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