Dimensional Analysis of GiveDirectly

	A	B	C	D	E	F
1	Cash Transfers - GiveDirectly	Dimension	Original	Corrected	Active	Check
2	Unit checks
3	Money multiplier		1.00	1.00	2.15
4	Household multiplier		1.00	1.00	3.43
5	People multiplier		1.00	1.00	5.75
6	Time multiplier		1.00	1.00	5.51
7
8	Size of transfer
9	Arbitrary donation size	M	$100,000	$100,000	$215,470	$100,000
10	Transfers as a percentage of total cost	1	83%	83%	83%	83%
11	Total funding available for cash transfers out of hypothetical donation	M	$83,000	$83,000	$178,840	$83,000
12	Total size of transfer per household (nominal USD)	M/H	$1,000	$1,000	$628	$1,000
13	Average household size	P/H	4.7	4.7	7.9	4.7
14	Size of transfer per person (nominal USD)	M/P	$212.77	$212.77	$79.71	$212.77
15
16	Investment returns
17	Percentage of transfers invested	1	39%	39%	39%	39%
18	Duration initial spending is spent	T		1.00	5.51	1.00
19	Amount invested (nominal USD)	M/P	$83	$83	$31	$83
20	Total increase in consumption per person made possible by funds transferred (nominal USD)	M/PT	$130	$130	$9	$130
21	Return on investment	1/T	10%	10%	2%	10%
22	Annual increase in consumption per person made possible by investment returns (nominal USD)	M/PT	$8.30	$8.30	$0.56	$8.30
23
24	Present value of transfer
25	Baseline annual consumption per capita (in nominal USD)	M/PT	$285.92	$285.92	$19.43	$285.92
26	Total immediate increase in ln(consumption) per person made possible by funds transferred	T	0.37	0.37	2.06	0.37
27	Future annual increase in ln(consumption) per person — from returns on investments	1	0.03	0.03	0.03	0.03
28	Discount rate	^(1/T)	4.00%	4.00%	0.71%	4.00%
29	Duration of investment benefits (in years)	T	10	10	55	10
30	Duration of the end of benefits	T		1.00	5.51	1.00
31	Present value of future increases in ln(consumption) per person (excluding the last year of expected benefits)	Unknown (But should be T)	0.21	0.21
32	My Continuous PV formula, approximate of above	T	0.22	0.22	1.20	0.22
33	Percent of investment returned when benefits end	1	20%	20%	20%	20%
34	Present value of ln(consumption) increase in the last year of expected benefits	T	0.06	0.06	0.31	0.06
35	Present value of all future increases in ln(consumption)	T	0.27	0.27	1.51	0.27
36	Total present value of cash transfer in terms of increases in ln(consumption)	T	0.65	0.65	3.57	0.65
37	Discount to the benefits of cash from potential negative spillover effects on consumption	1	5%	5%	5%	5%
38	Total present value of cash transfer accounting for spillovers	T	0.62	0.62	3.39	0.62
39	Total units of increase in ln(consumption) per household	TP/H	2.89	2.89	26.73	2.89
40
41	Number of transfers made	H	83	83	285	83
42	Total units of increase in ln(consumption)	TP	240	240	7,611	240
43	Value assigned to increasing ln(consumption) by one unit for one person for one year	V/PT	1.44	1.44	0.05	1.44
44
45	Total units of value generated	V	346	346	346	346
46	Units of value generated per dollar spent	V/M	0.00345597083	0.00345597083	0.00160392205	0.00345597083
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