## Problem 1

The cost of a project is $50,000 and it generates cash inflows of $20,000, $15,000, $25,000 and $10,000 in four years. Using present value index method, appraise profitability of the proposed investment assuming a 10% rate of discount.

### Solution

### Calculation of present value and profitability index

Year | Cash Inflows | Present Value Factor | Present Value |

$ | @10% | $ | |

1 | 20,000 | .909 | 18,180 |

2 | 15,000 | .826 | 12,390 |

3 | 25,000 | .751 | 18,775 |

4 | 10,000 | .683 | 6,830 |

56,175 |

Total present value = $56,175

Less: intial Outlay = $50,000

Net present value= $6,175

**Profitability Index (gross) = Present value of cash inflows / intial cash outflow**

= 56,175 / 50,000

= 1.1235

As the P.I. is higher than 1, the proposal can be accepted.

**Net Profitability = NPV / Initial cash outlay**

= 6,175 / 50,000 = .1235

N.P.I. = 1.1235 – 1 = 0.1235

As the net profitability index is positive, the proposal can be accepted.

## Problem 2

A company is considered the purchase of a machine. the machines A and B are available for $80,000 each. Earnings after taxation are as:

Year | Machine A | Machine B |

$ | $ | |

1 | 24,000 | 8,000 |

2 | 32,000 | 24,000 |

3 | 40,000 | 32,000 |

4 | 24,000 | 48,000 |

5 | 16,000 | 32,000 |

Evaluate the two alternatives according to (a). Payback Method, (b). Rate of Return Method and (c). Net Present Value Method (A discount rate of 10% is to be used).

### Solution

**(a). Payback Method**

24,000 of 40,000 = 2 years and 7.2 month

Payback period:

**Machine A:** (24,000 + 32,000 + 1 _{3/5 }of 40,000) = 2 _{3/5 }years.

**Machine B:** (8,000 + 24,000 + 32,000 + 1/3 of 48,000) = 3 _{1/3 }years.

According to the payback method Machine, A will be preferred.

**(b). Rate of return on Investment Method**

Particular | Machine A | Machine B |

Total Cash Flows | 1,36,000 | 1,44,000 |

Average Annual Cash Flows | 1,36,000 / 5 = $27,000 | 1,44,000 / 5 = $28,800 |

Annual Depreciation | 80,000 / 5 = $16,000 | 80,000 / 5 = $16,000 |

Annual Net Savings | 27,200 – 16,000 = $11,200 | 28,800 – 16,000 = $12,800 |

Average Investment | 80,000 / 2 = $40,000 | 80,000 / 2 = $40,000 |

ROI = (Annual Net Savings / Average Investments) x 100 | (11,200 / 40,000) x 100 | (12,800 / 40,000) x 100 |

= 28% | = 32% |

According to rate of return on investment method machine B will be preferred due to higher rate of return on investment.

**(c). Net Present Value Method**

**Calculation of Present Value of Cash Flows**

Year | Discount Factor | Machine A | Machine B | ||

(at 10%) | Cash Flows ($) | P.V ($) | Cash Flows ($) | P.V ($) | |

1 | .909 | 24,000 | 21,816 | 8,000 | 7,272 |

2 | .826 | 32,000 | 26,432 | 24,000 | 19,824 |

3 | .751 | 40,000 | 30,040 | 32,000 | 24,032 |

4 | .683 | 24,000 | 16,392 | 48,000 | 32,784 |

5 | .621 | 16,000 | 9,936 | 32,000 | 19,872 |

1,36,000 | 1,04,616 | 1,44,000 | 1,03,784 |

Net Present Valu = Present Value – Investment

Net Present Value of Machine A: $1,04,616 – $80,000 = $24,616

Net Present Value of Machine B: $1,03,784 – 80,000 = $23,784

Accroding to Net Present Value Method, Machine A will be preferred as its Net Present Value is higher than that of Machine B.

