Question

QUESTION 1.  

INFORMATION

Medico Limited intends investing in a project during March 2021. The project is expected to cost R2 500 000 with a five-year useful life, and no residual value.
The annual volume of production for the project is estimated at 150 000 units, which can be sold for cash at R12 per unit. Depreciation is expected to be R500 000 per year. Annual cash operating costs are as follows:
Variable costs  R225 000
Fixed costs   R750 000
The cost of capital is 15%.

REQUIRED
Use the information provided above to calculate the following:

2.1 Net Present Value

2.2 Accounting Rate of Return on average investment (answer expressed to two decimal places)  

2.3 Internal Rate of Return, if the net cash flows are R720 000 per year for five years (answer expressed to two decimal places).

Answer 1

A)  

Calculation for expected annual net cash inflows

Particulars	R	R
Sales [ 150,000 X R 12]		1,800,000
Less: Expenditures
Variable costs	225,000
Fixed cost (cash)	750,000
Fixed cost ( Depreciation )	500,000
Total expenditures		1,475,000
Net Operating income		325,000
Add: Non cash expenditure ( Depreciation)		500,000
Expected net annual cash inflow =		825,000

Calculation for present value of the investment

Year	Annual cash inflows	Discounting factor ( 15%)	Discounted cash inflows
1	825,000	0.870	R 717,750
2	825,000	0.756	R 623,700
3	825,000	0.658	R 542,850
4	825,000	0.572	R 471,900
5	825,000	0.497	R 410,025
		Present value of expected cash inflows	R 2,766,225
		Less: Initial investment	R 2,500,000
		Net present value of the investment	R 266,225

B)

Average investment =[ Initial investment + residual value ] / 2

Average investment = [ R 2,500,000 + R 0] / 2 = R 1,250,000

Accounting rate of return = [Net operating income / Average investment ] X 100 %

Accounting rate of return = [ R 325,000 / R 1,250,000] X 100 % = 26%

C)

We can use the formula to locate the factor

Factor = Initial investment / Annual cash inflow

Factor = R 2,500,000 / R 720,000 =  3.472

This factor 3.472 should be located in Table PVIFA ( i , n) in line of 5 years.The discounting rate would be somewhere between 12% ( 3.605) and 14% ( 3.433). It indicates that IRR is more than 12% but less than 14%.

Total present value of expected annual cash inflow at 14% discount rate = R 720,000 X [ PVIFA ( i = 14 , n = 5)

= R 720,000 X3.433 = R 2,471,760

Total present value of expected cash inflows at 12% discount rate = R 720,000 X [PVIFA ( i = 12 , n = 5)

= R 720,000 X 3.605 = R 2,595,600

IRR = Lower rate  + [ (PV at lower rate - Initial investment) / ( PV at higher rate - PV at lower rate )] X Difference in rate

IRR = 12% + [ ( R 2,595,600 - R 2,500,000) / ( R 2,595,600 - R 2,471,760)] X [ 14 - 12]

IRR = 12% + [ R 95,600/ R 123,840] X 2

IRR = 12% + 1.54%

IRR = 13.54%