## 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.