Chapter 13, Problem 1AE

To determine

Introduction:-

Capital Budgeting is used by organisations to evaluate a project in hand i.e. whether to proceed with it or leave it. There are various methods or techniques of capital budgeting. The most popular are Net Present value (NPV), internal rate of return (IRR), Profitability Index (Pi) etc.

To determine:-

Here, in the given problem we are supposed to calculate NPV based on the inputs given like sales, cost of goods sold, equipment cost, investment in working capital, discount rates at 14 %, 10% etc. Further, we are asked to explain as to why the NPV has increased as a result of fall in discount rate.

Answer to Problem 1AE

Solution:-

Net Present Value is a Capital Budgeting technique which is used by management to decide as to whether proceed with a given project or not. It is calculated by discounting all the cash flows (Inflows and outflows both) by an appropriate discount rate. If the final figure is positive, then it is viable to undertake the project and if it is negative, then it is not viable to undertake the given project.

When we solve the problem, the NPV of purchasing the equipment @14% is $31, 493 and NPV @10% is $56, 517 and as can be seen that NPV has increased when the discount rate is decreased.

Explanation of Solution

Explanation:-

Here, following key inputs given are as follows:-

Purchase of Equipment	60000
Investment in working capital	100000
Sales	200000
Cost of goods sold	125000
Out of pocket operating costs	35000
Overhaul of equipment	5000
Salvage value of equipment	10000

Now, calculating NPV at 14% and 10% discount rate At 14 % discount rate

		Years
	Now	1	2	3	4	5
Purchase of Equipment	-60000
Investment in working capital	-100000
Sales		200000	200000	200000	200000	200000
Cost of goods sold		125000	125000	125000	125000	125000
Out of pocket operating costs		35000	35000	35000	35000	35000
Overhaul of equipment					5000
Salvage value of equipment						10000
Working Capital Released						100000
Total Cash flows (a)	-160000	40000	40000	40000	35000	150000
Discount factor @14% (b)	1	0.87719	0.76947	0.67497	0.59208	0.51937
Present value of cash flows (a x b)	-160000	35087.7	30778.7	26998.9	20722.8	77905.3
Net Present Value	31493.4

At 10% discount rate

		Years
	Now	1	2	3	4	5
Purchase of Equipment	60000
Investment in working capital	100000
Sales		200000	200000	200000	200000	200000
Cost of goods sold		125000	125000	125000	125000	125000
Out of pocket operating costs		35000	35000	35000	35000	35000
Overhaul of equipment					5000
Salvage value of equipment						10000
Working Capital Released						100000
Total Cash flows (a)	-160000	40000	40000	40000	35000	150000
Discount factor @10% (b)	1	0.90909	0.82645	0.75131	0.68301	0.62092
Present value of cash flows (a x b)	-160000	36363.6	33057.9	30052.6	23905.5	93138.2
Net Present Value	56517.7

Now, we are asked to explain as to why the NPV has increased from $31493 to $56517 when the discount rate is reduced from 14% to 10%. Actually, with the decrease in the discount rate the Present Value factor increases and when we multiply that increased factor with the net cash flows, the resultant present value of the cash flows increases and ultimately the NPV figure.

Now, in the second query, the company is considering to purchase new equipment

		Years
	Now	1	2	3	4	5
Purchase of Equipment	120000
Investment in working capital	80000
Sales		255000	255000	255000	255000	255000
Cost of goods sold		160000	160000	160000	160000	160000
Out of pocket operating costs		50000	50000	50000	50000	50000
Overhaul of equipment					40000
Salvage value of equipment						20000
Working Capital Released						80000
Total Cash flows (a)	-200000	45000	45000	45000	5000	145000
Discount factor @14% (b)	1	0.87719	0.76947	0.67497	0.59208	0.51937
Present value of cash flows (a x b)	-200000	39473.7	34626	30373.7	2960.4	75308.5
Net Present Value @ 14%	-17258

Therefore, NPV of the project is - $17, 258 Now, we will calculate the NPV at various discount rates i.e.13%, 12%, 11% and 10% and determine on which discount rate NPV turns profitable from the negative figure.

Total Cash flows (a)	-200000	45000	45000	45000	5000	145000
Discount factor @13% (b)	1	0.88496	0.78315	0.69305	0.61332	0.54276
Present value of cash flows (a x b)	-200000	39823	35241.6	31187.3	3066.59	78700.2
Net Present Value @ 13%	-11981
Total Cash flows (a)	-200000	45000	45000	45000	5000	145000
Discount factor @12% (b)	1	0.89286	0.79719	0.71178	0.63552	0.56743
Present value of cash flows (a x b)	-200000	40178.6	35873.7	32030.1	3177.59	82276.9
Net Present Value @ 12%	-6463.1
Total Cash flows (a)	-200000	45000	45000	45000	5000	145000
Discount factor @11% (b)	1	0.9009	0.81162	0.73119	0.65873	0.59345
Present value of cash flows (a x b)	-200000	40540.5	36523	32903.6	3293.65	86050.4
Net Present Value @ 11%	-688.74
Total Cash flows (a)	-200000	45000	45000	45000	5000	145000
Discount factor @10% (b)	1	0.90909	0.82645	0.75131	0.68301	0.62092
Present value of cash flows (a x b)	-200000	40909.1	37190.1	33809.2	3415.07	90033.6
Net Present Value @ 10%	5357

As we can see that the NPV has turned positive from 14% discount rate to 10% discount rate.

Now, we are asked to determine the IRR of the project. As we can see above that NPV has turned positive at 10% discount rate, therefore the IRR of the project should lie between 10% and 11% discount rates i.e. at a place where NPV is zero. Actually, if calculated IRR is 10.88%. Now, we are asked to determine the salvage value of the equipment so that the NPV becomes positive, assuming that the amount given in the question is not given If we see in the initial table of discount rate of 14%, the NPV is -$17258 taking into account the salvage value of $20000 in the fifth year. Now, if we increase the salvage value, then only we will get the positive NPV.

Without taking into account the salvage value, then NPV is -$27645. Now dividing it by the PVIF @ 14% which is .51937, we will get the minimum salvage value of the equipment to turn NPV into positive figure.

=27645÷.51937

=$53,229

Therefore, the minimum salvage value should be $53229 to turn NPV into positive figure.

Conclusion

Conclusion:-

Since, the resultant net present value is positive in problem 1, therefore it is viable to proceed with the given project.

However, NPV is negative in project 2, therefore it is not viable to purchase the equipment.