Answer to Question #116778 in Financial Math for Deven

Question

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

2.1.

$NCF=150 000\times12-500 000-225 000-750 000=325 000$

$NPV=\frac{NCF}{(1+r)^1}+\frac{NCF}{(1+r)^2}+\frac{NCF}{(1+r)^3}+\frac{NCF}{(1+r)^4}+\frac{NCF}{(1+r)^5}-Inv=\frac{325 000}{(1+0.15)^1}+\frac{325 000}{(1+0.15)^2}+\frac{325 000}{(1+0.15)^3}+\frac{325 000}{(1+0.15)^4}+\frac{325 000}{(1+0.15)^5}-500 000=282 608.696+245 746.692+213 692.776+185 819.805+161 582.439-500 000=589 450.41$

2.2

$ARR=\frac{325 000}{\frac{500 000}{5}}=3.25$

2.3$0=\frac{NCF}{(1+IRR)^1}+\frac{NCF}{(1+IRR)^2}+\frac{NCF}{(1+IRR)^3}+\frac{NCF}{(1+IRR)^4}+\frac{NCF}{(1+IRR)^5}+(-Inv)=\frac{720 000}{(1+IRR)^1}+\frac{720 000}{(1+IRR^2)}+\frac{720 000}{(1+IRR)^3}+\frac{720 000}{(1+IRR)^4}+\frac{720 000}{(1+IRR)^5}+(-500 000)$ IRR=1.42