For a project having the following cash flows — capital of $100K (spent in Year 0) plus revenues and product costs of $30K per year and $25K per year (Year 1 through Year 10) — find the ROI for four situations: constant dollars, 5% per year, 10% per year, and 15% per year inflation rates. Use a 35

Question

For a project having the following cash flows — capital of $100K (spent in Year 0) plus revenues and product costs of $30K per year and $25K per year (Year 1 through Year 10) — find the ROI for four situations: constant dollars, 5% per year, 10% per year, and 15% per year inflation rates. Use a 35% tax rate and a project life of 10 years.

Accepted Answer

Compare ROIs calculated exactly to those estimated by Equation (AT5.1).

[latex]ROI_{ ext{Actual}} \sim (0.3) ( ext{Inflation rate}) + ROI_{ ext{Constant dollars}}[/latex]

Constant dollars:

[latex] ext{Cash flow}_{BT} = ext{Revenues} – ext{Product cost} = \$30K/yr – \$25K/yr = \$5K ext{per year}[/latex]

[latex] ext{Cash flow}_{AT} = ( ext{Cash flow}_{BT})(1 – ext{Tax rate}) + ext{Depreciation}[/latex]

= ($5K/yr)(1 – 0.35) + $100K/10 = $13.25K per year
Calculate P/A; and using the compound interest tables, find the ROI.
P/A = $100K/$13.25K = 7.547
(P/A, 5.5%, 10) = 7.538; (P/A, 5%, 10) = 7.722
Call the ROI 5.5%
Inflated dollars at 5% per year:
The calculations are summarized in Table AT5.2. Explaining a few calculations
is in order. These are shown for Year 1.
[latex] ext{BT Cash flow} = ( ext{Revenues} – ext{Product cost}) (1 + ext{Inflation rate})^{n}[/latex]
= (30K – 25K)(1 + 0.05)¹ = 5.25K
Depreciation = Capital/Project life = 100K/10 = 10K
AT Cash flow = (BT Cash flow)(1 – Tax rate) + Depreciation
= (5.25K)(1– 0.35) + 10 = 13.41K
P = F(P/F, 6%, 1) = 13.41K (0.9434) = 12.65K

TABLE AT5.2
Example AT5.3: 5% Inflation

Year	Capital	BT Cash Flow, 5% Inflation	Depreciation	AT Cash Flow	P, i = 6%	P, i = 7%
0	-100	—	—	—	—	—
1	—	5.25	10	13.41	12.65	12.54
2	—	5.51	10	13.58	12.09	11.86
3	—	5.79	10	13.76	11.56	11.23
4	—	6.08	10	13.95	11.05	10.64
5	—	6.38	10	14.15	10.57	10.09
6	—	6.70	10	14.36	10.12	9.57
7	—	7.04	10	14.57	9.69	9.08
8	—	7.39	10	14.8	9.29	8.61
9	—	7.76	10	15.04	8.90	8.18
10	—	8.14	10	15.29	8.54	7.77
Total P =	-100				104.46	99.58
				NPV=	4.46	-0.42

To find the ROI, interpolate to find where the NPV = 0. The ROI = 6.9%.
Inflated dollars at 10% per year and 15% per year:
Using similar methodology, the ROI at 10% inflation is 8.7% and at 15% inflation is 10.7%.
Summary: The table below compares the exact calculations to those from Equation (AT5.1). It shows good agreement when the inflation rate is 10% or less.

	Actual ROI (%)	ROI from Equation AT5.1 (%)
Constant dollars	5.5	5.5
5% inflation	6.9	7.0
10% inflation	8.7	8.5
15% inflation	10.7	10.1

Question 5.AT5.3: For a project having the following cash flows — capital of $...

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