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 $2.29 million fully installed and has a 10 year life. It will be depreciated to a book value of $254,843.00 and sold for that amount in year 10.

b. The Engineering Department spent $33,328.00 researching the various juicers.

c. Portions of the plant floor have been redesigned to accommodate the juicer at a cost of $20,361.00.

d. The PJX5 will reduce operating costs by $315,155.00 per year.

e. CSD’s marginal tax rate is 25.00%.

f. CSD is 71.00% equity-financed.

g. CSD’s 18.00-year, semi-annual pay, 6.31% coupon bond sells for $983.00.

h. CSD’s stock currently has a market value of $24.90 and Mr. Bensen believes the market estimates that dividends will grow at 2.15% forever. Next year’s dividend is projected to be $1.56.

Answer 1

The NPV of the project is -198,692

Step 1. calculation of cost of debt

cost of bond is yield to maturity (YTM)

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

Here,

C (coupon interest) = Coupon rate * Par value = 6.31% * $1000 = $63.1

P (Par Value) = $1000

M (Market Price) = $983

n (years to maturity) = 18 years

Tax rate = 25% or .25

By applying values into the formula, we get,

YTM = ($63.1 + (($1000 - $983) / 18)) / (($1000+$983) / 2)

YTM = ($63.1 + $.944 / $991.5

YTM = 0.0644 or 6.44%

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

After-tax cost of debt =6.44% * (1 - .25)

After-tax cost of debt =4.83

weight of debt = .29 (1-.71)

Step 2. Cost of equity = (1.56/ 24.90) + 2.15%

=6.21% + 2.15%

= 8.36%

weight of equity = .71

WACC = (8.36 * .71) + (4.83 * .29)

WACC = 5.94 + 2.79

WACC = 7.34

Step 3. NPV calculation: -

Research cost of $ by Engineering department will not be considered because it is a sunk cost, which is irrelevant for decision making.

Therefore, Initial cost = 2,290,000 + 20,361

Initial cost = 2310361

Net salvage value = $254,843 (the machine is sold at book value there will not be any gain or loss on sale, therefore there will not be any tax gain or loss on machine)

Reduction in operating cost = 315,155

After tax cost benefit = 315,155 * (1- tax rate)

=315,155 * .75

=$236,366.25

Depreciation tax shield = depreciable base / 10 * tax rate

here, there is a book value of $254843 in year 10 therefore,

Depreciable base = cost of purchase - book value in year 10

=2290000 - 254843 = 2035157

= $2,035157 / 10 * tax rate

=$203515.7 * .25

=$50879

After tax operating cash flows = after tax cost benefit + depreciation tax shield

=$236,366 + 50879

=$287,245

PV of operating cash flows =$287,245 * PVAF (7.34, 10)

=$287,245 * 6.9145

= $1,986,159

PV of salvage = 254,843 * PVIF (7.34%,10)

=254,843 * .4925

= 125,510

NPV = PV of operating cash flows + PV of salvage - initial investment

=1,986,159 + 125,510 - 2310361

NPV = -198,692