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 $2.38 million fully installed and has a 10 year life. It will be depreciated to a book value of $263,369.00 and sold for that amount in year 10.

b. The Engineering Department spent $17,966.00 researching the various juicers.

c. Portions of the plant floor have been redesigned to accommodate the juicer at a cost of $18,312.00.

d. The PJX5 will reduce operating costs by $359,801.00 per year.

e. CSD’s marginal tax rate is 21.00%.

f. CSD is 63.00% equity-financed.

g. CSD’s 16.00-year, semi-annual pay, 6.07% coupon bond sells for $1,015.00.

h. CSD’s stock currently has a market value of $21.09 and Mr. Bensen believes the market estimates that dividends will grow at 2.68% forever. Next year’s dividend is projected to be $1.55.

Answer 1

NPV is Net Present Value of the Future Cash Flows.

Present value is calculated by Discounting the Future cash flows based on the Discount Rate. Discount Rate is the rate of return expected for the Investment and Risk.

NPV = Sum of Today's/Present value of the Expected Cash flows.

Present Value of Expected Cash Flow =

where r = Discount Rate = WACC (Weighted average cost of Capital)

n = Time period in years.

So first step is to calculate Discount Rate using WACC formula.

WACC =

Where, E = Equity, Re = Cost of Equity, D = Debt, V = Total value of the company., Rd = Cost of Debt, Tax = Corporate Tax rate.

E/V = 0.63 (since CSD is 63% equity financed)

D/V = 1-0.63 = 0.37

Tax = 21% = 0.21.

Rd = Cost of Debt can be calculated based on the Bond Interest Rate = Coupon Rate on Bonds

Coupon Rate is 6.07% semi-annual, We need to convert this to Annual Rate = (1+6.07%/2)^2-1 = 6.8% (rounding off to 1 decimal).

Rd = 6.8%

Re = Cost of Equity based on Dividend Growth Model = D/P* + g = 1.55/21.09+2.68% = 10.0% approx.

So. WACC = 0.63*10% +0.37*6.8%*(1-21%) = 8.3% approx.

By Using the WACC and the Present Value formulas we calculate the Present value of each cash flow as given below. We get the NPV value of - $215,526.

Cash Flow Item	Year 0	Present Value	Calculation
Buy PJX	(2,680,000)	$   (2,680,000)
PJX Salvage Value after 10 years	263,369	$       118,789	Present value of Single Cash Flow = Cashflow/(1+r)^n = 263369/(1+8.3%)^10
Engineering Dept Expense	$         (17,966)	$        (17,966)
Plant Floor Redesign	$         (18,312)	$        (18,312)
Reduction in Operation Cost per Year	$         359,801	$    2,381,963	Present value of an Annuity = Cash flow *[(1-(1+r)^-n)/r} = 359801*[(1-(1+8.3%)^-10)/8.3%]
Net Present Value (NPV)		$      (215,526)

In the calculations above, r = WACC = Discount rate and n= time period which is 10 years.