Question

Scenario: An academic organisation is considering the purchase and operation of its own fleet of buses to transport its students to and from school at the end of this year. The bursar at the school has confirmed that, if this project can be implemented, the school will be able to cancel its current contract with the local bus operator, and as a result, the school will make cash savings of N$45 600 each year from 2011 onwards, after deducting operating costs.
The buses will cost the school N$255 000 and will have a scrap value of N$75 000 when they are sold after five years. The school’s cost of capital is 10%, and the maximum required payback is 3.5 years.

Questions:
1. Calculate the project’s payback period.
2. Calculate the project’s Net Present Value (NPV).
3. Calculate the project’s internal rate of return (IRR).
4. Determine with reasons which project (s) will finally be recommended.

Answer 1

Ans1. Payback period = Initial cost of investment / Annual cash inflows

= N$255,000/N$45,600

We see that annual cash flows of N$45,600 over life of project,i.e.,5 years are not sufficient to payback initial cost of project (N$45,600*5 = N$228,000). Adding the scrap value of buses to be received at end of Year 5 N$75,000, the cash flows will be N$303,000,i.e., sufficient to payback initial cost of project.

Therefore, payback period is 5 years.

Ans.2. Net Present value (NPV) = Present value of all cash inflows – Present value of all cash outflows

NPV has been calculated as per table below and it is – N$35,571

	Year 0	Year 1	Year 2	Year 3	Year 4	Year 5
Cost of buses	-255000
Residual value of buses						75000
Annual cash savings		45600	45600	45600	45600	45600
Total expected cash inflows		45600	45600	45600	45600	120600
Present value interest factor @10%		0.9091	0.8264	0.7513	0.6830	0.6209
Present value of cash flows		41454.55	37685.95	34259.95	31145.41	74883.11
Net Present value	-35571

Ans.3. IRR is the rate of return (Cost of capital) at which NPV becomes zero,i.e., Present value of cash inflows = Present value of cash outflows

Trying cost of capital 5%, the NPV is positive as below :

	Year 0	Year 1	Year 2	Year 3	Year 4	Year 5
Cost of buses	-255000
Residual value of buses						75000
Annual cash savings		45600	45600	45600	45600	45600
Total expected cash inflows		45600	45600	45600	45600	120600
Present value interest factor @5%		0.9524	0.9070	0.8638	0.8227	0.7835
Present value of cash flows		43428.57	41360.54	39390.99	37515.23	94493.26
Net Present value	1188.599

Trying cost of capital 6%, the NPV is negative :

	Year 0	Year 1	Year 2	Year 3	Year 4	Year 5
Cost of buses	-255000
Residual value of buses						75000
Annual cash savings		45600	45600	45600	45600	45600
Total expected cash inflows		45600	45600	45600	45600	120600
Present value interest factor @6%		0.9434	0.8900	0.8396	0.7921	0.7473
Present value of cash flows		43018.87	40583.84	38286.64	36119.47	90119.34
Net Present value	-6871.85

So, the IRR is between 5% and 6%

Using excel function IRR, we get IRR value 5.14%

Ans. 4. The project to buy own fleet of buses is not recommended due to negative NPV, Payback period higher than required and IRR less than cost of capital.