Question

Cummins Engines, Inc. is considering two alternative investment proposals. The first proposal calls for investment in plant and equipment to produce a new alternative fuel engine. The second proposal calls for investment in plant and equipment to expand production of a current, successful diesel engine. Cummins will choose only of these project since they are for similar markets.

Year	New Line	Expand Line
0	($65,000,000)	($20,000,000)
1	$20,000,000	$11,000,000
2	$20,000,000	$10,000,000
3	$20,000,000	$8,000,000
4	$20,000,000	$0
5	$20,000,000	$0

Use the information provided below to calculate Cummins weighted average cost of capital (WACC) to evaluate these two proposals. The following questions are asked to provide a guide for your analysis.

The WACC can be estimated based on Cummins long-term (capital) financing sources, including the use of retained earnings, and the use of proceeds from new issues of corporate bonds, preferred stock, and common stock. Issuance costs (flotation costs) for new issues are 3% for new issues of corporate bonds, 5% for new issues of preferred stock, and 12% for new issue of common stock. Cummins target capital structure is 35% debt, 10% preferred stock, and 55% equity. Cummins marginal tax rate is 32%. Cummins has $55,000,000 million in retained earnings.

Corporate Bonds

Cummins can sell 81⁄2% coupon, 30- year bonds (coupons are paid semi-annually) for $912.35. Cummins can issue an unlimited amount of new bonds at the same rate.

The risk premium for Cummins common stock is estimated to be 3% above its bond yield and is based on other companies in Cummins’ risk category.

Preferred Stock

Cummins preferred stock sells for $28.50 per share, the dividend rate is 8%, and the par value of this preferred stock is $50.

Common Stock

Cummins common stock sells for $18.47 per share, the growth rate is 7%, and Cummins just paid a dividend for last year in the amount of $1.52 (D0 = $1.52).

Cummins common stock has a beta of 1.45. For the general marketplace the risk-free rate is 3 percent (Rf = 3%) and the average rate of return on the market is expected to be 13 percent per year (Rm = 13%).

7. What is Cummins weighted average cost of capital based on the cheapest combination of sources of capital (WACC1) (i.e. corporate bonds, preferred stock, and retained earnings)? For the cost of retained earnings use the estimate from the Discounted Cash Flow (DCF) model.

8. How much will Cummins have to invest at this rate (what is the breakpoint)?

9. What is Cummins weighted average cost of capital based on the more expensive combination of sources of capital (WACC2) (i.e. corporate bonds, preferred stock, and a new issue of common stock)?

10. Calculate the payback period (PB) of each project and based on this criteria for which project would you recommend acceptance?

11. Calculate the discounted payback period (DPB) of each project and based on this criteria for which project would you recommend acceptance (use WACC1 as the discount rate)?

12. Calculate the net present value (NPV) of each project and based on this criteria for which project would you recommend acceptance (use WACC1 as the discount rate)?

Answer 1

We will use the PV of ordinary annuity formula,to find the before-tax cost of bond

PV/Price of the bond=(Pmt.*(1-(1+r)^-n)/r)+ (FV/(1+r)^n)

where,

PV = the present value or price of the bond less flotation costs=ie.912.35*(1-3%)= $ 884.98

Pmt.= The semi-annual coupon pmt. --1000*8.5%/2= $ 42.5

r=the effective interest rate /yield per semi-annual period to be found out---??

n= no.of periods pending to maturity=30*2= 60

FV= face valu eof the bond= $ 1000

so, plugging in the values, in the above formula,

912.35=(42.5*(1-(1+r)^-60)/r)+ (1000/(1+r)^60)

Solving the above, we get the semi-annual before-tax cost of the bond as

4.8415%

Now the annual before tax cost of the bond=

(1+4.8415%)^2-1=

9.9174%

so, the after-tax cost of the bond=

Before-tax cost*(1-Tax rate)

