Question

consider a project with the following cash flow;

Year cash flow shs '000' abandonment value shs '000'

0 (16,000)

1 7,000 ___________

2 6,000 1,100

3 4,000 9,000

4 4,000 5,000

The cost of capital is 15% and re-investment rate is 20%.

Required;

i) Determine the optimal abandonment period.

Answer 1

Project can be abandoned in year 1,2,3 or 4

Re-Investment Rate = 20%

Calculation of NPV of Cash flows if project is abandoned in Year 1

Year	Project Cash flows	Present Value Factor @ 15%	Present Value of Cash flows
1	7000	0.8696	6086.96

NPV = 6086.96 -16000 = -9913.04

Calculation of NPV of Cash flows if project is abandoned in Year 2

Year	Project Cash flows	Notes
1	7000	Reinvested Until Year 2 @ 20%
2	8400	Total Reinvested matured amount at the end of Year 2 @ 20% (7000*(1+20%))
2	6000	Normal Project Cash flows
2	1100	Abandoned Cash flows
	15500	Total Year 2 Cash flows

Total Year 2 Cash flows                                                                                                 =15500

Present Value Factor @ 15% for year 2   =1/((1+15%)^2)                                = 0.7561

PV of Cash flows if project is abandoned in Year 2 =(15500*0.7561)            =11720.22684    

NPV = 11720.23-16000                                                                                                    = -4279.77          

Calculation of NPV of Cash flows if project is abandoned in Year 3

Year	Project Cash flows	Notes
1	7000	Reinvested Until Year 3 @ 20% i.e., for 2 years
2	6000	Reinvested Until Year 3 @ 20% i.e., for 1 year
3	10080	Total Reinvested matured amount at the end of Year 3 @ 20% (7000*(1+20%)*(1+20%)) for year 1 reinvestment
3	7200	Total Reinvested matured amount at the end of Year 3 @ 20% (6000*(1+20%)) for year 2 reinvestment
3	4000	Normal Project Cash flows
3	9000	Abandoned Cash flows
	30280	Total Year 3 Cash flows

Total Year 3 Cash flows 30280

Present Value Factor @ 15% for year 3 =1/((1+15%)^3) = 0.6575

PV of Cash flows if project is abandoned in Year 3 '=(30280*0.6575)           = 19909.59152

NPV = 19910.59-16000 =              3910.59

Calculation of NPV of Cash flows if project is abandoned in Year 4

Year	Project Cash flows	Notes
1	7000	Reinvested Until Year 4 @ 20% i.e., for 3 years
2	6000	Reinvested Until Year 4 @ 20% i.e., for 2 years
3	4000	Reinvested Until Year 4 @ 20% i.e., for 1 year
4	12096	Total Reinvested matured amount at the end of Year 3 @ 20% (7000*(1+20%)^3) for year 1 reinvestment
4	8640	Total Reinvested matured amount at the end of Year 3 @ 20% (6000*(1+20%)^2) for year 2 reinvestment
4	4800	Total Reinvested matured amount at the end of Year 3 @ 20% (6000*(1+20%)) for year 3 reinvestment
4	4000	Normal Project Cash flows
4	5000	Abandoned Cash flows
	34536	Total Year 4 Cash flows

Total Year 4 Cash flows	34536
Present Value Factor @ 15% for year 3 =1/((1+15%)^4)	0.5718
PV of Cash flows if project is abandoned in Year 3 '=(34536*0.5718)	19746.07
NPV = 19746.07-16000	3746.07

Summary of NPVS

If project is abandoned in year	NPV
1	-9913.04
2	-4279.77
3	3910.59
4	3746.07

Year 3 is having highest NPV. Therefore, project shall be abandoned in year 3 which is the optimal abandonment period

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