Question

Mr. Piko Taro is a CEO of PPAP, Inc., a firm that manufactures high quality pens and produces apples and pineapples. Taro is considering replacing an old pineapple picking machine, which was bought for $2.5 million five years ago, with a new semi-auto pineapple picking machine. The new machine can be purchased for $3 million and it costs $250,000 to have it delivered and installed today. When the old machine was purchased five years ago, the machine was to be depreciated according to a 5-year MACRs schedule. Taro believes that the old machine can be sold for $200,000 today if the firm decides to replace it with the new one. The new machine will be depreciated using the straightline method over a 5 year life. The projected sales of pineapples harvested by the new machine will be $850,000 in Year 1, after which the sales will grow at a rate of 15 percent each year. Total fixed costs are $115,000 per year, while variable costs are 15 percent of each year’s sales. After 5 years, the firm will stop pineapple production and sell the machine for $350,000. Net working capital of $200,000 will be required immediately (Year 0) as well as in each year. PPAP’s tax rate is 21 percent.

Taro has hired you as a consultant: He wants you to estimate the project’s NPV and other discount cash flow criteria.

Q1. What is the project’s Year 0 net cash flow? Round your answer to two decimal places. (10 pts)

Q2. Calculate the net cash flows for Years 1, 2, 3, 4, and 5. Round your answer to two decimal places. (5 pts*5 years=25 pts)

Q3. What is the payback period? Round your answer to two decimal places. (5 pts)

Q4. If the discount rate is 15 percent, what is the NPV? Round your answer to two decimal places. (5 pts)

Q5. At exactly what discount rate should the firm be break-even, in terms of NPV? Round your answer to two decimal places. (5 pts)

Answer 1

Q1 = $3,248,267.50

	Incremental initial flow
	a)the cost of new asset	$    3,250,000.00
Add:	working capital on new asset	$       200,000.00
	Out flow	$    3,450,000.00
Less:	Salvage value of old asset after taxation today	$       201,732.50
Less:	Recapture of WC on old asset	$                         -
	Incremental flow	$    3,248,267.50

Salvage value of old asset today	$       200,000.00
Book value after 5 years	$       208,250.00
Profit / Loss on sale	$          (8,250.00)
Tax @ 21%	$          (1,732.50)
Salvage value of old asset after tax	$       201,732.50

Depreciation calculation of old machine
Year	Cost		Depreciation	Book Value	Method
1	$ 2,500,000.00	15%	375,000.00	$ 2,125,000.00	DB
2	$ 2,125,000.00	25.50%	637,500.00	$ 1,487,500.00	DB
3	$ 1,487,500.00	17.85%	446,250.00	$ 1,041,250.00	DB
4	$ 1,041,250.00	16.66%	416,500.00	$      624,750.00	Straight Line
5	$      624,750.00	16.66%	416,500.00	$      208,250.00	Straight Line
6	$      208,250.00	8.33%	208,250.00	$                       -	Straight Line

Q2.

Particulars	Year 0	Year 1	Year 2	Year 3	Year 4	Year 5
Initial Investment	$    3,248,267.50
Sales		$        850,000.00	$       977,500.00	$   1,124,125.00	$    1,292,743.75	$ 1,486,655.31
Less: Variable Cost		$        127,500.00	$       146,625.00	$       168,618.75	$       193,911.56	$      222,998.30
Less: Fixed Cost		$        115,000.00	$       115,000.00	$       115,000.00	$       115,000.00	$      115,000.00
Less: Depreciation		$        650,000.00	$       650,000.00	$       650,000.00	$       650,000.00	$      650,000.00
EBIT		$        (42,500.00)	$          65,875.00	$       190,506.25	$       333,832.19	$      498,657.02
Less Income tax @ 21%		$          (8,925.00)	$          13,833.75	$         40,006.31	$          70,104.76	$      104,717.97
Profit After Tax		$        (33,575.00)	$          52,041.25	$       150,499.94	$       263,727.43	$      393,939.04
Add: Depreciaiton		$        650,000.00	$       650,000.00	$       650,000.00	$       650,000.00	$      650,000.00
Cash flow After Tax		$        616,425.00	$       702,041.25	$       800,499.94	$       913,727.43	$ 1,043,939.04
Step 3 : Terminal Flow
Salvage value of new asset after taxation						$      276,500.00
Increase in working capital		$      (200,000.00)	$     (200,000.00)	$     (200,000.00)	$     (200,000.00)	$   (200,000.00)
Less salvage value of old asset after taxation -terminal flow						$                       -
Less Recapture of WC on old asset		$                          -	$                         -	$                         -	$                         -	$                       -
Total Net Cash flow	$ (3,248,267.50)	$        416,425.00	$       502,041.25	$       600,499.94	$       713,727.43	$ 1,120,439.04

Sales Value of new machine	350,000.00
Book Value	$                         -
Profit	350,000.00
Tax @ 21%	73,500.00
Sales Value of new machine after tax	276,500.00

Depreciaiton calculation of new machine
Year	Cost	Depreciation rate	Depreciation	Book Value	Method
1	$ 3,250,000.00	20%	650,000.00	$ 2,600,000.00	DB
2	$ 2,600,000.00	20%	650,000.00	$ 1,950,000.00	DB
3	$ 1,950,000.00	20%	650,000.00	$ 1,300,000.00	DB
4	$ 1,300,000.00	20%	650,000.00	$      650,000.00	SL
5	$      650,000.00	20%	650,000.00	$                       -	SL

Q3.

Payback period = Base year + unrecovered Cash flow in base year / Cash flow in subsequent year * 12
Unrecovered cash flow in base year		$ (1,015,573.88)
Cash flow in subsequent year		$    1,120,439.04
Base year = the year just proceeding the un recovered cash flow turns to be positive		$                     4.00		$                  (0.91)
Payback period =		4.91 Years

Note:

Total Net Cash flow	$ (3,248,267.50)	$        416,425.00	$       502,041.25	$       600,499.94	$       713,727.43	$ 1,120,439.04
Cumulative Cash Flow	$ (3,248,267.50)	$ (2,831,842.50)	$ (2,329,801.25)	$ (1,729,301.31)	$ (1,015,573.88)	$      104,865.16

Q5.

Firm Break Even = 0.919%