Question

Q1

a)

Given the following cashflows for Project Omega, what is the payback period in years assuming the cashflows occur annually?

Year	Cashflows of Project Omega
0	-90,000
1	20,000
2	25,000
3	50,000
4	40,000
5	150,000

b)

Project X and Y. The following are the cash flows of two projects:

Year	Project X	Project Y
0	-100,000	-50,000
1	50,000	20,000
2	40,000	30,000
3	30,000	30,000
4	20,000
5	10,000

If the discount rate is 18% is the project with the highest profitability index also the one with the highest NPV?

Yes

No

c)

he cashflows for an investment in Factory X are listed below. Using the discounted payback method of capital budgeting, what is the payback period for this investment expressed in years, assuming that the cashflows occur annually and using a discount rate of 20%.  

Year	Factory X
0	-       300,000
1	50,000
2	50,000
3	100,000
4	100,000
5	200,000
6	200,000

Answer 1

a. Payback period = 2 + (45000/50000) = 2.9 years

Year	Cash flows	Cumulative cash flows
1	20000	20000
2	25000	45000
3	50000	95000
4	40000	135000
5	150000	285000

b. Profitability index for Project X= Sum of discounted cash flows / Initial cash flow = 104046.0544/100,000 = 1.04

Profitability index for Project Y= Sum of discounted cash flows / Initial cash flow = 56753.6116/50,000 = 1.13

NPV of project X = 4046.0544

NPV of Project Y = 6753.6116

Year	Cash flows	PV factor @18%	Discounted cash flows
0	-100000	1	-100000
1	50000	0.847457627	42372.881
2	40000	0.71818443	28727.377
3	30000	0.608630873	18258.926
4	20000	0.515788875	10315.778
5	10000	0.437109216	4371.0922
NPV			4046.0544

Year	Cash flows	PV factor @18%	Discounted cash flows
0	-50000	1	-50000
1	20000	0.847457627	16949.153
2	30000	0.71818443	21545.533
3	30000	0.608630873	18258.926
NPV			6753.6116

c. Discounted payback = 5 years + (300,000 - 262860.0823) / 66979.595 = 5.554 years

Year	Cash flows	PV factor @20%	Discounted cash flows
0	-300000	1	-300000
1	50000	0.833333333	41666.667
2	50000	0.694444444	34722.222
3	100000	0.578703704	57870.37
4	100000	0.482253086	48225.309
5	200000	0.401877572	80375.514
6	200000	0.334897977	66979.595
NPV			29839.678