Question

PC Shopping Network may upgrade its modem pool. It last upgraded 2 years ago, when it spent $155 million on equipment with an assumed life of 5 years and an assumed salvage value of $20 million for tax purposes. The firm uses straight-line depreciation. The old equipment can be sold today for $120 million. A new modem pool can be installed today for $180 million. This will have a 3-year life and will be depreciated to zero using straight-line depreciation. The new equipment will enable the firm to increase sales by $33 million per year and decrease operating costs by $10 million per year. At the end of 3 years, the new equipment will be worthless. Assume the firm's tax rate is 30% and the discount rate for projects of this sort is 10% Required: a. What is the net cash flow at time of the old equipment is replaced? (Negative amounts should be indicated by a minus sign. Do not round Intermediate calculations. Enter your answer in millions rounded to 2 decimal places.) b. What are the incremental cash flows in years () 1: () 2:1) 3? (Do not round Intermediate calculations. Enter your answer in millions rounded to 2 decimal places.) c. What is the NPV of the replacement project? (Do not round Intermediate calculations. Enter the NPV in millions rounded to 2 decimal places.) d. What is the IRR of the replacement project? (Do not round intermediate calculations. Enter the IRR as a percent rounded to 2 decimal places.) mil on Net cash flow cremental cash flow million per year

Answer 1

a) First we need to find the depreciated value of the old equipment to see if we make a profit or a loss on its sale. Following is the depreciation schedule:

Year	Opening balance	Depreciation	Closing balance
1	155-20 = $135.00	$            27.00	$               108.00
2	$                  108.00	$            27.00	$                  81.00
3	$                    81.00	$            27.00	$                  54.00
4	$                    54.00	$            27.00	$                  27.00
5	$                    27.00	$            27.00	$                         -

• Opening balance at year 1 is cost - salvage value
  • Opening balance at year 1 is 155-20 = 135 million
• Annual depreciation = 135/5 = 27 million
• Closing balance = Opening balance - depreciation
• Opening balance = previous year's closing balance
• So after 2 years the closing balance or the depreciated value of the equipment was 81 million and it was sold for 120 million
• Therefore the profit made on the sale was 120-81 = 39 million.
• We will have to pay the tax @ 30% on this profit
  • Tax = 30% x 39 = 11.70 million
• So the net CF in year 0 = Cost of new equipment - (Sale price - Tax)
  • net CF in year 0 = 180 - (120- 11.70)
  • net CF in year 0 = 71.70 million
  • 71.70 million is the cash out flow

b) Next we need to find the annual CF for years 1-3

Particulars	Remark	Years 1-3
Sales increase	Given	33.00
Cost reduction	Given	10.00
EBITDA	Sales increase+Cost reduction	43.00
Depreciation	180/3	60.00
EBT	EBITDA-Depreciation	-17.00
Tax	30% x EBT	-5.10
EAT	EBT-Tax	-11.90
Depreciation	Added back as non cash	60.00
OCF	EAT+Depreciation	48.10

So annual CF is 48.10 million

c) NPV of the project is as follows:

Year	CF	Discount Factor		Discounted CF
0	$ -71.70	1/(1+0.1)^0=	1	1*-71.7=	$ -71.70
1	$   48.10	1/(1+0.1)^1=	0.909090909	0.909090909090909*48.1=	$   43.73
2	$   48.10	1/(1+0.1)^2=	0.826446281	0.826446280991735*48.1=	$   39.75
3	$   48.10	1/(1+0.1)^3=	0.751314801	0.751314800901578*48.1=	$   36.14
				NPV = Sum of all Discounted CF	$   47.92

NPV = $47.92 million

d) IRR is the rate at which NPV = 0

IRR can be calculated using either a financial calculator or excel or through hit and trial:

Using Excel we get the IRR = 45.15% rounded to two decimal places

Year	CF	Discount Factor		Discounted CF
0	$-71.70	1/(1+0.451457399111732)^0=	1	1*-71.7=	$ -71.70
1	$ 48.10	1/(1+0.451457399111732)^1=	0.688962694	0.688962694056321*48.1=	$   33.14
2	$ 48.10	1/(1+0.451457399111732)^2=	0.474669594	0.474669593801344*48.1=	$   22.83
3	$ 48.10	1/(1+0.451457399111732)^3=	0.327029642	0.327029642131994*48.1=	$   15.73
				NPV = Sum of all Discounted CF	$     0.00