the

the depreciation tax shield is as risky as the company's debt

WACC , 13.83% will be the correct rate to discount cash flows

NPV analysis
Year	0	1	2	3	4
Initial cost	-40000000
Operating Cash flows:
Annual after-tax net revenues(20000*(6900-5400)*(1-35%))		19500000	19500000	19500000	19500000
Annual after-tax admn. Costs(4000000*(1-35%))		-2600000	-2600000	-2600000	-2600000
Depn. Tax shileds(40 mln/4*35%)		3500000	3500000	3500000	3500000
After-tax rental income lost(220000*(1-35%))		-143000	-143000	-143000	-143000
Annual FCFs	-40000000	20257000	20257000	20257000	20257000
PV F at 13.83%(1/1.1383^ yr.n)	1	0.87850	0.77177	0.67800	0.59563
PV at 13.83%(FCF*PV F)	-40000000	17795836	15633696	13734249	12065579
NPV at 13.83% (WACC)	19229360