Question

3. [4 points total] You are production engineer at a baking facility that produces glazes and fillings for all major doughnut companies in the US. You are planning to increase production and therefore looking at new equipment that will help increase capacity. You team has come up with three alternative projects that would provide the needed capacity. The options are: Project 1: Pick Heater - To increase the water temperature faster, therefore clean all equipment and lines faster. Project 2: Canner-To automatically can the finished product (i.e. place it in the final saleable container) Project 3: Second production line - A duplicate set of equipment to expand production capacity. Cash flows associated with each of these machines are shown in the table below. Assume that the prevailing interest rate, regardless of which project is selected is 6% per year. 0 1 2 3 4 5 6 7 8 9 10 -87,750 0 2,000 5,000 5,000 12,000 18,000 24,000 46,000 60,000 80,000 -52,500 1,000 2,000 5,000 8,000 18,000 22,000 24,000 24,000 26,000 28,000 -40,000 0 -5,000 -5,000 10,000 10,000 14,000 14,000 24,000 24,000 30,000 Project 1 Project 2 Project 3

please show all work. no excel.

Answer 1

Ans.a

The payback period can be calculated as follows:

Project A

Year	Total Flow	Cumulative flow
0	-87750	-87750
1	0	-87750
2	2000	-85750
3	5000	-80750
4	5000	-75750
5	12000	-63750
6	18000	-45750
7	24000	-21750
8	46000	24250
9	60000	84250
10	80000	164250

Now to find out the payback period:

Step 1: We must pick the year in which the outflows have become positive. In other words, the year with the last negative outflow has to be selected. So, in this case, it will be year seven.

Step 2: Divide the total cumulative flow in the year in which the cash flows became positive by the total flow of the consecutive year.

So that is: 21750/46000 = 0.47

Step 3: Step 1 + Step 2 = The payback period is 7.47 years for project A.

Similarly for Project B,

Year	Total Flow	Cumulative flow
0	-52500	-52500
1	1000	-51500
2	2000	-49500
3	5000	-44500
4	8000	-36500
5	18000	-18500
6	22000	3500
7	24000	27500
8	24000	51500
9	26000	77500
10	28000	105500

Now to find out the payback period:

Step 1: We must pick the year in which the outflows have become positive. In other words, the year with the last negative outflow has to be selected. So, in this case, it will be year five.

Step 2: Divide the total cumulative flow in the year in which the cash flows became positive by the total flow of the consecutive year.

So that is: 18500/22000 = 0.84

Step 3: Step 1 + Step 2 = The payback period is 5.84 years for project B.

Similarly for Project B,

Year	Total Flow	Cumulative flow
0	-40000	-40000
1	0	-40000
2	-5000	-45000
3	-5000	-50000
4	10000	-40000
5	10000	-30000
6	14000	-16000
7	14000	-2000
8	24000	22000
9	24000	46000
10	30000	76000

Now to find out the payback period:

Step 1: We must pick the year in which the outflows have become positive. In other words, the year with the last negative outflow has to be selected. So, in this case, it will be year seven.

Step 2: Divide the total cumulative flow in the year in which the cash flows became positive by the total flow of the consecutive year.

So that is: 2000/24000 = 0.08

Step 3: Step 1 + Step 2 = The payback period is 7.08 years for project C.

Based on this approach, only Project B should be considered for installation and project A & project C should be eliminated.

Ans.b

Calculation of Discounted Payback Period

Project A

Year	Total Flow	PV Factor @6%	DCF	Cumulative flow
0	-87750	1	-87750	-87750
1	0	0.943	0.00	-87750.00
2	2000	0.890	1779.99	-85970.01
3	5000	0.840	4198.10	-81771.91
4	5000	0.792	3960.47	-77811.44
5	12000	0.747	8967.10	-68844.34
6	18000	0.705	12689.29	-56155.05
7	24000	0.665	15961.37	-40193.68
8	46000	0.627	28860.97	-11332.71
9	60000	0.592	35513.91	24181.19
10	80000	0.558	44671.58	68852.78

Now to find out the payback period:

Step 1: We must pick the year in which the outflows have become positive. In other words, the year with the last negative outflow has to be selected. So, in this case, it will be year eight.

Step 2: Divide the total cumulative flow in the year in which the cash flows became positive by the total flow of the consecutive year.

So that is: 11332.71/33513.91 = 0.34

Step 3: Step 1 + Step 2 = The payback period is 8.34 years for project A.

Project B

Year	Total Flow	PV Factor @6%	DCF	Cumulative flow
0	-52500	1	-52500	-52500
1	1000	0.943	943.40	-51556.60
2	2000	0.890	1779.99	-49776.61
3	5000	0.840	4198.10	-45578.51
4	8000	0.792	6336.75	-39241.77
5	18000	0.747	13450.65	-25791.12
6	22000	0.705	15509.13	-10281.99
7	24000	0.665	15961.37	5679.38
8	24000	0.627	15057.90	20737.28
9	26000	0.592	15389.36	36126.64
10	28000	0.558	15635.05	51761.70

Now to find out the payback period:

Step 1: We must pick the year in which the outflows have become positive. In other words, the year with the last negative outflow has to be selected. So, in this case, it will be year six.

Step 2: Divide the total cumulative flow in the year in which the cash flows became positive by the total flow of the consecutive year.

So that is: 10281.99/15961.37 = 0.64

Step 3: Step 1 + Step 2 = The payback period is 6.64 years for project B.

Project C

Year	Total Flow	PV Factor @6%	DCF	Cumulative flow
0	-40000	1	-40000	-40000
1	0	0.943	0.00	-40000.00
2	-5000	0.890	-4449.98	-44449.98
3	-5000	0.840	-4198.10	-48648.08
4	10000	0.792	7920.94	-40727.14
5	10000	0.747	7472.58	-33254.56
6	14000	0.705	9869.45	-23385.11
7	14000	0.665	9310.80	-14074.31
8	24000	0.627	15057.90	983.58
9	24000	0.592	14205.56	15189.15
10	30000	0.558	16751.84	31940.99

Now to find out the payback period:

Step 1: We must pick the year in which the outflows have become positive. In other words, the year with the last negative outflow has to be selected. So, in this case, it will be year seven.

Step 2: Divide the total cumulative flow in the year in which the cash flows became positive by the total flow of the consecutive year.

So that is: 14074.31/15057.9 = 0.93

Step 3: Step 1 + Step 2 = The payback period is 7.93 years for project C.

Based on this approach also, only Project B should be considered for installation and project A & project C should be eliminated