Tristan\'s Toys invested in a new manufacturing system. The initial cost was $32
ID: 2785325 • Letter: T
Question
Tristan's Toys invested in a new manufacturing system. The initial cost was $327030. Annual costs are projected to be $193637, increasing by 14% each subsequent year. The system will require a substantial overhaul of $37722 at the end of year 7. The line is estimated to have a lifespan of 13 years.
The company projects it will sell 55928 units the first year, with the number of units sold increasing by 36562 units each subsequent year. What is the minimum price that the company must charge per unit to breakeven on the investment? Use a MARR of 4% compounded annually to make the calculation.
*Note*- please use compound interest factors if possible.
Explanation / Answer
To calculate the unit price to breakeven investment, we first need to calculate the present value of all costs occurring during the project life. The calculation is given below:
Initial Cost = $327,030
Present value of annual cost growing at 14% each year:
Year
Nominal Value increasing at 14%
PV factor at 4%
Present Value = Nominal Value*PV factor
1
$193,637.00
0.961538462
$186,189.42
2
$220,746.18
0.924556213
$204,092.25
3
$251,650.65
0.888996359
$223,716.51
4
$286,881.74
0.854804191
$245,227.71
5
$327,045.18
0.821927107
$268,807.30
6
$372,831.50
0.790314526
$294,654.15
7
$425,027.91
0.759917813
$322,986.28
8
$484,531.82
0.730690205
$354,042.66
9
$552,366.28
0.702586736
$388,085.22
10
$629,697.56
0.675564169
$425,401.11
11
$717,855.21
0.649580932
$466,305.06
12
$818,354.94
0.62459705
$511,142.08
13
$932,924.64
0.600574086
$560,290.36
Present value of all annual costs
$4,450,940.11
Present value of Overhaul Cost occurring at the end of Year 7 = $37,722*0.759917813 = $28,665.62
Present value of all cost = $327,030 + $4,450,940.11 + $28,665.62 = $4,806,635.73
Total units to be sold during the project span:
Year
Units Sold
1
55,928
2
92,490
3
129,052
4
165,614
5
202,176
6
238,738
7
275,300
8
311,862
9
348,424
10
384,986
11
421,548
12
458,110
13
494,672
Total Units Sold
3,578,900
Unit price to break-even = Present value of all cost / Total Units Sold
=> $4,806,635.73/3,578,900 = $1.343
Please do give a thumbs-up for my answer as it works as a life-savior for us.
Year
Nominal Value increasing at 14%
PV factor at 4%
Present Value = Nominal Value*PV factor
1
$193,637.00
0.961538462
$186,189.42
2
$220,746.18
0.924556213
$204,092.25
3
$251,650.65
0.888996359
$223,716.51
4
$286,881.74
0.854804191
$245,227.71
5
$327,045.18
0.821927107
$268,807.30
6
$372,831.50
0.790314526
$294,654.15
7
$425,027.91
0.759917813
$322,986.28
8
$484,531.82
0.730690205
$354,042.66
9
$552,366.28
0.702586736
$388,085.22
10
$629,697.56
0.675564169
$425,401.11
11
$717,855.21
0.649580932
$466,305.06
12
$818,354.94
0.62459705
$511,142.08
13
$932,924.64
0.600574086
$560,290.36
Present value of all annual costs
$4,450,940.11
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.