9.9174%*(1-32%)=

6.74%

Cost of preferred stock , kps=

k ps=( $ dividend/Net proceeds on issue)

where net proceeds = Selling price*(1-Flotation cost)

so, k ps=(50*8%)/(28.50*(1-5%))=

14.77%

Cost of retained earnings k re:

as per Dividend discount model

k re=(Next dividend/Current market price)+ Growth rate of dividends

ie. ((1.52*1.07)/18.47)+7%=

15.81%

Cost of new common stock, k e=

as per Dividend discount model

k e=(Next dividend/Net proceeds on issue)+ Growth rate of dividends

where net proceeds = Selling price*(1-Flotation cost)

ie.((1.52*1.07)/(18.47*(1-12%))+7%=

17.01%

Cost of equity as per CAPM

The risk premium for Cummins common stock is estimated to be 3% above its bond yield of 6.74%, ie. 6.74%+3%=9.74%

so, ke= RFR+(beta*above risk premium)

ie. 3%+(1.45*9.74%)=

17.12%

Cummins weighted average cost of capital based on the cheapest combination of sources of capital (WACC1) (i.e. corporate bonds, preferred stock, and retained earnings)

Given the

target capital structure is 35% debt, 10% preferred stock, and 55% equity.

WACC= Wt.d*kd)+(Wt. ps*k ps)+(Wt. re*k re)

ie.(35%*6.74%)+(10%*14.77%)+(55%*15.81%)=

12.53%

How much will Cummins have to invest at this rate (what is the breakpoint)

Cummins has $55,000,000 million in retained earnings

As NPV is the decider(as per which NEW LINE is preferred) ,he needs to invest $ 65 mln.

given the ,target capital structure is 35% debt, 10% preferred stock, and 55% equity.

55%*65mln= $ 35.75 mln. Has to come from equity,ie. Retained earnings

35%*65 ln.=$ 22.75 mln. , debt

10%*65 mln.= $ 6.5 mln. , pref. stock.

9.Cummins weighted average cost of capital based on the more expensive combination of sources of capital (WACC2) (i.e. corporate bonds, preferred stock, and a new issue of common stock)?

Given the

target capital structure is 35% debt, 10% preferred stock, and 55% equity.

WACC= Wt.d*kd)+(Wt. ps*k ps)+(Wt. re*k e)---- taking 17.12% as ke as per CAPM

ie.(35%*6.74%)+(10%*14.77%)+(55%*17.12%)=

13.25%

10..
Year	New Line	Cumulative cash flows	Expand Line	Cumulative cash flows
0	-65000000	-65000000	-20000000	-20000000
1	20000000	-45000000	11000000	-9000000
2	20000000	-25000000	10000000	1000000
3	20000000	-5000000	8000000	9000000
4	20000000	15000000	0	9000000
5	20000000	35000000	0	9000000
	35000000		9000000

Ordinary payback:

New line

3+(5000000/20000000)=

3.25

Years

Expand Line

2+(9000000/10000000)=

2.9

Years

Based on ordinary payback,EXPAND LINE is recommended ,as it pays back , in shorter no.of yrs.(2.9) than new line( 3.25)

11.Discounted payback using WACC 1, ie. 12.53%
Year	New Line	PV of Cash flows	Cumulative cash flows	Expand Line	PV of Cash flows	Cumulative cash flows
1	2	3=2/(1+12.53%)^yr.n	4	5	6=5/(1+12.53%)^yr.n	7
0	-65000000	-65000000	-65000000	-20000000	-20000000	-20000000
1	20000000	17773038	-47226962	11000000	9775171	-10224829
2	20000000	15794045	-31432917	10000000	7897022	-2327807
3	20000000	14035408	-17397509	8000000	5614163	3286356
4	20000000	12472592	-4924917	0	0	3286356
5	20000000	11083793	6158876	0	0	3286356
	NPV=	6158876		NPV=	3286356

Discounted payback using WACC 1, ie. 12.53%

New line

4+(4924917/11083793)=

4.44

Years

Expand Line

3+(2327807/5614163)=

3.41

Years

Based on discounted payback(DPB) also EXPAND LINE is recommended ,as it pays back , in shorter no.of yrs.(3.41 ) than new line( 4.44)

12. Based on NPV (same table for DPB) ---NEW LINE is recommended as its NPV ($ 6158876) > that for the expand line option ($ 3286356)