Question

Caspian Sea Drinks is considering the purchase of a plum juicer – the PJX5. There is no planned increase in production. The PJX5 will reduce costs by squeezing more juice from each plum and doing so in a more efficient manner. Mr. Bensen gave Derek the following information. What is the NPV of the PJX5? a. The PJX5 will cost $2.08 million fully installed and has a 10 year life. It will be depreciated to a book value of $225,010.00 and sold for that amount in year 10. b. The Engineering Department spent $18,809.00 researching the various juicers. c. Portions of the plant floor have been redesigned to accommodate the juicer at a cost of $20,707.00. d. The PJX5 will reduce operating costs by $306,424.00 per year. e. CSD’s marginal tax rate is 21.00%. f. CSD is 57.00% equity-financed. g. CSD’s 12.00-year, semi-annual pay, 5.15% coupon bond sells for $952.00. h. CSD’s stock currently has a market value of $20.75 and Mr. Bensen believes the market estimates that dividends will grow at 3.77% forever. Next year’s dividend is projected to be $1.79.

Answer 1

First, we shall find the weighted average cost of capital(WACC)

to discount the resulting cash flows of the purchase

for which we need cost of bond & cost of equity

so, After-tax cost of bond=

Using the formula, to find the Present Value of bonds

& plugging in the available details, we will find

the before-tax cost/Yield or YTM on the bond

Price/PV of the bond=PV of future coupons+PV of Face value at maturity ---both discounted at the YTM

ie.Price=(Pmt.*(1-(1+r)^-n)/r)+(Sale Value/(1+r)^n)

where,

Price=the current market price= $ 952.00

Pmt.= The semi-annual coupon pmt.=1000*5.15%/2= $ 25.75

r= the effective rate of interest or Yield per coupon period(semi-annual)----to be found--??

n= no.of semi-annual coupon periods still to maturity-- 12*2=24

Face value = $ 1000

So, now, plugging in the values, in the formula,

ie.952=(25.75*(1-(1+r)^-24)/r)+(1000/(1+r)^24)

Solving the above, we get the before-tax semi-annual r/YTM/cost as

2.85399%

so, the annual before-tax cost=

ie.(1+2.85399%)^2-1=

5.78943%

Now,

the annual after-tax cost=

Before-tax cost*(1-Tax rate)

ie.5.78943%*(1-21%)=

4.57%

Cost of Equity

as per dividend discount model for constant growth of dividends

ke=(D1/P0)+g

where,

ke= the required rate of return to equity or cost of equity---to be found out---??

D1=next dividend , given as = $ 1.79

P0----is given as $ 20.75

g= growth rate of dividends, = 3.77%

So, now, plugging in the values, in the formula,

ke=(1.79/20.75)+3.77%

12.40%

Now, the WACC=(Wt.e*ke)+(Wt.d*kd)

ie.(57%*12.40%)+(43%*4.57%)=

9.03%

NPV analysis of the purchase of a plum juicer – the PJX5
Initial cost	-2080000
PV of After-tax sale value at end Yr. 10 (Sale value=book value)(225010*(1-21%)/1.0903^10)	74880.51
One-time after-tax redesigning costs(20707*(1-21%))	-16358.53
PV of after-tax reduction in operating costs (306424*(1-21%)*6.40919)	1551504.41
PV of depn. Tax shields((2080000-225010)/10 yrs.*21%*6.40919)	249668.65
NPV of the purchase	-220304.96
NOTE: P/A,i=9.03%; n=10---(1-1.0903^-10)/0.0903= 6.40919
The purchase is NOT RECOMMENDED as the NPV of its cash flows at this WACC is NEGATIVE.