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 IRR of the PJX5?

a. The PJX5 will cost $1.65 million fully installed and has a 10 year life. It will be depreciated to a book value of $105,364.00 and sold for that amount in year 10.

b. The Engineering Department spent $37,610.00 researching the various juicers.

c. Portions of the plant floor have been redesigned to accommodate the juicer at a cost of $24,737.00.

d. The PJX5 will reduce operating costs by $391,299.00 per year.

e. CSD’s marginal tax rate is 33.00%.

f. CSD is 75.00% equity-financed.

g. CSD’s 16.00-year, semi-annual pay, 6.68% coupon bond sells for $1,033.00.

h. CSD’s stock currently has a market value of $22.74 and Mr. Bensen believes the market estimates that dividends will grow at 3.50% forever. Next year’s dividend is projected to be $1.67.

Answer 1

for answering this qustion first we calculate the comany WACC = discount rate

WACC = (Cost of equty * weight) + (cost of debt * weigh)

= cost of debt = yeild to maturity (YTM) =

The formula for YTM = (C+ ((P-M) / n)) / ((p+m) / 2)

Here,

C (coupon interest) = Coupon rate * Par value = 6.8% * $1000 = $ 68

P (Par Value ) = $1000

M (Market Price) = $ 1033

n (years to maturity) = 16 years

Tax rate = 33% or .3

By applying values into the formula we get,

YTM = ($68 + (($1000 - $1033) / 16)) / (($1000+$1033) / 2)

YTM = ($68 + $2.0625) / $ 1016.5

YTM = 0.069 or 6.9%

After-tax cost of debt = YTM * (1 - tax rate)

After-tax cost of debt =6.9% * (1 - .33)

After-tax cost of debt =  4.62%

weight of debt = 100 - 75 = 25%

Cost of equity = (D1 / V) + G

Here

D1 = Next year dividend = $ 1.67

V = market value of stock = $ 22.74

G= growth rate = 3.5%

Cost of equity = (1.67./ 22.74) + 0.035

Cost of equity = 0.073 + 0.035 = 0.108 = 10.8 %

weight of equity = 75%

WACC = (10.8% * 75% ) + ( 4.62% * 25%)

WACC = 8.1 + 1.155= 9.26%

For the purpose of calculating IRR, we should calculate a positive NPV and a negetive NPV

IRR( Internal rate of return ) is the discount rate at which the NPV of a project will be Zero

For we calculate NPV at the Discount rate (WACC) of 9.26%

NPV calculation = Discount rate = 9.26%

Initial cost = $ 1.65 million + $ 37610 + $ 24737

Initial cost = $ 1712347

Operating cash flow

Saving s from operating cost = $391299 each year

Tax expense for this savings = $129129 same as each year

( at rate of 33% )=391299*33%)

operain cf (not taking dep.) = $ 262170 same as each year

Depr. Tax sheild : Depr. exp. * Tax rate = 154464 * 33% = 50973 same as each year

= operating net CF = 262170 + 50973 = 313143   same as each year 1 to 10

Depreciable base = 1650000-105364 = 1544636

dep. exp = Depreciable base / life

= 1544636 / 10 = 154464 each year

Terminal value

Book value = 105364

Sale value =105364

No gain and loss,so there is no tax effect

net cash flow from sale of asset = 105364

cash flows

0th year initial cost	1st year to 10 the year Operating Cash Flows	10th yearTerminal CF cash flow from sale
($ 1712347)	$ 313143 ( same each year)	$ 105364

Here we use the Trail and Error method to find IRR

NPV @ 9.26%

So the cash flow is discounted at the rate of 9.26%

PV of Initial cost = 1712347 * 1 (0th year) = $ 1712347 out flow

PV 1 to 10 year OCF = 313143 * ( 1/1+9.26)10GT  = 313143 * 6.345 = $ 1986849 inflow

PV of Terminal CF = 105364 * (1/1+9.26%)10 = 105364 * 0.4124 = $ 43459 inflow

therefore NPV = PV of Cash inflow - PV cash outflow

NPV = (1986849 + 43459) - 1712347 = 317961 This is positive NPV

so the IRR should be higher than 9.26% of WACC

For take another discount rate

by considering payback period = 1712347 / 313143 = 5.468 ( just look at the PV factor $1 table the row of year 10)

apprx.13% is the IRR for find correct IRR take a discount rate that higher than 13%. for that we take 15% for calculating IRR. When using the 15%discount rate, we get negative NPV and the IRR is between 15% and 9.26%

NPV @ 15%

So the cash flow is discounted at the rate of 15%

PV of Initial cost = 1712347 * 1 (0th year) = $ 1712347 out flow

PV 1 to 10 year OCF = 313143 * ( 1/1+15%)10GT  = 313143 * 5.019= $ 1571592 inflow

PV of Terminal CF = 105364 * (1/1+15%)10 = 105364 * 0.247 = $ 26025 inflow

therefore NPV = PV of Cash inflow - PV cash outflow

NPV = (1571592 + 26025) - 1712347 = (114730) This is negativ NPV

IRR = Discount rate where NPV is positive + (NPV@ Lower Discount rate / Difference between two NPV) * Higher Dis. rate - Lower Dic. rate

IRR = 9.26% + ( 317961 / 432691 ) * 15 % - 9.26%

IRR = 9.26% + 0.73 * 5.74%

IRR = 9.26% + 4.22 % = 13.48%