Question

Your firm is contemplating the purchase of a new $1,350,500 computer-based order entry system. The system will be depreciated straight-line to zero over its 5-year life. It will be worth $131,400 at the end of that time. You will be able to reduce working capital by $182,500 (this is a one-time reduction). The tax rate is 25 percent and your required return on the project is 20 percent and your pretax cost savings are $401,150 per year.

a. What is the NPV of this project?

b. What is the NPV if the pretax cost savings are $557,200 per year?

c. At what level of pretax cost savings would you be indifferent between accepting the project and not accepting it?

Answer 1

a.)

Annual depreciation charge = $1,350,500/5 = $270,100 ( Straight line depreciation)

Aftertax salvage value = $131,400*(1-0.25) = $98,550

Operating Cash Flow (OCF) = Pre-tax cost saving (1-t) + Annual depreciation charge * t

Operating Cash Flow (OCF) = $401,150*(1-0.25) + 0.25*($270,100) = $368,387

Cash Flow at t(0) = -Initial investment + One time working capital reduction

Cash Flow at t(0) = -$1,350,500+$182,500 = -$11,68,000

At the end of 5 years, the system can be sold for $131,400 and the working capital reduction will be reversed.

Hence the additional cash flow at the end of year 5 = 131,400*(1-0.25) - 182,500 = -$83,950

Cash flow at t(5) = Operating cash flow - additional cash flow at the end of year 5 = $284,437

Substituting the values in the financial calculator

CFo = -11,68,000

C01 = 368,387

F01 = 4

C02 = 284,437

F02 = 1
NPV I = 20

CPT NPV = -100,034

Hence, we will reject the project since NPV < 0

b)

Pretax cost savings are $557,200 per year

Using depreciation & salvage values as calculated in part a)

Operating Cash Flow (OCF) = $557,200(1-0.25) + 0.25*($270,100) = $485,425

At the end of 5 years, the system can be sold for $131,400 and the working capital reduction will be reversed.

Hence the additional cash flow at the end of year 5 = 131,400*(1-0.25) - 182,500 = $-83,950

Cash Flow at t(0) = -11,68,000

At the end of 5 years, the system can be sold for $131,400 and the working capital reduction will be reversed.

Hence the additional cash flow at the end of year 5 = 131,400*(1-0.25) - 182,500 = -$83,950

Cash flow at t(5) = Operating cash flow - additional cash flow at the end of year 5 = $401,475

Substituting the values in the financial calculator,

CFo = -11,68,000

C01 = 485,425

F01 = 4

C02 = 401,475

F02 = 1

NPV I = 20
CPT NPV = $249,980.28

Hence, we will accept the project since NPV > 0

c)

At NPV = 0, we would be indifferent between accepting the project and not accepting it

The present value interest factor of annuity (PVIFA) =

where r=0.2

n=5

Substituting, we get

PVIFA = 2.990

Solving for Operating cash flows (OCF) by substituting NPV=0

OCF = 401,918.94

Now, we use the Tax shield approach

OCF = Pre-tax cost saving (1-t) + Annual depreciation charge * t

401,918.94 = Pre-tax cost saving(1-0.25) + 0.25*($270,100)

Pre-tax cost saving = $445.858.59

Minimum cost savings for indifference = $169,904.63