In: Finance
The payback of a project is the number of years it takes before the project’s total cash flow is positive. Payback ignores the time value of money. It is interesting, however, to see how differing assumptions on project growth impact payback. Suppose, for example, that a project requires a $300 million investment at year 0 (right now). The project yields cash flows for 10 years. The annual cash flow growth is assumed to be 15% per year. Assume that this growth is the same each year. The first year’s cash flow will be between $30 million and $100 million: {$30 million, $40 million, $50 million, $60 million, $70 million, · · · , $100 million}. Compute the project payback year as a function of the year 1 cash flow. PRovide answers in a spreadsheet model.
Year |
Cashflows in (USD) ---> Previous year cashflows x 115% |
|||||
1st year cashflow = 30Mn USD |
1st year cashflow = 40Mn USD |
1st year cashflow = 50Mn USD |
||||
Annual cashflows |
Cumulative cashflows |
Annual cashflows |
Cumulative cashflows |
Annual cashflows |
Cumulative cashflows |
|
1 |
30.00 |
30.00 |
40.00 |
40.00 |
50.00 |
50.00 |
2 |
34.50 |
64.50 |
46.00 |
86.00 |
57.50 |
107.50 |
3 |
39.68 |
104.18 |
52.90 |
138.90 |
66.13 |
173.63 |
4 |
45.63 |
149.80 |
60.84 |
199.74 |
76.04 |
249.67 |
5 |
52.47 |
202.27 |
69.96 |
269.70 |
87.45 |
337.12 |
6 |
60.34 |
262.61 |
80.45 |
350.15 |
100.57 |
437.69 |
7 |
69.39 |
332.00 |
92.52 |
442.67 |
115.65 |
553.34 |
8 |
79.80 |
411.80 |
106.40 |
549.07 |
133.00 |
686.34 |
9 |
91.77 |
503.58 |
122.36 |
671.43 |
152.95 |
839.29 |
10 |
105.54 |
609.11 |
140.72 |
812.15 |
175.89 |
1,015.19 |
Step 1 : Monthly cash inflows of upper bound of 300 Mn of initial investment---> marked in green --> (Annual cashflow /12) |
5.78 |
6.70 |
7.29 |
|||
Step 2 : Additional cashinflow
required post lower bound year of 300 Mn investment (marked in
yellow) |
37.39 |
30.30 |
50.33 |
|||
No. of months post lower
bound year ---> |
6 |
5 |
7 |
|||
Payback period (lower bound year + months in upper bound year); rounded off to nearest month |
6 year 6 months |
5 year 5 months |
4 year 7 months |
Year |
Cashflows in (USD) ---> Previous year cashflows x 115% |
|||||
1st year cashflow = 60Mn USD |
1st year cashflow = 70Mn USD |
1st year cashflow = 80Mn USD |
||||
Annual cashflows |
Cumulative cashflows |
Annual cashflows |
Cumulative cashflows |
Annual cashflows |
Cumulative cashflows |
|
1 |
60.00 |
60.00 |
70.00 |
70.00 |
80.00 |
80.00 |
2 |
69.00 |
129.00 |
80.50 |
150.50 |
92.00 |
172.00 |
3 |
79.35 |
208.35 |
92.58 |
243.08 |
105.80 |
277.80 |
4 |
91.25 |
299.60 |
106.46 |
349.54 |
121.67 |
399.47 |
5 |
104.94 |
404.54 |
122.43 |
471.97 |
139.92 |
539.39 |
6 |
120.68 |
525.22 |
140.80 |
612.76 |
160.91 |
700.30 |
7 |
138.78 |
664.01 |
161.91 |
774.68 |
185.04 |
885.34 |
8 |
159.60 |
823.61 |
186.20 |
960.88 |
212.80 |
1,098.15 |
9 |
183.54 |
1,007.15 |
214.13 |
1,175.01 |
244.72 |
1,342.87 |
10 |
211.07 |
1,218.22 |
246.25 |
1,421.26 |
281.43 |
1,624.30 |
Step 1 : Monthly cash inflows of upper bound of 300 Mn of initial investment---> marked in green --> (Annual cashflow /12) |
8.75 |
8.87 |
10.14 |
|||
Step 2 : Additional cashinflow
required post lower bound year of 300 Mn investment (marked in
yellow) |
0.40 |
56.93 |
22.20 |
|||
No. of months post lower
bound year ---> |
0 |
6 |
2 |
|||
Payback period (lower bound year + months in upper bound year); rounded off to nearest month |
4 years |
3 year 6 months |
3year 2 months |
Year |
Cashflows in (USD) ---> Previous year cashflows x 115% |
|||
1st year cashflow = 90Mn USD |
1st year cashflow = 100Mn USD |
|||
Annual cashflows |
Cumulative cashflows |
Annual cashflows |
Cumulative cashflows |
|
1 |
90.00 |
90.00 |
100.00 |
100.00 |
2 |
103.50 |
193.50 |
115.00 |
215.00 |
3 |
119.03 |
312.53 |
132.25 |
347.25 |
4 |
136.88 |
449.40 |
152.09 |
499.34 |
5 |
157.41 |
606.81 |
174.90 |
674.24 |
6 |
181.02 |
787.84 |
201.14 |
875.37 |
7 |
208.18 |
996.01 |
231.31 |
1,106.68 |
8 |
239.40 |
1,235.41 |
266.00 |
1,372.68 |
9 |
275.31 |
1,510.73 |
305.90 |
1,678.58 |
10 |
316.61 |
1,827.33 |
351.79 |
2,030.37 |
Step 1 : Monthly cash inflows of upper bound of 300 Mn of initial investment---> marked in green --> (Annual cashflow /12) |
9.92 |
11.02 |
||
Step 2 : Additional cashinflow
required post lower bound year of 300 Mn investment (marked in
yellow) |
106.50 |
85.00 |
||
No. of months post lower
bound year ---> |
11 |
8 |
||
Payback period (lower bound year + months in upper bound year); rounded off to nearest month |
2 year 11 months |
2 year 8 months |
Summary of payback back period as a function of year 1 cashflows
Year 1 Cashflows |
Payback period |
30 |
6 year 6 months |
40 |
5 year 5 months |
50 |
4 year 7 months |
60 |
4 years |
70 |
3 year 6 months |
80 |
3 year 2 months |
90 |
2 year 11 months |
100 |
2 year 8 months |