Question

QUESTION 1 [41 MARKS]
ABC Holdings is considering two projects. The projects are similar in nature and are expected to both operate for four years. Due to unavailability of funds to undertake both of them, only one project can be accepted. The cost of capital is 12%.
The following information is available:

		Net cash flows
	Project A	Project B
	N$000	N$000
Initial Investment	46000	46000
Year 1	17000	15000
Year 2	14000	13000
Year 3	24000	15000
Year 4	9000	25000
Estimated scrap value at the end of year 4	4000	4000

Depreciation is charged on the straight line basis.

a) Calculate the following for both proposals:

(i) the payback period (round off your answer to one decimal place)

(ii) the net present value (NPV)

(iii) the return on investments (ROI)

(iv) the residual income (RI)

(v) If the two projects are mutually exclusive, which project should be chosen and why?

(b) Determine the sensitivity of Project A to a change in cost of capital

(c) Determine the sensitivity of Project B to a change in initial investment

(d) Assuming that the management of ABC holdings have decided to undertake both projects and the projects can be undertaken in part, how much NPV will they get if they have N$80 000 000 available to invest.

(e) Explain three non-financial considerations that should be taken into account before a project is chosen.

Answer 1

We need to consider the following points:

1. We are given net cashflows so we don't need to consider the depreciation
2. We are not given the tax rate so the entire scrap value at the end of year 4 is an inflow

(i) Payback period:

• Opening balance = previous year's closing balance
• Closing balance = Opening balance+Initial investment-Cash inflow

Project A
Year	Opening Balance	Initial investment	Cash inflow	Closing Balance
0		$              46,000.00		$         46,000.00
1	$            46,000.00		$                   17,000.00	$         29,000.00
2	$            29,000.00		$                   14,000.00	$         15,000.00
3	$            15,000.00		$                   24,000.00	$          -9,000.00
4	$            -9,000.00		$                     9,000.00	$       -18,000.00
4	$          -18,000.00		$                     4,000.00	$       -22,000.00

We see that till the end of year 2, the closing balance is positive but at the end of year 3 it becomes negative, which means that during the year 3 the entire initial investment is recovered. Required recovery is the opening balance of 15000 while the total inflow is 24000. We assume that the inflow is uniform throughout the year so we can calculate the part of the year in which the opening balance is recovered as 15000/24000 x 12 = 7.5 months so the payback period = 2 years and 7.5 months

Project B
Year	Opening Balance	Initial investment	Cash inflow	Closing Balance
0		$              46,000.00		$         46,000.00
1	$            46,000.00		$                   15,000.00	$         31,000.00
2	$            31,000.00		$                   13,000.00	$         18,000.00
3	$            18,000.00		$                   15,000.00	$           3,000.00
4	$              3,000.00		25000 + 4000 = $ 29,000.00	$       -26,000.00

We see that till the end of year 3, the closing balance is positive but at the end of year 4 it becomes negative, which means that during the year 4 the entire initial investment is recovered. Required recovery is the opening balance of 3000 while the total inflow is 29000 . We assume that the inflow is uniform throughout the year so we can calculate the part of the year in which the opening balance is recovered as 3000/29000 x 12 = 1.25 months so the payback period = 3 years and 1.25 months

According to payback period project A should be chosen because it leads to quicker recovery of initial investment

(ii) NPV calculations are as follows:

Project A
Year	CF	Discount Factor		Discounted CF
0	$   -46,000.00	1/(1+0.12)^0=	1	1*-46000=	$   -46,000.00
1	$    17,000.00	1/(1+0.12)^1=	0.892857	0.892857142857143*17000=	$    15,178.57
2	$    14,000.00	1/(1+0.12)^2=	0.797194	0.79719387755102*14000=	$    11,160.71
3	$    24,000.00	1/(1+0.12)^3=	0.71178	0.711780247813411*24000=	$    17,082.73
4	$       9,000.00	1/(1+0.12)^4=	0.635518	0.635518078404831*9000=	$       5,719.66
4	$       4,000.00	1/(1+0.12)^4=	0.635518	0.635518078404831*4000=	$       2,542.07
				NPV = Sum of all Discounted CF	$       5,683.75
				Return on investment	12.36%
Project B
Year	CF	Discount Factor		Discounted CF
0	$   -46,000.00	1/(1+0.12)^0=	1	1*-46000=	$   -46,000.00
1	$    15,000.00	1/(1+0.12)^1=	0.892857	0.892857142857143*15000=	$    13,392.86
2	$    13,000.00	1/(1+0.12)^2=	0.797194	0.79719387755102*13000=	$    10,363.52
3	$    15,000.00	1/(1+0.12)^3=	0.71178	0.711780247813411*15000=	$    10,676.70
4	$    25,000.00	1/(1+0.12)^4=	0.635518	0.635518078404831*25000=	$    15,887.95
4	$       4,000.00	1/(1+0.12)^4=	0.635518	0.635518078404831*4000=	$       2,542.07
				NPV = Sum of all Discounted CF	$       6,863.11
				Return on investment	14.92%

According to NPV method, project B should be selected as it has higher NPV if the projects are mutually exclusive

(iii)

(V) Whenever there is a conflict under different methods, NPV method reign supreme as it is the most comprehensive approach which considers time value of money and the entire lifetime of the project. Therefore if projects are mutually exclusive, then project B with higher positive NPV should be selected

(b) Sensitivity analysis of project A to a 10% change in initial investment:

• As all other CFs remain the same, and the only change is in the initial investment, we can simply add back the 46000 investment to the basecase NPV and subtract the 10% up or down initial investment to calculate the respective new NPV as shown in the below table

Project A	Base case	-10%	10%
Initial investment	$   46,000.00	$   41,400.00	$   50,600.00
NPV	$     5,683.75	$   10,283.75	$     1,083.75
Percentage Change		81%	-81%

Due to a 10% change in initial investment, the NPV changes by 81% in the opposite direction or we can say if the initial investment changes by 1%, NPV changes by 8.1% in the opposite direction

(c)Sensitivity analysis of project B to a 10% change in initial investment:

Project B	Base case	-10%	10%
Initial investment	$   46,000.00	$   41,400.00	$   50,600.00
NPV	$     6,863.11	$   11,463.11	$     2,263.11
Percentage Change		67%	-67%

Due to a 10% change in initial investment, the NPV changes by 67% in the opposite direction or we can say if the initial investment changes by 1%, NPV changes by 6.7% in the opposite direction

Therefore project A is more sensitive to changes in the initial investment