FM – L2 – Q75 – Discounted cash flow

Calculate NPV to decide between maintaining old equipment or buying new equipment for Wisdom Ltd, using a 20% cost of capital.

Question

The maintenance manager of Wisdom Ltd insists that management should maintain an old piece of equipment that had been used for 5 years and is fully depreciated rather than buy a new one. The old equipment has a current operating cost of GH₵53,000.00 per annum. The operating cost of the equipment is expected to increase at 5% every year over the next four years, with a sale value of GH₵6,500.00 in the fifth year.

The maintenance manager has proposed that a new system with enhanced technology to reduce operating cost to GH₵32,000.00 for the next three years and GH₵33,600.00 for the fourth and fifth years be introduced. The new equipment will cost GH₵60,000.00 and when introduced, a redundancy cost of GH₵25,000.00 will be paid, with the old equipment sold for GH₵12,000.00. The sale value of the new equipment will be GH₵10,200.00 after its five years’ useful life.

Required:

Using net present value (NPV) method of capital appraisal with 20% cost of capital, advise management on which option Wisdom Ltd should go for.

Answer

To determine which option Wisdom Ltd should choose, we calculate the NPV of both maintaining the old equipment and purchasing the new equipment, using a 20% cost of capital. The option with the lower present value of costs (or higher NPV if considering savings) is preferred.

Option 1: Maintain Old Equipment
Operating costs increase by 5% annually, starting at GH₵53,000. Sale value in year 5 is GH₵6,500.

Year 1: GH₵53,000
Year 2: GH₵53,000 × 1.05 = GH₵55,650
Year 3: GH₵55,650 × 1.05 = GH₵58,432.50
Year 4: GH₵58,432.50 × 1.05 = GH₵61,354.13
Year 5: GH₵61,354.13 × 1.05 = GH₵64,421.83
Year 5 sale value: GH₵6,500 (inflow, treated as negative cost)

Discount factors at 20%:

Year 1: 1 / (1.2) = 0.8333
Year 2: 1 / (1.2)² = 0.6944
Year 3: 1 / (1.2)³ = 0.5787
Year 4: 1 / (1.2)⁴ = 0.4823
Year 5: 1 / (1.2)⁵ = 0.4019

Year	Cash Flow (GH₵)	Discount Factor (20%)	Present Value (GH₵)
1	53,000	0.8333	44,164.90
2	55,650	0.6944	38,643.36
3	58,432.50	0.5787	33,803.49
4	61,354.13	0.4823	29,595.06
5	64,421.83 – 6,500 = 57,921.83	0.4019	23,280.88
Total PV of Costs			169,487.69

Option 2: Purchase New Equipment

Initial cost: GH₵60,000 (equipment) + GH₵25,000 (redundancy) – GH₵12,000 (sale of old equipment) = GH₵73,000 outflow in Year 0.
Operating costs: GH₵32,000 (Years 1–3), GH₵33,600 (Years 4–5).
Sale value in Year 5: GH₵10,200 (inflow).

Year	Cash Flow (GH₵)	Discount Factor (20%)	Present Value (GH₵)
0	73,000	1.0000	73,000.00
1	32,000	0.8333	26,666.67
2	32,000	0.6944	22,222.22
3	32,000	0.5787	18,518.52
4	33,600	0.4823	16,204.08
5	33,600 – 10,200 = 23,400	0.4019	9,404.44
Total PV of Costs			166,015.93

Comparison and Recommendation:

PV of costs for old equipment: GH₵169,487.69
PV of costs for new equipment: GH₵166,015.93
The new equipment has a lower present value of costs by GH₵169,487.69 – GH₵166,015.93 = GH₵3,471.76.

Alternatively, we can compute the NPV of the new equipment relative to the old by considering incremental cash flows (savings from new equipment):

Year 0: -GH₵73,000 (net initial outlay).
Year 1: 53,000 – 32,000 = GH₵21,000 savings.
Year 2: 55,650 – 32,000 = GH₵23,650 savings.
Year 3: 58,432.50 – 32,000 = GH₵26,432.50 savings.
Year 4: 61,354.13 – 33,600 = GH₵27,754.13 savings.
Year 5: (64,421.83 – 6,500) – (33,600 – 10,200) = 57,921.83 – 23,400 = GH₵34,521.83 savings.

Year	Incremental Cash Flow (GH₵)	Discount Factor (20%)	Present Value (GH₵)
0	-73,000	1.0000	-73,000.00
1	21,000	0.8333	17,499.93
2	23,650	0.6944	16,422.56
3	26,432.50	0.5787	15,296.46
4	27,754.13	0.4823	13,385.91
5	34,521.83	0.4019	13,876.35
NPV			3,471.21

Conclusion:
The NPV of replacing the old equipment with the new equipment is positive (GH₵3,471.21), indicating that the new equipment is financially preferable. Wisdom Ltd should purchase the new equipment, as it reduces the present value of costs compared to maintaining the old equipment.

Tags: Cost of Capital, Discounted cash flow, Equipment replacement, NPV, operating costs
Level: Level 2

Topic: Discounted cash flow

Uploader: Samuel Duah