Question

The sales and finance team of a car company is evaluating a new proposed luxury model of its
brand that will require an investment of $1Billion in a new machine for car interior decoration.
Demand for the company’s car is expected to begin at 100,000 units in year 1, with 10% annual
growth thereafter. Production cost will be $35,000 per unit in the first year, and increase by a rate
of either 3% or 5% per year as a result of wage increase. Selling price will start at $37,000 and
increase by 4% of the production cost. The model will be phased out at the end of year 10. In
addition, 0.3%, 2% and 1.5% of before tax profit per year will be spent on social corporate
responsibility, commercial (including promotions) and recalls respectively. Assume taxes will be
30% of yearly profit and that inflation will remain at 0% per year throughout the 10 year of
production. Also assume interest rate is expected to be 3% per year in the first 5 years and 5% in
the last 5 years.
a. Based on present worth analysis, is the proposed investment profitable if production cost
increases by a rate of 3% per year as a result of wage increase? Justify your answer.
b. Based on present worth analysis, is the proposed investment profitable if production cost
increases by a rate of 5% per year as a result of wage increase? Justify your answer.

Answer 1

a.

	1	2	3	4	5	6	7	8	9	10
Units	100000.00	110000.00	121000.00	133100.00	146410.00	161051.00	177156.00	194872.00	214359.00	235795.00
Sale Price p.u	37000.00	38442.00	39927.26	41457.08	43032.79	44655.77	46327.45	48049.27	49822.75	51649.43
Total Selling price A	3700000000.00	4228620000.00	4831198460.00	5517937055.18	6300430803.52	7191857032.39	8207185210.15	9363457434.01	10679954562.58	12178677591.15
Production cost p.u	35000.00	36050.00	37131.50	38245.45	39392.81	40574.59	41791.83	43045.59	44336.95	45667.06
Total production cost B	3500000000.00	3965500000.00	4492911500.00	5090468729.50	5767501070.52	6534578712.90	7403673502.54	8388379296.61	9504024875.67	10768064750.84
Total Profit A-B	200000000.00	263120000.00	338286960.00	427468325.68	532929733.00	657278319.48	803511707.61	975078137.40	1175929686.92	1410612840.31
Less:Social Corporate responsibility	600000.00	789360.00	1014860.88	1282404.98	1598789.20	1971834.96	2410535.12	2925234.41	3527789.06	4231838.52
Less:Commercial	4000000.00	5262400.00	6765739.20	8549366.51	10658594.66	13145566.39	16070234.15	19501562.75	23518593.74	28212256.81
Less:Recalls	3000000.00	3946800.00	5074304.40	6412024.89	7993945.99	9859174.79	12052675.61	14626172.06	17638945.30	21159192.60
Profit before taxes	192400000.00	253121440.00	325432055.52	411224529.30	512678403.14	632301743.34	772978262.72	938025168.18	1131244358.81	1357009552.38
Less:Taxes	57720000.00	75936432.00	97629616.66	123367358.79	153803520.94	189690523.00	231893478.82	281407550.45	339373307.64	407102865.71
Profit after taxes	134680000.00	177185008.00	227802438.86	287857170.51	358874882.20	442611220.34	541084783.91	656617617.73	791871051.17	949906686.67
PV Factor	0.97087	0.94260	0.91514	0.88849	0.86261	0.74622	0.71068	0.67684	0.64461	0.61391
Cash Flow	130756771.6	167014588.5	208471123.9	255758217.4	309569062.1	330285344.8	384538134.2	444425068.4	510447998.3	583157214

PV of cash flows = 3324423523

Initial outlay = 1000000000

NPV = 3324423523 - 1000000000 = 2324423523

Since NPV is positive, the proposed investment is profitable.

b.

PV of cash flows = 364812812

Initial outlay = 1000000000

NPV = 364812812 - 1000000000 = -635187188

Since NPV is negative, the proposed investment is not profitable.

	1	2	3	4	5	6	7	8	9	10
Units	100000.00	110000.00	121000.00	133100.00	146410.00	161051.00	177156.00	194872.00	214359.00	235795.00
Sale Price p.u	37000.00	38470.00	40013.50	41634.18	43335.88	45122.68	46998.81	48968.75	51037.19	53209.05
Total Selling price A	3700000000.00	4231700000.00	4841633500.00	5541508692.50	6344806739.84	7267052404.51	8326121509.33	9542638722.78	10940281021.37	12546427838.59
Production cost p.u	35000.00	36750.00	38587.50	40516.88	42542.72	44669.85	46903.35	49248.51	51710.94	54296.49
Total production cost B	3500000000.00	4042500000.00	4669087500.00	5392796062.50	6228679452.19	7194124767.28	8309209415.87	9597156574.74	11084705501.63	12802840284.03
Total Profit A-B	200000000.00	189200000.00	172546000.00	148712630.00	116127287.65	72927637.24	16912093.46	-54517851.96	-144424480.26	-256412445.45
Less:Social Corporate responsibility	600000.00	567600.00	517638.00	446137.89	348381.86	218782.91	50736.28	-163553.56	-433273.44	-769237.34
Less:Commercial	4000000.00	3784000.00	3450920.00	2974252.60	2322545.75	1458552.74	338241.87	-1090357.04	-2888489.61	-5128248.91
Less:Recalls	3000000.00	2838000.00	2588190.00	2230689.45	1741909.31	1093914.56	253681.40	-817767.78	-2166367.20	-3846186.68
Profit before taxes	192400000.00	182010400.00	165989252.00	143061550.06	111714450.72	70156387.02	16269433.91	-52446173.58	-138936350.01	-246668772.52
Less:Taxes	57720000.00	54603120.00	49796775.60	42918465.02	33514335.22	21046916.11	4880830.17	-15733852.07	-41680905.00	-74000631.76
Profit after taxes	134680000.00	127407280.00	116192476.40	100143085.04	78200115.50	49109470.91	11388603.74	-36712321.51	-97255445.01	-172668140.76
PV Factor	0.97087	0.94260	0.91514	0.88849	0.86261	0.74622	0.71068	0.67684	0.64461	0.61391
Cash Flow	130756771.6	120094102.1	106332382.9	88976129.63	67456201.63	36646469.39	8093652.903	-24848367.69	-62691832.41	-106002698.3