The payback of a project is the number of years it takes before the project’s total cash flow is positive.

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.

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Expert Solution

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) (Initial capital outlay - cumulative cash inflows as on lower bound year of 300 Mn investment)	37.39	30.30	50.33
No. of months post lower bound year ---> (Additional cashinflow required / monthly cashinflows for upper 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) (Initial capital outlay - cumulative cash inflows as on lower bound year of 300 Mn investment)	0.40	56.93	22.20
No. of months post lower bound year ---> (Additional cashinflow required / monthly cashinflows for upper 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) (Initial capital outlay - cumulative cash inflows as on lower bound year of 300 Mn investment)	106.50	85.00
No. of months post lower bound year ---> (Additional cashinflow required / monthly cashinflows for upper 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

jeff jeffy answered 1 year ago

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