1. PROBLEM SOLVING

2. Payback Period
PDAF Ltd. A manufacturing company is faced with the problem of choosing between two mutually exclusive projects.
Project A requires a cash outlay of P2,500,000 and generates a net cash flow of P1,000,000 per year for 4 years.
Project B costs P1,500,00 and is expected to generate net cash flow of P650,000, P550,000, P400,000 and P500,000 over its life of 4 years, the management of the company had set the maximum acceptable period of 2 ½ years, which of the projects should be embarked upon?

3. Payback Period
Company Bong is planning to undertake a project requiring initial investment of P105 million. The project is expected to generate P25 million per year for 7 years. Calculate the payback period of the project.

4. Payback Period
Company Jingoy is planning to undertake another project requiring initial investment of P50 million and is expected to generate P10 million in Year 1, P13 million in Year 2, P16 million in year 3, P19 million in Year 4 and P22 million in Year 5. Calculate the payback period of the project.

5. Payback Period
Solution: Company Bong Payback Period = Initial Investment ÷ Annual Cash Flow
= 105M / 25M = 4.2 years

6. Payback Period Solution: Company Jingoy
(cash flows in millions) Cumulative Year Cash Flow Cash Flow
(50) (50)
(40)
(27)
(11)
Payback Period = 3 + (P11M ÷ P19M) ≈ ≈ 3.58 years

7. Accounting Rate of Return
The Fine Clothing Factory wants to replace an old machine with a new one. The old machine can be sold to a small factory for P10,000. The new machine would increase annual revenue by P150,000 and annual operating expenses by P60,000. The new machine would cost P360,000. The estimated useful life of the machine is 12 years with zero salvage value.
Required:
Compute accounting rate of return (ARR) of the machine using above information.
Should Fine Clothing Factory purchase the machine if management wants an accounting rate of return of 15% on all capital investments?

8. Accounting Rate of Return
Solution: (1): Computation of accounting rate of return:
= P60,000* / P350,000**
= 17.14%
*Incremental net operating income: Incremental revenues – Incremental expenses including depreciation P150,000 – (P60,000 cash operating expenses + P30,000 depreciation) P150,000 – P90,000 P 60,000
** The amount of initial investment has been reduced by net realizable value of the old machine (P360,000 – P10,000).

9. Accounting Rate of Return
(2). Conclusion:
According to accounting rate of return method, the Fine Clothing Factory should purchase the machine because its estimated accounting rate of return is 17.14% which is greater than the management’s desired rate of return of 15%.

10. Accounting Rate of Return
Cost reduction projects:
The accounting rate of return method is equally beneficial to evaluate cost reduction projects. The accounting rate of return of the assets that are purchased with a view to reduce business costs is computed using the following formula:

11. Accounting Rate of Return
The P & G company is considering to purchase an equipment costing P45,000 to be used in packing department. It would reduce annual labor cost by P12,000. The useful life of the equipment would be 15 years with no salvage value. The operating expenses of the equipment other than depreciation would be P3,000 per year.
Required: Compute accounting rate of return/simple rate of return of the equipment.

12. Accounting Rate of Return
Solution:
= P6,000* / P45,000
= 13.33%
*Net cost savings: P12,000 – (P3,000 cash operating expenses + P3,000 depreciation expenses) P12,000 – $6,000 P6,000

13. Accounting Rate of Return

14. Accounting Rate of Return
A proposal to purchase a new machine is being considered by the management of  HiTech manufacturing company. The new machine would increase production and revenues. HiTech uses accounting rate of return method to evaluate capital investments like this. The relevant data is given below:
Cost of new machine P1,200,000
Useful life of the machine 10 years
Expected annual revenues associated with the new machine P450,000
Operating expenses associated with the new machine P26,000
Salvage value of the machine at the end of 10-year period P80,000
HiTech company uses straight line method of depreciation for all plant assets.
Required:
Compute accounting rate of return of the machine.
Would HiTec company purchase the machine if its desired accounting rate of return is 20%?

15. Accounting Rate of Return
Solution:
 (1) Accounting rate of return:
Incremental operating income per year = P450,000 – (P26,000 exp. + P112,000 dep.*)
= P312,000
*(P1,200,000 Cost – P80,000 Salvage value)/10 years = P1,120,000/10 years = P112,000
= P312,000/P1,200,000
= 26%
(2) Decision of the management:
Management should purchase new machine because it promises a 26% accounting rate of return that is higher than the management’s desired accounting rate of return

16. Net Present Value
A machine costing P200,000 will provide an annual net cash inflow of P60,000 for six years at a cost of capital of 10 percent.
Required:
Calculate the net present value (NPV) of the machine
Should the machine be purchased?

17. Net Present Value quiz
1. Determine the net present value for a project that costs P104,000 and would yield after-tax cash flows of P16,000 the first year, P18,000 the second year, P21,000 the third year, P23,000 the fourth year, P27,000 the fifth year, and P33,000 the sixth year. Your firm's cost of capital is 12.00%.

18. Net Present Value - quiz
2. Determine the net present value for a project that costs P253, and is expected to yield after-tax cash flows of P29,000 on year 1, P37,000 on year 2, and P50,000 on year 3. Your firm's cost of capital is 12.00%. Required: Compute for the Net Present Value

19. IRR - sw
A firm invests P 200,000 in machinery that yields net after tax cash flows of P90,000 at the end of the next three years. The opportunity costs of capital is 12%. Required: Compute for the NPV and the IRR

20. A capital investment of 100,000 can be made in a project that will produce a uniform annual revenue of P53,100 for five years and then have a salvage value of P20,000. Annual expenses will be P30,000. The company is willing to accept any project that will earn at least 10% per year, before income taxes, on all invested capital. Determine whether it is acceptable by using the IRR method.

21. 10% PV
15%
Cash Outflow
(90,000)
Cash Inflow 1
23,100.00
21,000
20,087 2
19,091
17,467 3
17,355
15,189 4
15,778
13,207 5
14,343
11,485
salvage value
20,000.00
12,418
99,986
9,944
87,378
Net Present Value
9,986
(2,622)
IRR
14%

22. Profitability index
Company c is undertaking a project at a cost of P50M which is expected to generate future net cash flows with a present value of P65M. Calculate the PI

23. PI = PV cf/ initial investment
= 65/ 50 = 1.3
Npv = pv cash flows – initial investment
Npv = =15
PI = 1+(npv/initial investment)
= 1 + (15/50) = 1.3

24. Discounted payback period - sw
A machine will cost P300,000 and will provide an annual net cash inflow of P100,000 for five years. The opportunity cost of capital is 10%.