Question

QUESTION THREE [20]

3.1 Explain the rationale behind the internal rate of return. (IRR) (3)

3.2 Super Max Investments have just made an investment of R550 000 in a new Tata Telcoline delivery vehicle. This vehicle will be used for deliveries and generate revenues from such activities.

Further details:

 Expected useful life 5 years (straight line depreciation)

 Salvage value 50 000

 Cost of Capital 10% after tax

 Tax rate 30%

Year Cash flows

1 -220 000

2 -200 000

3 -120 000

4 -110 000

5 -50 000

Required:

3 3.2.1 Calculate the payback period and the accounting rate of return. (8)

3.2.2 Super Max Investments requires a payback period of no more than 3 years and a return of at least 30%. Purely on the basis of these criteria, should this project be accepted? Explain your answer (2)

3.2.3 The payback period method makes a crucial omission in the calculation, namely the time value of money. Can you complete the above computation using a method that accounts for the time value of money? On the basis of this calculation, should the project be accepted? Explain your answer.

Answer 1

3.1) Internal Rate of Return: It is defined as the discount rate where NPV is equal to zero. NPV and IRR will always give same accept/reject decision.  If NPV is positive IRR must be greater than r.

Rationale behind the IRR are:

a) IRR on a project is the expected return of the project

b) If IRR > Cost of capital , there will be a surplus left after paying for the capital and this surplus will accrue to the firm's shareholders.

c) By taking that project whose IRR > Cost of capital will always increase the shareholder's wealth.

3.2) Given:

Cash outflow= 5,50,000
Salvage value= 50,000
cost of capital 10%
Tax rate 30%

Now,

3.2.1)) Payback Period:

when there are single cashflow we use Cumulative casflows to count the payback period.

Year	Cashflow	Cumulative Cashflow
1	220000	220000
2	200000	420000
3	120000	540000
4	110000	650000
5	50000	700000

540000 will be recovered in 3 years and rest of the amount i.e 550000 - 540000 = 10000 will be recovered by dividing the remaining amount by the cashflow of next year.

Payback period= 3 year + 10000 / 110000

= 3 + 0.09

= 3.09 or 3.1 years

Internal Rate of Return: It is calculate by Hit and trial method and Payback period method.

Here, I'm using hit and trial method.

I'm taking IRR @ 11% and @ 12% . [ Just choosing it randomly i.e. what called IRR method ]

Now,

Year	Cash Flow	PVF @ 11%	Discounted cashflow @ 11%	PVF @ 12%	Discounted cashflow @ 12%
1	220000	0.9009	198198	0.8929	196438
2	200000	0.8417	168340	0.7972	159440
3	120000	0.7722	92664	0.7118	85416
4	110000	0.7084	77924	0.6355	69905
5	50000	0.6499	32495	0.5674	28370

Discounted Cashflow at 11% = 569621

NPV at 11% = Present Value of Cash inflow - Present Value of Cash outflow

= 569621 - 550000

= 19621

Dicsounted cashflow at 12% = 539569

NPV at 12% = Present Value of Cash inflow - Present Value of Cash outflow

= 539569 - 550000

= (-10431)

Now, using the Interpolation formula for calculating exact IRR will be=

[ Lower Rate + ( Lower Rate NPV / Lower Rate NPV - Higher Rate NPV ) ] * change in r %

[ 11 + ( 19621 / 19621- {-10431} ) * 1% ]

[ 11 + ( 19621 / 30052 ) * 1% ]

11 + 0.65 * 1

11.65 %

IRR will be 11.65 %

3.2.2)  Super Max Investments requires a payback period of no more than 3 years and a return of at least 30%. Purely on the basis of these criteria, this project should not be accepted. Because the payback period is 3.09 years and IRR rate is 11.65 % which is below the criteria of Super max investments.

3.2.3) The above computation using a method that accounts for the time value of money is NPV method.