Question

Wind Company is considering replacing an old machine with a new one.

The new machine has a cost of $320,000, an expected life of five years

and zero salvage value. The before-tax cost savings generated by the

new machine are shown as below:

Year	Before-tax cost savings($)
1	120,000
2	120,000
3	95,000
4	95,000
5	70,000

In this replacement exercise, the old machine can be sold for $80,000

today. Assume a 25% tax rate and a required rate of return of 12%.

Ignore the tax savings on depreciation and the tax gain/loss on disposal

of the old machine.

Please answer the following questions:

(a) According to the information above, find out the:

(i) net present value

(ii) payback period

(iii) discount payback

(iv) profitability index

for this replacement decision.

(b) Provide one advantage and disadvantage of each project

evaluation method. Among these four methods, which one is the

best within the scope of financial management? And Why?

Answer 1

It was asked to ignore tax saving on depreciation. In a case, annual cash flows = Before tax savings * ( 1 - tax rate)

Investment at ...... t = 0 ............will be cost of new machine - sale of old machine

= 320,000 - 80,000 = 240,000

(I) Calculation of NPV

Year	CF	DF	PV
0	-240000	1	-240000
1	90000	0.892857	80357.14
2	90000	0.797194	71747.45
3	71250	0.71178	50714.34
4	71250	0.635518	45280.66
5	52500	0.567427	29789.91
		NPV	37889.51

In the above table .......CF = Cash flows are computed as ...... year - 1 = 120,000 * ( 1 - 0.25) = 90,000. Year - 3 =  95000 * ( 1 - 0.25) = 71250.

DF = discounting factors are taken at 12%

PV = CF * DF.

(II) Payback period

Year	CF	CCF
0	-240000	-240000
1	90000	-150000
2	90000	-60000
3	71250	11250
4	71250	82500
5	52500	135000

CCF = Cumulative Cash flow. This obtained by adding current CF to the total of previous CF. This is like a running total CF.

By the end of 2nd Year we have still 60,000 to be recoverable from year - 3 cash flow of 71250.

Hence payback = 2 + 60,000 / 71250 =  2.84 years

(iii) Discounting payback

Year	CF	DF	DCF	CDCF
0	-240000	1	-240000	-240000
1	90000	0.892857	80357.14	-159643
2	90000	0.797194	71747.45	-87895.4
3	71250	0.71178	50714.34	-37181.1
4	71250	0.635518	45280.66	8099.598
5	52500	0.567427	29789.91	37889.51

DCF = Discounted cash flow = CF * DF

CDCF = Cumulative discounted cash flow

By the end of 3rd year we still have 37181.10 to be recovered out of DCF of 4th year = 45280.66

Post pay back period = 3 + 37181.10 / 45280.66 = 3.82 years.

(iv) Profitability Index = Total PV / Investment = 277889.50 / 240000 = 1.1579 or 115.79 %

Year	CF	DF	DCF
1	90000	0.892857	80357.14
2	90000	0.797194	71747.45
3	71250	0.71178	50714.34
4	71250	0.635518	45280.66
5	52500	0.567427	29789.91
	Total PV		277889.5

Question - (b)

NPV had the advantage of considering the time value of money. But fails to provide accurate results when comparing projects with different life times and investments.

Payback had the only advantage of easy to understand and simple to calculate. But it is not a recommended method for modern financial management, because it does not consider the time value of money and not considering all the cash flows in the project.

Discounted payback period shall overcome the disadvantage of time value of money, because we consider the discounted cash flows instead of original cash flows for computing the pay back period. But it still suffers from the disadvantage of not considering the post payback profitability.

Profitability Index is a variation of NPV method. It can handle the investment differences between the projects. But for time difference still this method had its own concerns in its application.

NPV, due to its many advantages is considered as the best of the capital budgeting techniques in financial management.