NON-DISCOUNTED CASH FLOW METHODS
1. Accounting rate of return (ARR)
ARR = Average annual income
Average investment
Where Average annual income = Average cashflows - Average Depreciation
Average investment = 1/2 (Cost of investment - Salvage value)
(assuming straight line depreciation method).
Projects with higher ARR are preferable.
2. Payback Period
This is defined as the time taken by the project to recoup the initial cash outlay.
The decision rule depends on the firms target payback period (i.e. the maximum period beyond which the project should not be accepted.
ILLUSTRATION
A company is considering two mutually exclusive projects requiring an initial cash outlay of Sh 10,000 each and with a useful life of 5 years. The company required rate of return is 10% and the appropriate corporate tax rate is 50%. The projects will be depreciated on a straight line basis. The before depreciation and taxes cashflows expected to be generated by the projects are as follows.
YEAR 1 2 3 4 5
Project A Shs 4,000 4,000 4,000 4,000 4,000
Project B Shs 6,000 3,000 2,000 5,000 5,000
Required:
Calculate for each project
i. The payback period
ii. The average rate of return
iii. The net present value
iv. Profitability index
v. The internal rate of return
Which project should be accepted? Why?
Suggested Solution
Computation of after tax cashflows
Depreciation = 10,000 - 0 = Sh 2,000
5
Project A Annual Cashflow
Cashflows before depreciation 4,000
Less Depreciation 2,000
Profits before taxes 2,000
Less taxes (50%) 1,000
Profits after tax 1,000
Add back depreciation 2,000
Cashflows after taxes 3,000
Project B
Year 1 2 3 4 5
Cashflow before depreciation 6,000 3,000 2,000 5,000 5,000
Less depreciation 2,0002,0002,0002,0002,000
Profits before taxes 4,000 1,000 0 3,000 3,000
Less taxes (50%) 2,000 500 01,5001,500
Profits after taxes 2,000 500 0 1,500 1,500
Add back depreciation 2,0002,0002,0002,0002,000
Net cashflows after taxes 4,0002,5002,0003,5003,500
i. Payback Period (PB)
Project A = 10,000 = 3 1/3 years
3,000
Project B
Sh 4,000 + Sh 2,500 + Sh 2,000 = Sh 8,500 is recovered in three years. The remaining amount of Sh 10,000 - 8,500 = 1,500 is to be recovered in the fourth year.
Thus PB = 3 years + 1,500 = 3 3/7 years
3,500
According to PB Project A is better.
ii. Average Rate of Return (ARR)
Project A
Average income = 5 x 1,000 = Shs 1,000
5
Average investment = 10,000/2 = Shs 5,000
ARR = 1,000 = 0.20 or 20%
5,000
Project B
Average income = 2,000 + 500 + 0 + 1,500 + 1,500
5
= 5,500 = Shs 1,100
5
ARR = 1,100 = 0.22 or 22%
5,000
According to ARR Project B is better.
iii. Net Present Value Method
Project A
NPV = Annual Cashflows x PVIFA 10%, 5 years - Initial Cost (where PVIFA is the Present Value Interest Factor of annuity)
= 3,000 x 3.791 - 10,000 = Sh 1,373
Project B
NPV can be computed using the following table:
Year Cashflows PV.F 10% PV
1 4,000 0.909 3,636
2 2,500 0.826 2,065
3 2,000 0.751 1,502
4 3,500 0.683 2,390.5
5 3,500 0.621 2,173.5
Total PV 11,767
Less initial cost 10,000
NPV 1,767
Project B is better because it has a higher NPV.
iv. Profitability index (PI)
Project A
PI = 11,373 = 1.1373
10,000
Project B
PI = 11,767 = 1.1767
10,000
Project B is better since it has a higher PI.
v. The Internal Rate of Return
Project A
NPV = 3,000 X PVIFA r%, 5years - 10,000 = 0
PVIFA r%, 5years = 10,000 = 3.333
3,000
From the table r lies between 15% and 16%. We use linear interpolation to compute the exact rate
PVIFA 15% = 3.352 PVIFA 15% = 3.352
PVIFA required = 3.333 PVIFA 16% = 3.274
Difference 0.019 Difference 0.078
IRR = 15% + (16 - 15) (0.019) = 15.24%
0.078
Project B
We use trial and error method since the cashflow are uneven:
NPV at 16% = 10,186 - 10,000 = 186
NPV at 17% = 9,960.5 - 10,000 = (39.5)
Project B
We use trial and error method since the cashflow are uneven:
NPV at 16% = 10,186 - 10,000 = 186
NPV at 17% = 9,960.5 - 10,000 = (39.5)
1
Using Similar Triangle
IRR - 16 = 17 - IRR
186 39.5
39.5 (IRR - 16) = 186 (17 - IRR)
39.5 IRR - 632 = 3,162 - 186 IRR
225.5 IRR = 3.794
IRR 16.8%
Project B is better because it has a higher IRR.
Generally, Project B should be selected because the discounted cashflow methods supports this decision.
Note: The methods discussed so far assume that investment decisions are made under conditions of certainty. In real life, however, this is not the case and therefore we shall consider risk and other complications in the following sections.
Using Similar Triangle
IRR - 16 = 17 - IRR
186 39.5
39.5 (IRR - 16) = 186 (17 - IRR)
39.5 IRR - 632 = 3,162 - 186 IRR
225.5 IRR = 3.794
IRR 16.8%
Project B is better because it has a higher IRR.
Generally, Project B should be selected because the discounted cashflow methods supports this decision.
Note: The methods discussed so far assume that investment decisions are made under conditions of certainty. In real life, however, this is not the case and therefore we shall consider risk and other complications in the following sections.