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 $40,000 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 $35,000 and increase by 5% of the production cost. The model will be phased out at the end of year 10. In addition, 0.3%, 2% and 1% 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

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

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Question 1

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 $40,000 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 $35,000 and increase by 5% of the production cost. The model will be phased out at the end of year 10. In addition, 0.3%, 2% and 1% 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.

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Step 1

The question is based on the concept of present worth calculation in different cash flow situation.

Step 2

Answer a) Production cost increases by a rate of 3% per year

year		0	1	2	3	4	5	6	7	8	9	10
Cost of Machine		-$1,00,00,00,000

Demand in units with growth of 10% every year	D		100000	110000	121000	133100	146410	161051	177156.1	194871.71	214358.881	235794.7691
Production Cost per unit with growth of 3%	C		$40,000	$41,200.00	$42,436.00	$43,709.08	$45,020.35	$46,370.96	$47,762.09	$49,194.95	$50,670.80	$52,190.93
Selling Price per Unit increase by 5% of the production cost	S		$35,000	$37,060.00	$39,181.80	$41,367.25	$43,618.27	$45,936.82	$48,324.92	$50,784.67	$53,318.21	$55,927.76

Revenue from sales	R=D*S		$3,50,00,00,000	$4,07,66,00,000	$4,74,09,97,800	$5,50,59,81,507	$6,38,61,51,148	$7,39,81,70,761	$8,56,10,55,133	$9,89,64,95,892	$11,42,92,32,316	$13,18,74,72,931
Production cost	PC=D*C		-$4,00,00,00,000	-$4,53,20,00,000	-$5,13,47,56,000	-$5,81,76,78,548	-$6,59,14,29,795	-$7,46,80,89,958	-$8,46,13,45,922	-$9,58,67,04,930	-$10,86,17,36,685	-$12,30,63,47,664
Gross Profit	GP=R-PC		-$50,00,00,000	-$45,54,00,000	-$39,37,58,200	-$31,16,97,041	-$20,52,78,647	-$6,99,19,197	$9,97,09,211	$30,97,90,963	$56,74,95,631	$88,11,25,266
Social corporate responsibility (0.3%)	CSR=GP*0.3%		0	0	0	0	0	0	-299127.6322	-929372.8886	-1702486.892	-2643375.799
Commercial (including promotions) (2%)	CP=GP*2%		0	0	0	0	0	0	-1994184.215	-6195819.257	-11349912.61	-17622505.33
Recall (1%)	R=GP*1%		0	0	0	0	0	0	-997092.1074	-3097909.629	-5674956.307	-8811252.664

Profit Before tax	PBT=GP+CSR+CP+R		-$50,00,00,000	-$45,54,00,000	-$39,37,58,200	-$31,16,97,041	-$20,52,78,647	-$6,99,19,197	$9,64,18,807	$29,95,67,861	$54,87,68,275	$85,20,48,133
Tax (30%)	T=PBT*-30%		$15,00,00,000	$13,66,20,000	$11,81,27,460	$9,35,09,112	$6,15,83,594	$2,09,75,759	-$2,89,25,642	-$8,98,70,358	-$16,46,30,482	-$25,56,14,440
Net cash flow after tax	NP=PBT-T	-$1,00,00,00,000	-$35,00,00,000	-$31,87,80,000	-$27,56,30,740	-$21,81,87,928	-$14,36,95,053	-$4,89,43,438	$6,74,93,165	$20,96,97,503	$38,41,37,792	$59,64,33,693

Present value factor 3% for first 5 year	PV	1	0.970873786	0.942595909	0.915141659	0.888487048	0.862608784
Present value factor 5% for last 5 year	PV							0.746215397	0.71068133	0.676839362	0.644608916	0.613913254

Present value of cash flow	PCF=PV*NP	-$1,00,00,00,000	-$33,98,05,825	-$30,04,80,724	-$25,22,41,173	-$19,38,57,148	-$12,39,52,615	-$3,65,22,346.95	$4,79,66,132.10	$14,19,31,523.99	$24,76,18,646.07	$36,61,58,548.89

Present worth	PW = SUM of PCF	-$1,44,31,84,981

The project is not profitable at 3% growth in production cost

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