## Problem 3

A business enterprise can make either of two investments at the beginning of 2015. assuming required rate of return in 10% p.a. evaluate the investment proposals under:

(a). Return on investment

(b). Payback Period

(c). Discounted payback period

(d). profitability index

The forecast particular are given below:

Proposal A | Proposal B | |

Cost of Investment | $20,000 | 28,000 |

Life | 4 years | 5 years |

Scrap Value | Nil | Nil |

Net Income (After depreciation and tax): | ||

End of 2015 | $500 | Nil |

End of 2016 | $2,000 | $3,400 |

End of 2017 | $3,500 | $3,400 |

End of 2018 | $2,500 | $3,400 |

End of 2019 | Nil | $3,400 |

It is estimated that each of the alternative projects will require an additional working capital of $2,000 which will be received back in full after the expiry of each project life. Depreciation is provided under the straight-line method. The present value of $1 to be received at the end of each year, at 10% p.a. is given below:

Year | 1 | 2 | 3 | 4 | 5 |

P.V. | .91 | .83 | .75 | .68 | .62 |

### Solution

**Calculation of Profit after Tax**

Year | Proposal A $20,000 | Proposal B $28,000 | ||||

Net Income | Dep. | Cash Inflow | Net Income | Dep. | Cash Inflow | |

$ | $ | $ | $ | $ | $ | |

2015 | 500 | 5,000 | 5,500 | – | 5,600 | 5,600 |

2016 | 2,000 | 5,000 | 7,000 | 3,400 | 5,600 | 9,000 |

2017 | 3,500 | 5,000 | 8,500 | 3,400 | 5,600 | 9,000 |

2018 | 2,500 | 5,000 | 7,500 | 3,400 | 5,600 | 9,000 |

2019 | – | – | – | 3,400 | 5,600 | 9,000 |

Total | 8,500 | 20,000 | 28,500 | 13,600 | 28,000 | 41,600 |

**(a). Return on Investment**

Proposal A | Proposal B | |

Investment | 20,000 + 2,000 = 22,000 | 28,000 + 2,000 = 30,000 |

Life | 4 years | 5 years |

Total Net income | $8,500 | $13,600 |

Average Return ($) | 8,500 / 4 = 2,125 | 13,600 / 5 = 2,720 |

Average investment ($) | (22,000 + 2,000) / 2 = 12,000 | (30,000 + 2,000) / 2 = 16,000 |

Average return on Average Investment ($) | (2,125 / 12,000) x 100 = 17.7% | (2,720 / 16,000) x 100 = 17% |

**(b). Payback Period**

Proposal A | Cash Inflow ($) |

2015 | 5,500 |

2016 | 7,000 |

2017 | 7,500 (7,500 / 8,500 = 0.9) |

20,000 |

Payback Period = 2.9 years

Proposal B | Cash inflow |

$ | |

2015 | 5,600 |

2016 | 9,000 |

2017 | 9,000 |

2018 | 4,400 (4,400 / 9,000 = 0.5) |

Payback period = 3.5 years

**(c). Discounted Payback Period**

Proposal A | Proposal B | ||

P.V. of cash inflow | P.V. of cash inflow | ||

Year | $ | Year | $ |

2015 | 5,005 | 2015 | 5,096 |

2016 | 5,810 | 2016 | 7,470 |

2017 | 6,375 | 2017 | 6,750 |

2018 | 2,810 (2,810 / 5,100 = 0.5) | 2018 | 6,120 |

2019 | 2,564 (2,564 / 5,580 = 0.4) | ||

20,000 | 28,000 | ||

Discounted Payback Period = 3.5 years | Discounted Payback Period = 4.4 years |

**(d). Profitability Index method**

Proposal A | Proposal B | |

Gross Profitability Index | (22,290 / 20,000) x 100 = 111.45% | (31,016 / 28,000) x 100 = 111.08% |

Net Profitability Index | (2,290 / 20,000) x 100 = 11.45% | (3,016 / 28,000) x 100 = 10.8% |