Question

 

Assume project lasts 4 years

Operating income 100

Tax rate 21%

Machine cost 50

Straight line depreciation over 5 years

Salvage value after 5 years = 20

Working capital 2 per year , 3 initially

WACC = 10%

1. What is the IRR
2. What is the NPV
3. What is the payback

Answer 1

1. IRR of the project is = 153.7% Approx.

CALCULATION: -

Internal Rate Of return (IRR) is the interest rate (discount rate) that makes the NPV of the project zero. In other words, the present value of its expected cash inflows will be equal to the present value of its expected cash outflows. IRR of this project can be calculated using trial and error method as follows: -

The NPV of the project using 10% discount rate is 218.6. This NPV is larger value than the initial investment of the project therefore, lets assume a very higher discount rate (i.e. 150%) for the calculation of IRR.

NPV with 150%: -

NPV = after-tax operating cashflows *(PVIFA. 10%,4 years) + Terminal cashflow * (PVIF.10%, year 4)- initial investment

NPV= 81.1 * .6496) + 19.9 * .0256) - 52

NPV=    52.6825 + .50944 - 52

NPV = 1.19194

Since the NPV with discount rate 150% is positive, let’s assume another discount rate (i.e. 160%) for the IRR calculation.

NPV with 160%: -

NPV = after-tax operating cashflows *(PVIFA. 10%,4 years) + Terminal cashflow * (PVIF.10%, year 4)- initial investment

NPV= 81.1 * .611323) + 19.9 * .021883) - 52

NPV=    49.5783 + .4357 - 52

NPV = -1.98623

Since the NPV of 150% is positive and 160% is negative IRR lies between 150% and 160%, to get the exact IRR we have to interpolate using the following formula: -

IRR = 150% + [(160%-150%) *1.19194 / 1.19194 - -1.98623)}]

= 150 + 3.7%

IRR = 153.7% Approx.

2. NPV of the project is 218.6

Step 1: -

Initial investment of the project is 52

Initial investment = cost of new equipment + increase in Net working capital

1.cost of cost of new equipment = 50

2.increase in Net working capital = 2

Initial investment = 50+2 = 52

Step 2: -

Yearly after-tax operating Cash Flow for each year is 81.1

early after-tax operating Cash Flow

Operating income	100
Taxes (21%)	21
Net income	79
Add depreciation tax shield (50/5 * .21)	2.1
Yearly operating Cash Flow	81.1

Step 3: -

Terminal cash flow of the project is 19.9

Terminal cashflow = NSV of project assets + Recovered Net working capital

Recovered Net working capital =2

Net salvage value of machine = 17.9

Terminal cashflow= 17.9+2= 19.9

Net salvage value of machine

Book value of old asset (BV)	Depreciation basis - Accumulated Depreciation
	= 50 - (4 * 10)
	= 10
Market value (MV)	= 20
NSV of project old asset	= MV - tax rate (MV-BV)
	= 20 - .21 *(20- 10)
	= 17.9

Step 4: - calculation of NPV

NPV = after-tax operating cashflows *(PVIFA. 10%,4 years) + Terminal cashflow * (PVIF.10%, year 4)- initial investment

NPV= 81.1 * 3.170) + 19.9 * .683) - 52

NPV=    257 + 13.6 - 52

NPV = 218.6

3. The payback period of the project is .641 years

The payback period can be calculated as follows: -

Year	Total flow	Cumulative flow
0	(52)	(52)
1	81.1	29.1
2	81.1	110.2
3	81.1	191.3
4	81.1	272.4

Now to find out the payback period:

Step 1: We must pick the year in which the outflows have become positive.

in this case it is: -

A = Year 0

Step 2: Divide the total cumulative flow in the year in which the cash flows became positive by the total flow of the consecutive year.

So that is:

A = 52 / 81.1 = .641

The payback period of A is .641 years.