Question

Premium Pie Company needs to purchase a new baking oven to replace an older oven that requires too much energy to run. The industrial size oven will cost $1,200,000. The oven will be fully depreciated on a straight-line basis over its six-year useful life. The old oven cost the company $800,000 just four years ago. The old oven is being depreciated on a straight-line basis over its expected ten-year useful life. (That is, the old oven is expected to last six more years if it is not replaced now.) Due to changes in fuel costs, the old oven may only be sold today for $100,000. The new oven will allow the company to expand, increasing sales by $300,000 per year. Expenses will also decrease by $50,000 per year due to the more energy efficient design of the new oven. Premium Pie Company is in the 40% marginal tax bracket and has a required rate of return of 10%.

a. Calculate the net present value and internal rate of return of replacing the existing machine

b. Explain the impact on NPV of the following:

i. Required rate of return increases

ii. Operating costs of new machine are increased

iii. Existing machine sold for less

Answer 1

The industrial size oven will cost $1,200,000

depreciated on a straight-line basis over its six-year useful life.

The old oven cost the company $800,000 just four years ago

The old oven is being depreciated on a straight-line basis over its expected ten-year useful life.

the old oven may only be sold today for $100,000

increasing sales by $300,000 per yea

. Expenses will also decrease by $50,000 per year

the 40% marginal tax bracket and has a required rate of return of 10%.

a. Calculate the net present value and internal rate of return of replacing the existing machine

Net Initial investment =

New industrial size oven will cost   = $1,200,000

Proceeds from oven = 100000 (inflow)

Tax on proceeds as benefits = 152000 (out flow)

Net Initial investment = 1200000 - 100000 - 152000 = 948000

Old depreciation = 800000 / 10 = 80000

Accumulated depreciation for 4 year = 80000 * 4 = 320000

Book value = 800000 - 320000 = 480000

Tax able loss = 100000 - 480000 = 380000

Tax benefit from proceeds = 380000 * 40% = 152000

Operating cash flow 1st year to 6th years

Annual incremental sale = 300000

-Incremental cost = 50000

=incremental earnings = 250000

-Tax exp. @40% = 100000

=Earning after tax (excluding depreciation) = 150000

+Depreciation tax shield = 80000

= incremental operating cash flow = 230000

Depreciation tax shield =

Depreciation on new oven = 1200000 / 6 = 200000

Depreciation tax shield = 200000 * 40% = 80000

NPV calculation

years	CF	PV of $1 factor	PV of CF
Initial investment	-948000	1	-948000
1st year to 6th year	230000	(1 / 1 + 10%)^6GT = 6.1445	1413250.42

NPV = PV of CF - initial investment

NPV = 1413250.42 - 948000 =   $ 465250

IRR calculation

IRR is the rate at which NPV of the project become zero

NPV = 0 = PV of CF - initial investment

0 = (230000 * ( 1 / 1 + irr )^6GT) - 948000

( 1 / 1 + irr )^6GT) = 948000 / 230000 = 4.1217

( 1 / 1 + irr )^6GT) = 4.1217 = PV of annuity $1 factor discounted @ IRR

**Consult the PV of $1 annuity table and find closest value of 4.1217 in the 6 years period (n) row. Also find its correspondent discount rate on top of that column. This is the IRR of this project.

Closest value = 4.1114 on the table and its rate is 12%

Also that correct irr is just below 12%

So 12% is the approx. IRR of this project

Correct IRR is between 10% ( actual cost of capital) and 12%

IF you want to find correct irr just use a formula

IRR = Lower discount rate + ( NPV @ Lower discount rate / difference between NPV ) * Higher discount rate - lower discount rate

Lower discount rate = 10%

NPV @ Lower discount rate = 465250

Higher discount rate = 12%

NPV @ Higher discount rate

Find NPV @ 12% = ( 230000 * ( 1 / 1 + 12%)^6GT) - 948000 = - 2376.32

difference between NPV = 465250 - - 2376.32 = 467626.32

IRR = 10% + (465250 / 467626.32 ) * 12 - 10

IRR = 10 + 0.99 * 2

IRR = 10 + 1.98 = 11.98%

b. Explain the impact on NPV of the following:

i. Required rate of return increases

If the required rate of return will increse, the project's NPV will decrease. Because more value are discounted to find present value

ii. Operating costs of new machine are increased

IF cost increase, The cash flow will decrease, that will leads to decrease the NPV of the project.

iii. Existing machine sold for less

Existing machine sold for less, The initial investment will increase. if initial investment increase, the NPV will decrease.